Add files using upload-large-folder tool

.gitattributes

@@ -249,3 +249,17 @@ data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Bicategory.
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Comma.StructuredArrow.Basic.sym.json filter=lfs diff=lfs merge=lfs -text
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.MeasureTheory.Function.Holder.sym.json filter=lfs diff=lfs merge=lfs -text
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.LinearAlgebra.CliffordAlgebra.Grading.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.RingTheory.ClassGroup.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.MorphismProperty.Comma.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Calculus.ContDiff.FaaDiBruno.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Limits.Final.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Bicategory.Strict.Pseudofunctor.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Module.HahnEmbedding.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.CStarAlgebra.Matrix.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.FieldTheory.CardinalEmb.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.FieldTheory.Extension.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.InnerProductSpace.Positive.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Geometry.RingedSpace.OpenImmersion.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Topology.Basic.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Topology.Algebra.Category.ProfiniteGrp.Basic.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.ShortComplex.Abelian.sym.json filter=lfs diff=lfs merge=lfs -text

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Algebra.ZMod.sym.json

@@ -0,0 +1 @@
+[{"isProp":false,"kind":"definition","name":["ZMod","algebra'"],"typeFallback":"forall (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3 : Ring.{u_1} R] {n : Nat} (m : Nat) [inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.12 : CharP.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3)) m], (Dvd.dvd.{0} Nat Nat.instDvd m n) -> (Algebra.{0, u_1} (ZMod n) R (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n)) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3))","typeFull":"(R : Type u_1) → [inst : Ring R] → {n : ℕ} → (m : ℕ) → [CharP R m] → m ∣ n → Algebra (ZMod n) R","typeReadable":"(R : Type u_1) → [inst : Ring R] → {n : ℕ} → (m : ℕ) → [CharP R m] → m ∣ n → Algebra (ZMod n) R","typeReferences":[["ZMod"],["CommRing","toCommSemiring"],["Nat"],["Dvd","dvd"],["Ring","toAddGroupWithOne"],["CharP"],["ZMod","commRing"],["AddGroupWithOne","toAddMonoidWithOne"],["Ring","toSemiring"],["Algebra"],["Nat","instDvd"],["Ring"]],"valueReferences":[["ZMod"],["SMul","mk"],["ZMod","castHom"],["CommRing","toCommSemiring"],["Ring","toNonAssocRing"],["ZMod","algebra'","_proof_1"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["ZMod","commRing"],["HMul","hMul"],["Ring","toSemiring"],["ZMod","algebra'","_proof_2"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["ZMod","cast"],["instHMul"],["Algebra","mk"],["NonAssocRing","toNonUnitalNonAssocRing"]]},{"isProp":true,"kind":"theorem","name":["ZMod","algebra'","_proof_2"],"typeFallback":"forall (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3 : Ring.{u_1} R] {n : Nat} (x._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.77 : ZMod n) (x._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.79 : R), Eq.{succ u_1} R (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMul.mk.{0, u_1} (ZMod n) R (fun (a : ZMod n) (r : R) => HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3)))))) (ZMod.cast.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3) n a) r))) x._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.77 x._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.79) (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMul.mk.{0, u_1} (ZMod n) R (fun (a : ZMod n) (r : R) => HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3)))))) (ZMod.cast.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3) n a) r))) x._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.77 x._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.79)","typeFull":"∀ (R : Type u_1) [inst : Ring R] {n : ℕ} (x : ZMod n) (x_1 : R), x • x_1 = x • x_1","typeReadable":"∀ (R : Type u_1) [inst : Ring R] {n : ℕ} (x : ZMod n) (x_1 : R), x • x_1 = x • x_1","typeReferences":[["ZMod"],["SMul","mk"],["Ring","toNonAssocRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["HMul","hMul"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Nat"],["Ring","toAddGroupWithOne"],["ZMod","cast"],["HSMul","hSMul"],["instHSMul"],["instHMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["Ring"]],"valueReferences":[["rfl"],["ZMod"],["SMul","mk"],["Ring","toNonAssocRing"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["HMul","hMul"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["ZMod","cast"],["HSMul","hSMul"],["instHSMul"],["instHMul"],["NonAssocRing","toNonUnitalNonAssocRing"]]},{"isProp":true,"kind":"theorem","name":["ZMod","instSubsingletonAlgebra"],"typeFallback":"forall (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.1151269331._hygCtx._hyg.3 : Ring.{u_1} R] (p : Nat), Subsingleton.{max (succ u_1) 1} (Algebra.{0, u_1} (ZMod p) R (CommRing.toCommSemiring.{0} (ZMod p) (ZMod.commRing p)) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1151269331._hygCtx._hyg.3))","typeFull":"∀ (R : Type u_1) [inst : Ring R] (p : ℕ), Subsingleton (Algebra (ZMod p) R)","typeReadable":"∀ (R : Type u_1) [inst : Ring R] (p : ℕ), Subsingleton (Algebra (ZMod p) R)","typeReferences":[["ZMod"],["CommRing","toCommSemiring"],["Subsingleton"],["Nat"],["ZMod","commRing"],["Ring","toSemiring"],["Algebra"],["Ring"]],"valueReferences":[["ZMod"],["RingHom"],["CommRing","toCommSemiring"],["Subsingleton","intro"],["Subsingleton","elim"],["Algebra","algebra_ext"],["CommSemiring","toSemiring"],["ZMod","commRing"],["Algebra"],["Ring","toSemiring"],["RingHom","congr_fun"],["Semiring","toNonAssocSemiring"],["ZMod","subsingleton_ringHom"],["algebraMap"]]},{"isProp":true,"kind":"theorem","name":["ZMod","algebraOfModule","_proof_1"],"typeFallback":"forall (n : Nat) (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10 : Ring.{u_1} R] [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13 : Module.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))] (r : ZMod n) (x : R), And (Eq.{succ u_1} R (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) x) (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r x)) (Eq.{succ u_1} R (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) x (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))))) (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r x))","typeFull":"∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [inst_1 : Module (ZMod n) R] (r : ZMod n) (x : R),\n  r • 1 * x = r • x ∧ x * r • 1 = r • x","typeReadable":"∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [inst_1 : Module (ZMod n) R] (r : ZMod n) (x : R),\n  r • 1 * x = r • x ∧ x * r • 1 = r • x","typeReferences":[["Ring","toNonAssocRing"],["Module"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Distrib","toMul"],["DistribMulAction","toDistribSMul"],["And"],["Semiring","toMonoidWithZero"],["ZMod","commRing"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["Nat"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["instHMul"],["AddZero","toZero"],["Ring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["instAddNat"],["AddCommMonoid","subsingletonIntModule"],["Ring","toNonAssocRing"],["Eq","trans"],["Subsingleton","elim"],["AddGroupWithOne","toAddMonoidWithOne"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["Ring","toAddGroupWithOne"],["AddGroup","toSubNegMonoid"],["Eq","ndrec"],["NonAssocSemiring","toAddCommMonoidWithOne"],["NonAssocSemiring","toMulZeroOneClass"],["NonAssocRing","toNonUnitalNonAssocRing"],["Nat","casesAuxOn"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toDistrib"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["And"],["DistribMulAction","toDistribSMul"],["ZMod","commRing"],["AddZeroClass","toAddZero"],["instNeZeroNatHAdd_1"],["AddCommGroup","toIntModule"],["Ring","toSemiring"],["Exists","casesOn"],["zsmul_eq_mul"],["Nat"],["AddMonoidWithOne","toNatCast"],["AddMonoid","toNSMul"],["ZMod","natCast_zmod_surjective"],["HSMul","hSMul"],["AddMonoidWithOne","toOne"],["instHMul"],["SubNegMonoid","toZSMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Nat","cast"],["Module"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["Int","cast"],["congrArg"],["Nat","instNeZeroSucc"],["instOfNatNat"],["NonAssocRing","toAddCommGroupWithOne"],["congr"],["MonoidWithZero","toMonoid"],["instHSMul"],["congrFun'"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["Nat","cast_comm"],["ZMod"],["CommRing","toCommSemiring"],["True"],["instHAdd"],["Distrib","toMul"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Semiring","toMonoidWithZero"],["mul_one"],["Int","cast_comm"],["OfNat","ofNat"],["Int"],["HAdd","hAdd"],["Ring","toAddCommGroup"],["CommRing","toRing"],["eq_self"],["and_self"],["Module","toDistribMulAction"],["AddCommGroupWithOne","toAddGroupWithOne"],["AddGroupWithOne","toAddGroup"],["One","toOfNat1"],["of_eq_true"],["Nat","cast_smul_eq_nsmul"],["Int","instSemiring"],["nsmul_eq_mul"],["AddGroupWithOne","toIntCast"],["inferInstance"]]},{"isProp":true,"kind":"theorem","name":["ZMod","instIsScalarTower"],"typeFallback":"forall (n : Nat) (R : Type.{u_2}) (M : Type.{u_3}) [inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11 : Ring.{u_2} R] [inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14 : AddCommGroup.{u_3} M] [inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.17 : Module.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11))))] [m₁ : Module.{0, u_3} (ZMod n) M (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (AddCommGroup.toAddCommMonoid.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14)] [inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.30 : Module.{u_2, u_3} R M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14)], IsScalarTower.{0, u_2, u_3} (ZMod n) R M (SMulZeroClass.toSMul.{0, u_2} (ZMod n) R (AddZero.toZero.{u_2} R (AddZeroClass.toAddZero.{u_2} R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11)))))) (DistribSMul.toSMulZeroClass.{0, u_2} (ZMod n) R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11)))) (DistribMulAction.toDistribSMul.{0, u_2} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11))) (Module.toDistribMulAction.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11)))) inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.17)))) (SMulZeroClass.toSMul.{u_2, u_3} R M (AddZero.toZero.{u_3} M (AddZeroClass.toAddZero.{u_3} M (AddMonoid.toAddZeroClass.{u_3} M (SubNegMonoid.toAddMonoid.{u_3} M (AddGroup.toSubNegMonoid.{u_3} M (AddCommGroup.toAddGroup.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14)))))) (DistribSMul.toSMulZeroClass.{u_2, u_3} R M (AddMonoid.toAddZeroClass.{u_3} M (SubNegMonoid.toAddMonoid.{u_3} M (AddGroup.toSubNegMonoid.{u_3} M (AddCommGroup.toAddGroup.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14)))) (DistribMulAction.toDistribSMul.{u_2, u_3} R M (MonoidWithZero.toMonoid.{u_2} R (Semiring.toMonoidWithZero.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11))) (SubNegMonoid.toAddMonoid.{u_3} M (AddGroup.toSubNegMonoid.{u_3} M (AddCommGroup.toAddGroup.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14))) (Module.toDistribMulAction.{u_2, u_3} R M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.11) (AddCommGroup.toAddCommMonoid.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14) inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.30)))) (SMulZeroClass.toSMul.{0, u_3} (ZMod n) M (AddZero.toZero.{u_3} M (AddZeroClass.toAddZero.{u_3} M (AddMonoid.toAddZeroClass.{u_3} M (SubNegMonoid.toAddMonoid.{u_3} M (AddGroup.toSubNegMonoid.{u_3} M (AddCommGroup.toAddGroup.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14)))))) (DistribSMul.toSMulZeroClass.{0, u_3} (ZMod n) M (AddMonoid.toAddZeroClass.{u_3} M (SubNegMonoid.toAddMonoid.{u_3} M (AddGroup.toSubNegMonoid.{u_3} M (AddCommGroup.toAddGroup.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14)))) (DistribMulAction.toDistribSMul.{0, u_3} (ZMod n) M (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (SubNegMonoid.toAddMonoid.{u_3} M (AddGroup.toSubNegMonoid.{u_3} M (AddCommGroup.toAddGroup.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14))) (Module.toDistribMulAction.{0, u_3} (ZMod n) M (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (AddCommGroup.toAddCommMonoid.{u_3} M inst._@.Mathlib.Algebra.Algebra.ZMod.772748180._hygCtx._hyg.14) m₁))))","typeFull":"∀ (n : ℕ) (R : Type u_2) (M : Type u_3) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module (ZMod n) R]\n  [m₁ : Module (ZMod n) M] [inst_3 : Module R M], IsScalarTower (ZMod n) R M","typeReadable":"∀ (n : ℕ) (R : Type u_2) (M : Type u_3) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module (ZMod n) R]\n  [m₁ : Module (ZMod n) M] [inst_3 : Module R M], IsScalarTower (ZMod n) R M","typeReferences":[["Ring","toNonAssocRing"],["Module"],["IsScalarTower"],["AddCommGroup","toAddGroup"],["AddGroupWithOne","toAddMonoidWithOne"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["AddGroup","toSubNegMonoid"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["ZMod","commRing"],["AddCommGroup"],["AddZeroClass","toAddZero"],["Ring","toSemiring"],["Module","toDistribMulAction"],["Nat"],["SubNegMonoid","toAddMonoid"],["AddCommGroup","toAddCommMonoid"],["AddZero","toZero"],["Ring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["RingHom"],["Ring","toNonAssocRing"],["IsScalarTower"],["Subsingleton","elim"],["AddCommGroup","toAddGroup"],["NonUnitalSemiring","toSemigroupWithZero"],["SemigroupAction","toSMul"],["AddGroupWithOne","toAddMonoidWithOne"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["Ring","toAddGroupWithOne"],["Eq","symm"],["DistribMulAction","toMulAction"],["ZMod","algebraOfModule"],["AddGroup","toSubNegMonoid"],["Eq","ndrec"],["Semiring","toNonUnitalSemiring"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toDistrib"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["ZMod","commRing"],["AddZeroClass","toAddZero"],["Ring","toSemiring"],["Eq","refl"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["id"],["instHMul"],["Eq","mpr"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Module","compHom"],["algebraMap"],["Module"],["RingHom","instFunLike"],["AddCommMonoid","toAddMonoid"],["IsScalarTower","mk"],["DFunLike","coe"],["Semigroup","toMul"],["congrArg"],["MonoidWithZero","toMonoid"],["Algebra","toSMul"],["instHSMul"],["Eq"],["ZMod","instSubsingletonModule"],["SemigroupAction","mul_smul"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Distrib","toMul"],["Semiring","toMonoidWithZero"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["Algebra","smul_def"],["SemigroupWithZero","toSemigroup"],["MulAction","toSemigroupAction"]]},{"isProp":true,"kind":"theorem","name":["ZMod","algebraOfModule","_proof_3"],"typeFallback":"forall (n : Nat) (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10 : Ring.{u_1} R] [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13 : Module.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))] (x1._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.70 : ZMod n) (x2._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.70 : R), Eq.{succ u_1} R (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) x2._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.70 (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) x1._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.70 (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))))) (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) x1._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.70 x2._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.70)","typeFull":"∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [inst_1 : Module (ZMod n) R] (x1 : ZMod n) (x2 : R), x2 * x1 • 1 = x1 • x2","typeReadable":"∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [inst_1 : Module (ZMod n) R] (x1 : ZMod n) (x2 : R), x2 * x1 • 1 = x1 • x2","typeReferences":[["Ring","toNonAssocRing"],["Module"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Distrib","toMul"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["ZMod","commRing"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["Nat"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["instHMul"],["AddZero","toZero"],["Ring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Ring","toNonAssocRing"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["SMulZeroClass","toSMul"],["ZMod","algebraOfModule","proof"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Distrib","toMul"],["And","right"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["ZMod","commRing"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":false,"kind":"definition","name":["ZMod","algebraOfModule"],"typeFallback":"forall (n : Nat) (R : Type.{u_2}) [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10 : Ring.{u_2} R] [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13 : Module.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))], Algebra.{0, u_2} (ZMod n) R (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n)) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)","typeFull":"(n : ℕ) → (R : Type u_2) → [inst : Ring R] → [Module (ZMod n) R] → Algebra (ZMod n) R","typeReadable":"(n : ℕ) → (R : Type u_2) → [inst : Ring R] → [Module (ZMod n) R] → Algebra (ZMod n) R","typeReferences":[["ZMod"],["CommRing","toCommSemiring"],["Ring","toNonAssocRing"],["Module"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["ZMod","commRing"],["Algebra"],["Ring","toSemiring"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Nat"],["NonAssocRing","toNonUnitalNonAssocRing"],["Ring"]],"valueReferences":[["ZMod"],["CommRing","toCommSemiring"],["ZMod","algebraOfModule","_proof_2"],["ZMod","commRing"],["ZMod","algebraOfModule","_proof_3"],["Algebra","ofModule'"],["Ring","toSemiring"]]},{"isProp":true,"kind":"theorem","name":["ZMod","algebra'","_proof_1"],"typeFallback":"forall (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3 : Ring.{u_1} R] {n : Nat} (m : Nat) [inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.12 : CharP.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3)) m], (Dvd.dvd.{0} Nat Nat.instDvd m n) -> (forall (a : ZMod n) (r : R), Eq.{succ u_1} R (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3)))))) (ZMod.cast.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3) n a) r) (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3)))))) r (ZMod.cast.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.1134821990._hygCtx._hyg.3) n a)))","typeFull":"∀ (R : Type u_1) [inst : Ring R] {n : ℕ} (m : ℕ) [CharP R m], m ∣ n → ∀ (a : ZMod n) (r : R), a.cast * r = r * a.cast","typeReadable":"∀ (R : Type u_1) [inst : Ring R] {n : ℕ} (m : ℕ) [CharP R m], m ∣ n → ∀ (a : ZMod n) (r : R), a.cast * r = r * a.cast","typeReferences":[["ZMod"],["Ring","toNonAssocRing"],["Dvd","dvd"],["NonUnitalNonAssocSemiring","toDistrib"],["CharP"],["Distrib","toMul"],["AddGroupWithOne","toAddMonoidWithOne"],["HMul","hMul"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Nat"],["Ring","toAddGroupWithOne"],["ZMod","cast"],["instHMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["Ring"],["Nat","instDvd"]],"valueReferences":[["RingHom"],["ZMod","castHom"],["Ring","toNonAssocRing"],["RingHom","instFunLike"],["HMul","hMul"],["RingHom","instRingHomClass"],["Int","cast"],["ZMod","intCast_surjective"],["DFunLike","coe"],["congrArg"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["Ring","toAddGroupWithOne"],["NonAssocRing","toAddCommGroupWithOne"],["map_intCast"],["NonAssocCommRing","toNonAssocRing"],["Eq"],["Eq","ndrec"],["NonAssocRing","toNonUnitalNonAssocRing"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["CommRing","toNonAssocCommRing"],["Distrib","toMul"],["CommSemiring","toSemiring"],["ZMod","commRing"],["Int","cast_comm"],["Ring","toSemiring"],["Int"],["Exists","casesOn"],["CommRing","toRing"],["AddCommGroupWithOne","toAddGroupWithOne"],["ZMod","cast"],["Eq","refl"],["AddGroupWithOne","toIntCast"],["id"],["instHMul"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["ZMod","algebraOfModule","proof"],"typeFallback":"forall (n : Nat) (R : Type.{u_2}) [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10 : Ring.{u_2} R] [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13 : Module.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))] (r : ZMod n) (x : R), And (Eq.{succ u_2} R (HMul.hMul.{u_2, u_2, u_2} R R R (instHMul.{u_2} R (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (HSMul.hSMul.{0, u_2, u_2} (ZMod n) R R (instHSMul.{0, u_2} (ZMod n) R (SMulZeroClass.toSMul.{0, u_2} (ZMod n) R (AddZero.toZero.{u_2} R (AddZeroClass.toAddZero.{u_2} R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_2} (ZMod n) R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_2} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r (OfNat.ofNat.{u_2} R 1 (One.toOfNat1.{u_2} R (AddMonoidWithOne.toOne.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) x) (HSMul.hSMul.{0, u_2, u_2} (ZMod n) R R (instHSMul.{0, u_2} (ZMod n) R (SMulZeroClass.toSMul.{0, u_2} (ZMod n) R (AddZero.toZero.{u_2} R (AddZeroClass.toAddZero.{u_2} R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_2} (ZMod n) R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_2} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r x)) (Eq.{succ u_2} R (HMul.hMul.{u_2, u_2, u_2} R R R (instHMul.{u_2} R (Distrib.toMul.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) x (HSMul.hSMul.{0, u_2, u_2} (ZMod n) R R (instHSMul.{0, u_2} (ZMod n) R (SMulZeroClass.toSMul.{0, u_2} (ZMod n) R (AddZero.toZero.{u_2} R (AddZeroClass.toAddZero.{u_2} R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_2} (ZMod n) R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_2} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r (OfNat.ofNat.{u_2} R 1 (One.toOfNat1.{u_2} R (AddMonoidWithOne.toOne.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))))) (HSMul.hSMul.{0, u_2, u_2} (ZMod n) R R (instHSMul.{0, u_2} (ZMod n) R (SMulZeroClass.toSMul.{0, u_2} (ZMod n) R (AddZero.toZero.{u_2} R (AddZeroClass.toAddZero.{u_2} R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_2} (ZMod n) R (AddMonoid.toAddZeroClass.{u_2} R (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_2} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_2} R (AddGroupWithOne.toAddMonoidWithOne.{u_2} R (Ring.toAddGroupWithOne.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_2} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R (NonAssocRing.toNonUnitalNonAssocRing.{u_2} R (Ring.toNonAssocRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) r x))","typeFull":"∀ (n : ℕ) (R : Type u_2) [inst : Ring R] [inst_1 : Module (ZMod n) R] (r : ZMod n) (x : R),\n  r • 1 * x = r • x ∧ x * r • 1 = r • x","typeReadable":"∀ (n : ℕ) (R : Type u_2) [inst : Ring R] [inst_1 : Module (ZMod n) R] (r : ZMod n) (x : R),\n  r • 1 * x = r • x ∧ x * r • 1 = r • x","typeReferences":[["Ring","toNonAssocRing"],["Module"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Distrib","toMul"],["DistribMulAction","toDistribSMul"],["And"],["Semiring","toMonoidWithZero"],["ZMod","commRing"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["Nat"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["instHMul"],["AddZero","toZero"],["Ring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["ZMod","algebraOfModule","_proof_1"]]},{"isProp":true,"kind":"theorem","name":["ZMod","algebraOfModule","_proof_2"],"typeFallback":"forall (n : Nat) (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10 : Ring.{u_1} R] [inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13 : Module.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))))] (x1._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.59 : ZMod n) (x2._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.59 : R), Eq.{succ u_1} R (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) x1._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.59 (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (AddMonoidWithOne.toOne.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) x2._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.59) (HSMul.hSMul.{0, u_1, u_1} (ZMod n) R R (instHSMul.{0, u_1} (ZMod n) R (SMulZeroClass.toSMul.{0, u_1} (ZMod n) R (AddZero.toZero.{u_1} R (AddZeroClass.toAddZero.{u_1} R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))))) (DistribSMul.toSMulZeroClass.{0, u_1} (ZMod n) R (AddMonoid.toAddZeroClass.{u_1} R (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) (DistribMulAction.toDistribSMul.{0, u_1} (ZMod n) R (MonoidWithZero.toMonoid.{0} (ZMod n) (Semiring.toMonoidWithZero.{0} (ZMod n) (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))))) (AddMonoidWithOne.toAddMonoid.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10))) (Module.toDistribMulAction.{0, u_1} (ZMod n) R (CommSemiring.toSemiring.{0} (ZMod n) (CommRing.toCommSemiring.{0} (ZMod n) (ZMod.commRing n))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_1} R (NonAssocRing.toNonUnitalNonAssocRing.{u_1} R (Ring.toNonAssocRing.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.10)))) inst._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.13))))) x1._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.59 x2._@.Mathlib.Algebra.Algebra.ZMod.3373313806._hygCtx._hyg.59)","typeFull":"∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [inst_1 : Module (ZMod n) R] (x1 : ZMod n) (x2 : R), x1 • 1 * x2 = x1 • x2","typeReadable":"∀ (n : ℕ) (R : Type u_1) [inst : Ring R] [inst_1 : Module (ZMod n) R] (x1 : ZMod n) (x2 : R), x1 • 1 * x2 = x1 • x2","typeReferences":[["Ring","toNonAssocRing"],["Module"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["SMulZeroClass","toSMul"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Distrib","toMul"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["ZMod","commRing"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["Nat"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["instHMul"],["AddZero","toZero"],["Ring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Ring","toNonAssocRing"],["HMul","hMul"],["AddGroupWithOne","toAddMonoidWithOne"],["SMulZeroClass","toSMul"],["ZMod","algebraOfModule","proof"],["AddMonoidWithOne","toAddMonoid"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["MonoidWithZero","toMonoid"],["instHSMul"],["Eq"],["NonAssocRing","toNonUnitalNonAssocRing"],["And","left"],["DistribSMul","toSMulZeroClass"],["ZMod"],["CommRing","toCommSemiring"],["NonUnitalNonAssocSemiring","toDistrib"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Distrib","toMul"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["ZMod","commRing"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["One","toOfNat1"],["AddMonoidWithOne","toOne"],["HSMul","hSMul"],["instHMul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":false,"kind":"definition","name":["ZMod","algebra"],"typeFallback":"forall (R : Type.{u_1}) [inst._@.Mathlib.Algebra.Algebra.ZMod.2065703575._hygCtx._hyg.3 : Ring.{u_1} R] (p : Nat) [inst._@.Mathlib.Algebra.Algebra.ZMod.2065703575._hygCtx._hyg.9 : CharP.{u_1} R (AddGroupWithOne.toAddMonoidWithOne.{u_1} R (Ring.toAddGroupWithOne.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.2065703575._hygCtx._hyg.3)) p], Algebra.{0, u_1} (ZMod p) R (CommRing.toCommSemiring.{0} (ZMod p) (ZMod.commRing p)) (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.Algebra.ZMod.2065703575._hygCtx._hyg.3)","typeFull":"(R : Type u_1) → [inst : Ring R] → (p : ℕ) → [CharP R p] → Algebra (ZMod p) R","typeReadable":"(R : Type u_1) → [inst : Ring R] → (p : ℕ) → [CharP R p] → Algebra (ZMod p) R","typeReferences":[["ZMod"],["CommRing","toCommSemiring"],["Nat"],["Ring","toAddGroupWithOne"],["CharP"],["ZMod","commRing"],["AddGroupWithOne","toAddMonoidWithOne"],["Ring","toSemiring"],["Algebra"],["Ring"]],"valueReferences":[["Nat"],["Nat","instMonoid"],["dvd_rfl"],["ZMod","algebra'"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.Grp.Abelian.sym.json

@@ -0,0 +1 @@
+[{"isProp":false,"kind":"definition","name":["AddCommGrpCat","instAbelian"],"typeFallback":"CategoryTheory.Abelian.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u}","typeFull":"CategoryTheory.Abelian AddCommGrpCat","typeReadable":"CategoryTheory.Abelian AddCommGrpCat","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","Abelian"]],"valueReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["AddCommGrpCat","instAbelian","_proof_4"],["AddCommGrpCat","instAbelian","_proof_1"],["AddCommGrpCat","instAbelian","_proof_3"],["AddCommGrpCat","instAbelian","_proof_2"],["CategoryTheory","Abelian","mk"],["AddCommGrpCat","instAbelian","_proof_5"],["AddCommGrpCat","instPreadditive"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","instAbelian","_proof_2"],"typeFallback":"CategoryTheory.IsNormalEpiCategory.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} AddCommGrpCat.instPreadditive.{u_1})","typeFull":"CategoryTheory.IsNormalEpiCategory AddCommGrpCat","typeReadable":"CategoryTheory.IsNormalEpiCategory AddCommGrpCat","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","IsNormalEpiCategory"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["AddCommGrpCat","instPreadditive"]],"valueReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["Nonempty","intro"],["CategoryTheory","NormalEpi"],["AddCommGrpCat","normalEpi"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["CategoryTheory","IsNormalEpiCategory","mk"],["AddCommGrpCat","instPreadditive"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","normalMono","_proof_1"],"typeFallback":"CategoryTheory.Functor.IsEquivalence.{u_1, u_1, succ u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.inv.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.forget₂.{u_1, u_1, succ u_1, u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.{0, 0, u_1, u_1} Int Int (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing))) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, 0} Int Int.instRing) (fun (X : ModuleCat.{u_1, 0} Int Int.instRing) (Y : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.instFunLike.{0, 0, u_1, u_1} Int Int (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing Y)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing X) (ModuleCat.isModule.{u_1, 0} Int Int.instRing Y) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1} (ModuleCat.hasForgetToAddCommGroup.{0, u_1} Int Int.instRing)) ModuleCat.forget₂AddCommGroupIsEquivalence.{u_1})","typeFull":"(CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGrpCat).inv.IsEquivalence","typeReadable":"(CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGrpCat).inv.IsEquivalence","typeReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["ModuleCat","moduleCategory"],["Int","instRing"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["AddMonoidHom","instFunLike"],["CategoryTheory","Functor","inv"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat"],["ModuleCat","carrier"],["AddCommGrpCat","instCategory"],["ModuleCat","isAddCommGroup"],["LinearMap"],["AddZeroClass","toAddZero"],["Ring","toSemiring"],["Int"],["AddCommGrpCat"],["CategoryTheory","Functor","IsEquivalence"],["AddCommGrpCat","str"],["SubNegMonoid","toAddMonoid"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["ModuleCat","moduleCategory"],["Int","instRing"],["CategoryTheory","Functor","isEquivalence_inv"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["AddMonoidHom","instFunLike"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat","carrier"],["ModuleCat"],["AddCommGrpCat","instCategory"],["ModuleCat","isAddCommGroup"],["LinearMap"],["AddZeroClass","toAddZero"],["Ring","toSemiring"],["Int"],["AddCommGrpCat"],["AddCommGrpCat","str"],["SubNegMonoid","toAddMonoid"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","instAbelian","_proof_5"],"typeFallback":"CategoryTheory.Limits.HasCokernels.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} AddCommGrpCat.instPreadditive.{u_1})","typeFull":"CategoryTheory.Limits.HasCokernels AddCommGrpCat","typeReadable":"CategoryTheory.Limits.HasCokernels AddCommGrpCat","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","Limits","HasCokernels"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["AddCommGrpCat","instPreadditive"]],"valueReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["UnivLE","self"],["CategoryTheory","Limits","WalkingParallelPair"],["univLE_of_max"],["UnivLE","small"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["CategoryTheory","Limits","walkingParallelPairHomCategory"],["AddCommGrpCat","hasColimitsOfShape"],["AddCommGrpCat","instPreadditive"],["CategoryTheory","Limits","hasCokernels_of_hasCoequalizers"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","instAbelian","_proof_1"],"typeFallback":"CategoryTheory.IsNormalMonoCategory.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} AddCommGrpCat.instPreadditive.{u_1})","typeFull":"CategoryTheory.IsNormalMonoCategory AddCommGrpCat","typeReadable":"CategoryTheory.IsNormalMonoCategory AddCommGrpCat","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","IsNormalMonoCategory"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["AddCommGrpCat","instPreadditive"]],"valueReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["Nonempty","intro"],["CategoryTheory","IsNormalMonoCategory","mk"],["CategoryTheory","NormalMono"],["AddCommGrpCat","normalMono"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["AddCommGrpCat","instPreadditive"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","instAbelian","_proof_4"],"typeFallback":"CategoryTheory.Limits.HasKernels.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} AddCommGrpCat.instPreadditive.{u_1})","typeFull":"CategoryTheory.Limits.HasKernels AddCommGrpCat","typeReadable":"CategoryTheory.Limits.HasKernels AddCommGrpCat","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","Limits","HasKernels"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["AddCommGrpCat","instPreadditive"]],"valueReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["UnivLE","self"],["CategoryTheory","Limits","WalkingParallelPair"],["AddCommGrpCat","hasLimitsOfShape"],["CategoryTheory","Limits","hasKernels_of_hasEqualizers"],["univLE_of_max"],["UnivLE","small"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["CategoryTheory","Limits","walkingParallelPairHomCategory"],["AddCommGrpCat","instPreadditive"]]},{"isProp":false,"kind":"definition","name":["AddCommGrpCat","normalMono"],"typeFallback":"forall {X : AddCommGrpCat.{u}} {Y : AddCommGrpCat.{u}} (f : Quiver.Hom.{u, succ u} AddCommGrpCat.{u} (CategoryTheory.CategoryStruct.toQuiver.{u, succ u} AddCommGrpCat.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u})) X Y), (CategoryTheory.Mono.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u} X Y f) -> (CategoryTheory.NormalMono.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u} X Y (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u} AddCommGrpCat.instPreadditive.{u}) f)","typeFull":"{X Y : AddCommGrpCat} → (f : X ⟶ Y) → CategoryTheory.Mono f → CategoryTheory.NormalMono f","typeReadable":"{X Y : AddCommGrpCat} → (f : X ⟶ Y) → CategoryTheory.Mono f → CategoryTheory.NormalMono f","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","CategoryStruct","toQuiver"],["Quiver","Hom"],["CategoryTheory","NormalMono"],["CategoryTheory","Mono"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["CategoryTheory","Category","toCategoryStruct"],["AddCommGrpCat","instPreadditive"]],"valueReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["ModuleCat","moduleCategory"],["CategoryTheory","Functor","obj"],["Int","instRing"],["ModuleCat","normalMono"],["CategoryTheory","Functor","map"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["AddMonoidHom","instFunLike"],["CategoryTheory","Functor","inv"],["AddGroup","toSubNegMonoid"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["CategoryTheory","equivalenceReflectsNormalMono"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat"],["ModuleCat","carrier"],["AddCommGrpCat","instCategory"],["ModuleCat","isAddCommGroup"],["ModuleCat","instPreadditive"],["AddCommGrpCat","normalMono","_proof_1"],["LinearMap"],["AddZeroClass","toAddZero"],["AddCommGrpCat","normalMono","_proof_2"],["Int"],["Ring","toSemiring"],["AddCommGrpCat"],["AddCommGrpCat","str"],["SubNegMonoid","toAddMonoid"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["AddCommGrpCat","instPreadditive"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","instAbelian","_proof_3"],"typeFallback":"CategoryTheory.Limits.HasFiniteProducts.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1}","typeFull":"CategoryTheory.Limits.HasFiniteProducts AddCommGrpCat","typeReadable":"CategoryTheory.Limits.HasFiniteProducts AddCommGrpCat","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","Limits","HasFiniteProducts"]],"valueReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["AddCommGrpCat","hasLimits"],["CategoryTheory","Limits","hasFiniteLimits_of_hasLimits"],["CategoryTheory","Limits","hasFiniteProducts_of_hasFiniteLimits"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","normalEpi","_proof_1"],"typeFallback":"forall {X : AddCommGrpCat.{u_1}} {Y : AddCommGrpCat.{u_1}} (f : Quiver.Hom.{u_1, succ u_1} AddCommGrpCat.{u_1} (CategoryTheory.CategoryStruct.toQuiver.{u_1, succ u_1} AddCommGrpCat.{u_1} (CategoryTheory.Category.toCategoryStruct.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1})) X Y), (CategoryTheory.Epi.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} X Y f) -> (CategoryTheory.Epi.{u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.obj.{u_1, u_1, succ u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.inv.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.forget₂.{u_1, u_1, succ u_1, u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.{0, 0, u_1, u_1} Int Int (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing))) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, 0} Int Int.instRing) (fun (X : ModuleCat.{u_1, 0} Int Int.instRing) (Y : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.instFunLike.{0, 0, u_1, u_1} Int Int (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing Y)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing X) (ModuleCat.isModule.{u_1, 0} Int Int.instRing Y) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1} (ModuleCat.hasForgetToAddCommGroup.{0, u_1} Int Int.instRing)) ModuleCat.forget₂AddCommGroupIsEquivalence.{u_1}) X) (CategoryTheory.Functor.obj.{u_1, u_1, succ u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.inv.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.forget₂.{u_1, u_1, succ u_1, u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.{0, 0, u_1, u_1} Int Int (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing))) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, 0} Int Int.instRing) (fun (X : ModuleCat.{u_1, 0} Int Int.instRing) (Y : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.instFunLike.{0, 0, u_1, u_1} Int Int (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing Y)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing X) (ModuleCat.isModule.{u_1, 0} Int Int.instRing Y) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1} (ModuleCat.hasForgetToAddCommGroup.{0, u_1} Int Int.instRing)) ModuleCat.forget₂AddCommGroupIsEquivalence.{u_1}) Y) (CategoryTheory.Functor.map.{u_1, u_1, succ u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.inv.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.forget₂.{u_1, u_1, succ u_1, u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.{0, 0, u_1, u_1} Int Int (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing))) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, 0} Int Int.instRing) (fun (X : ModuleCat.{u_1, 0} Int Int.instRing) (Y : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.instFunLike.{0, 0, u_1, u_1} Int Int (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing Y)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing X) (ModuleCat.isModule.{u_1, 0} Int Int.instRing Y) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1} (ModuleCat.hasForgetToAddCommGroup.{0, u_1} Int Int.instRing)) ModuleCat.forget₂AddCommGroupIsEquivalence.{u_1}) X Y f))","typeFull":"∀ {X Y : AddCommGrpCat} (f : X ⟶ Y),\n  CategoryTheory.Epi f → CategoryTheory.Epi ((CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGrpCat).inv.map f)","typeReadable":"∀ {X Y : AddCommGrpCat} (f : X ⟶ Y),\n  CategoryTheory.Epi f → CategoryTheory.Epi ((CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGrpCat).inv.map f)","typeReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["ModuleCat","moduleCategory"],["CategoryTheory","Functor","obj"],["Int","instRing"],["CategoryTheory","Functor","map"],["Semiring","toNonAssocSemiring"],["Quiver","Hom"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["CategoryTheory","Epi"],["AddMonoidHom","instFunLike"],["CategoryTheory","Functor","inv"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat"],["ModuleCat","carrier"],["AddCommGrpCat","instCategory"],["ModuleCat","isAddCommGroup"],["AddZeroClass","toAddZero"],["LinearMap"],["CategoryTheory","Category","toCategoryStruct"],["Int"],["Ring","toSemiring"],["AddCommGrpCat"],["AddCommGrpCat","str"],["CategoryTheory","CategoryStruct","toQuiver"],["SubNegMonoid","toAddMonoid"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["ModuleCat","moduleCategory"],["CategoryTheory","Functor","map_epi"],["CategoryTheory","Functor","obj"],["Int","instRing"],["CategoryTheory","Functor","isEquivalence_inv"],["CategoryTheory","Functor","map"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["CategoryTheory","preservesEpimorphisms_of_preservesColimitsOfShape"],["CategoryTheory","Epi"],["AddMonoidHom","instFunLike"],["CategoryTheory","Functor","inv"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat"],["ModuleCat","carrier"],["AddCommGrpCat","instCategory"],["ModuleCat","isAddCommGroup"],["CategoryTheory","Limits","WalkingPair"],["CategoryTheory","Limits","WidePushoutShape","category"],["CategoryTheory","Functor","instPreservesColimitsOfShapeOfIsLeftAdjoint"],["LinearMap"],["AddZeroClass","toAddZero"],["CategoryTheory","Limits","WalkingSpan"],["Ring","toSemiring"],["Int"],["AddCommGrpCat"],["AddCommGrpCat","str"],["SubNegMonoid","toAddMonoid"],["CategoryTheory","Functor","isLeftAdjoint_of_isEquivalence"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["inferInstance"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddCommGrpCat","normalMono","_proof_2"],"typeFallback":"forall {X : AddCommGrpCat.{u_1}} {Y : AddCommGrpCat.{u_1}} (f : Quiver.Hom.{u_1, succ u_1} AddCommGrpCat.{u_1} (CategoryTheory.CategoryStruct.toQuiver.{u_1, succ u_1} AddCommGrpCat.{u_1} (CategoryTheory.Category.toCategoryStruct.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1})) X Y), (CategoryTheory.Mono.{u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} X Y f) -> (CategoryTheory.Mono.{u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.obj.{u_1, u_1, succ u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.inv.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.forget₂.{u_1, u_1, succ u_1, u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.{0, 0, u_1, u_1} Int Int (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing))) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, 0} Int Int.instRing) (fun (X : ModuleCat.{u_1, 0} Int Int.instRing) (Y : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.instFunLike.{0, 0, u_1, u_1} Int Int (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing Y)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing X) (ModuleCat.isModule.{u_1, 0} Int Int.instRing Y) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1} (ModuleCat.hasForgetToAddCommGroup.{0, u_1} Int Int.instRing)) ModuleCat.forget₂AddCommGroupIsEquivalence.{u_1}) X) (CategoryTheory.Functor.obj.{u_1, u_1, succ u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.inv.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.forget₂.{u_1, u_1, succ u_1, u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.{0, 0, u_1, u_1} Int Int (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing))) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, 0} Int Int.instRing) (fun (X : ModuleCat.{u_1, 0} Int Int.instRing) (Y : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.instFunLike.{0, 0, u_1, u_1} Int Int (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing Y)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing X) (ModuleCat.isModule.{u_1, 0} Int Int.instRing Y) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1} (ModuleCat.hasForgetToAddCommGroup.{0, u_1} Int Int.instRing)) ModuleCat.forget₂AddCommGroupIsEquivalence.{u_1}) Y) (CategoryTheory.Functor.map.{u_1, u_1, succ u_1, succ u_1} AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (CategoryTheory.Functor.inv.{u_1, u_1, succ u_1, succ u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (CategoryTheory.forget₂.{u_1, u_1, succ u_1, u_1, u_1, succ u_1, u_1} (ModuleCat.{u_1, 0} Int Int.instRing) (ModuleCat.moduleCategory.{u_1, 0} Int Int.instRing) (fun (x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) (x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13 : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.{0, 0, u_1, u_1} Int Int (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing))) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x1._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13) (ModuleCat.isModule.{u_1, 0} Int Int.instRing x2._@.Mathlib.Algebra.Category.ModuleCat.Basic.3153568637._hygCtx._hyg.13)) (ModuleCat.carrier.{u_1, 0} Int Int.instRing) (fun (X : ModuleCat.{u_1, 0} Int Int.instRing) (Y : ModuleCat.{u_1, 0} Int Int.instRing) => LinearMap.instFunLike.{0, 0, u_1, u_1} Int Int (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (Ring.toSemiring.{0} Int Int.instRing) (Ring.toSemiring.{0} Int Int.instRing) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing X) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing X)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, 0} Int Int.instRing Y) (ModuleCat.isAddCommGroup.{u_1, 0} Int Int.instRing Y)) (ModuleCat.isModule.{u_1, 0} Int Int.instRing X) (ModuleCat.isModule.{u_1, 0} Int Int.instRing Y) (RingHom.id.{0} Int (Semiring.toNonAssocSemiring.{0} Int (Ring.toSemiring.{0} Int Int.instRing)))) (ModuleCat.instConcreteCategoryLinearMapIdCarrier.{u_1, 0} Int Int.instRing) AddCommGrpCat.{u_1} AddCommGrpCat.instCategory.{u_1} (fun (x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) (x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6 : AddCommGrpCat.{u_1}) => AddMonoidHom.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x1._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6) (AddCommGrpCat.str.{u_1} x2._@.Mathlib.Algebra.Category.Grp.Basic.4010222601._hygCtx._hyg.6))))))) AddCommGrpCat.carrier.{u_1} (fun (X : AddCommGrpCat.{u_1}) (Y : AddCommGrpCat.{u_1}) => AddMonoidHom.instFunLike.{u_1, u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.carrier.{u_1} Y) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} X) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} X) (AddCommGrpCat.str.{u_1} X)))))) (AddZeroClass.toAddZero.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddMonoid.toAddZeroClass.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (SubNegMonoid.toAddMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddGroup.toSubNegMonoid.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGroup.toAddGroup.{u_1} (AddCommGrpCat.carrier.{u_1} Y) (AddCommGrpCat.str.{u_1} Y))))))) AddCommGrpCat.instConcreteCategoryAddMonoidHomCarrier.{u_1} (ModuleCat.hasForgetToAddCommGroup.{0, u_1} Int Int.instRing)) ModuleCat.forget₂AddCommGroupIsEquivalence.{u_1}) X Y f))","typeFull":"∀ {X Y : AddCommGrpCat} (f : X ⟶ Y),\n  CategoryTheory.Mono f → CategoryTheory.Mono ((CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGrpCat).inv.map f)","typeReadable":"∀ {X Y : AddCommGrpCat} (f : X ⟶ Y),\n  CategoryTheory.Mono f → CategoryTheory.Mono ((CategoryTheory.forget₂ (ModuleCat ℤ) AddCommGrpCat).inv.map f)","typeReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["ModuleCat","moduleCategory"],["CategoryTheory","Mono"],["CategoryTheory","Functor","obj"],["Int","instRing"],["CategoryTheory","Functor","map"],["Semiring","toNonAssocSemiring"],["Quiver","Hom"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["AddMonoidHom","instFunLike"],["CategoryTheory","Functor","inv"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat"],["ModuleCat","carrier"],["AddCommGrpCat","instCategory"],["ModuleCat","isAddCommGroup"],["AddZeroClass","toAddZero"],["LinearMap"],["CategoryTheory","Category","toCategoryStruct"],["Int"],["Ring","toSemiring"],["AddCommGrpCat"],["AddCommGrpCat","str"],["CategoryTheory","CategoryStruct","toQuiver"],["SubNegMonoid","toAddMonoid"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["CategoryTheory","Functor","isRightAdjoint_of_isEquivalence"],["CategoryTheory","Functor","map_mono"],["AddCommGroup","toAddGroup"],["CategoryTheory","Limits","WidePullbackShape","category"],["ModuleCat","moduleCategory"],["CategoryTheory","Mono"],["CategoryTheory","Functor","obj"],["Int","instRing"],["CategoryTheory","Functor","isEquivalence_inv"],["CategoryTheory","Functor","instPreservesLimitsOfShapeOfIsRightAdjoint"],["CategoryTheory","Functor","map"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["CategoryTheory","preservesMonomorphisms_of_preservesLimitsOfShape"],["AddMonoidHom","instFunLike"],["CategoryTheory","Functor","inv"],["AddGroup","toSubNegMonoid"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat"],["ModuleCat","carrier"],["AddCommGrpCat","instCategory"],["ModuleCat","isAddCommGroup"],["CategoryTheory","Limits","WalkingCospan"],["CategoryTheory","Limits","WalkingPair"],["LinearMap"],["AddZeroClass","toAddZero"],["Ring","toSemiring"],["Int"],["AddCommGrpCat"],["AddCommGrpCat","str"],["SubNegMonoid","toAddMonoid"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["inferInstance"],["AddMonoid","toAddZeroClass"]]},{"isProp":false,"kind":"definition","name":["AddCommGrpCat","normalEpi"],"typeFallback":"forall {X : AddCommGrpCat.{u}} {Y : AddCommGrpCat.{u}} (f : Quiver.Hom.{u, succ u} AddCommGrpCat.{u} (CategoryTheory.CategoryStruct.toQuiver.{u, succ u} AddCommGrpCat.{u} (CategoryTheory.Category.toCategoryStruct.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u})) X Y), (CategoryTheory.Epi.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u} X Y f) -> (CategoryTheory.NormalEpi.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u} X Y (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u, succ u} AddCommGrpCat.{u} AddCommGrpCat.instCategory.{u} AddCommGrpCat.instPreadditive.{u}) f)","typeFull":"{X Y : AddCommGrpCat} → (f : X ⟶ Y) → CategoryTheory.Epi f → CategoryTheory.NormalEpi f","typeReadable":"{X Y : AddCommGrpCat} → (f : X ⟶ Y) → CategoryTheory.Epi f → CategoryTheory.NormalEpi f","typeReferences":[["AddCommGrpCat"],["AddCommGrpCat","instCategory"],["CategoryTheory","CategoryStruct","toQuiver"],["CategoryTheory","NormalEpi"],["Quiver","Hom"],["CategoryTheory","Epi"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["CategoryTheory","Category","toCategoryStruct"],["AddCommGrpCat","instPreadditive"]],"valueReferences":[["ModuleCat","isModule"],["CategoryTheory","forget₂"],["LinearMap","instFunLike"],["AddCommGroup","toAddGroup"],["ModuleCat","moduleCategory"],["CategoryTheory","Functor","obj"],["Int","instRing"],["CategoryTheory","Functor","map"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["AddMonoidHom"],["AddMonoidHom","instFunLike"],["CategoryTheory","Functor","inv"],["AddGroup","toSubNegMonoid"],["CategoryTheory","Preadditive","preadditiveHasZeroMorphisms"],["AddCommGrpCat","carrier"],["ModuleCat","forget₂AddCommGroupIsEquivalence"],["AddCommGrpCat","instConcreteCategoryAddMonoidHomCarrier"],["ModuleCat"],["ModuleCat","carrier"],["AddCommGrpCat","instCategory"],["CategoryTheory","equivalenceReflectsNormalEpi"],["ModuleCat","isAddCommGroup"],["ModuleCat","instPreadditive"],["AddCommGrpCat","normalMono","_proof_1"],["LinearMap"],["AddZeroClass","toAddZero"],["Int"],["Ring","toSemiring"],["AddCommGrpCat"],["AddCommGrpCat","str"],["SubNegMonoid","toAddMonoid"],["ModuleCat","hasForgetToAddCommGroup"],["AddCommGroup","toAddCommMonoid"],["AddCommGrpCat","normalEpi","_proof_1"],["AddCommGrpCat","instPreadditive"],["ModuleCat","normalEpi"],["AddMonoid","toAddZeroClass"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Injective.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Module","injective_iff_injective_object"],"typeFallback":"forall (R : Type.{u}) (M : Type.{v}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.4 : Ring.{u} R] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.7 : AddCommGroup.{v} M] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.10 : Module.{u, v} R M (Ring.toSemiring.{u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.7)], Iff (Module.Injective.{u, v} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.10) (CategoryTheory.Injective.{v, max u (succ v)} (ModuleCat.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.4) (ModuleCat.moduleCategory.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.4) (ModuleCat.of.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3960626226._hygCtx._hyg.10))","typeFull":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M],\n  Module.Injective R M ↔ CategoryTheory.Injective (ModuleCat.of R M)","typeReadable":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M],\n  Module.Injective R M ↔ CategoryTheory.Injective (ModuleCat.of R M)","typeReferences":[["Module","Injective"],["Module"],["Iff"],["CategoryTheory","Injective"],["AddCommGroup","toAddCommMonoid"],["ModuleCat","moduleCategory"],["ModuleCat","of"],["AddCommGroup"],["ModuleCat"],["Ring","toSemiring"],["Ring"]],"valueReferences":[["Module","injective_object_of_injective_module"],["Module","Injective"],["Module","injective_module_of_injective_object"],["CategoryTheory","Injective"],["ModuleCat","moduleCategory"],["ModuleCat","of"],["ModuleCat"],["Iff","intro"]]},{"isProp":true,"kind":"theorem","name":["Module","injective_object_of_injective_module"],"typeFallback":"forall (R : Type.{u}) (M : Type.{v}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 : Ring.{u} R] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 : AddCommGroup.{v} M] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 : Module.{u, v} R M (Ring.toSemiring.{u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7)] [inj : Module.Injective.{u, v} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10], CategoryTheory.Injective.{v, max u (succ v)} (ModuleCat.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (ModuleCat.moduleCategory.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (ModuleCat.of.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10)","typeFull":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]\n  [inj : Module.Injective R M], CategoryTheory.Injective (ModuleCat.of R M)","typeReadable":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]\n  [inj : Module.Injective R M], CategoryTheory.Injective (ModuleCat.of R M)","typeReferences":[["Module","Injective"],["Module"],["CategoryTheory","Injective"],["AddCommGroup","toAddCommMonoid"],["ModuleCat","moduleCategory"],["ModuleCat","of"],["AddCommGroup"],["ModuleCat"],["Ring","toSemiring"],["Ring"]],"valueReferences":[["_private","Mathlib","Algebra","Category","ModuleCat","Injective",0,"Module","injective_object_of_injective_module","match_1_1"],["Module","Injective","out"],["ModuleCat","isModule"],["ModuleCat","ofHom"],["LinearMap","instFunLike"],["CategoryTheory","Injective","mk"],["Iff","mp"],["Exists","intro"],["ModuleCat","moduleCategory"],["CategoryTheory","Mono"],["DFunLike","coe"],["ModuleCat","mono_iff_injective"],["CategoryTheory","ConcreteCategory","hom"],["Semiring","toNonAssocSemiring"],["Quiver","Hom"],["RingHom","id"],["LinearMap","ext"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["Eq"],["ModuleCat","carrier"],["ModuleCat"],["ModuleCat","isAddCommGroup"],["ModuleCat","hom_ext"],["Exists"],["ModuleCat","Hom","hom"],["ModuleCat","of"],["LinearMap"],["CategoryTheory","Category","toCategoryStruct"],["Ring","toSemiring"],["CategoryTheory","CategoryStruct","toQuiver"],["CategoryTheory","CategoryStruct","comp"],["id"],["AddCommGroup","toAddCommMonoid"],["Function","Injective"]]},{"isProp":true,"kind":"definition","name":["_private","Mathlib","Algebra","Category","ModuleCat","Injective",0,"Module","injective_object_of_injective_module","match_1_1"],"typeFallback":"forall (R : Type.{u_2}) (M : Type.{u_1}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 : Ring.{u_2} R] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 : AddCommGroup.{u_1} M] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 : Module.{u_2, u_1} R M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7)] {X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 : ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4} {Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33 : ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4} (g : Quiver.Hom.{u_1, max u_2 (succ u_1)} (ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (CategoryTheory.CategoryStruct.toQuiver.{u_1, max u_2 (succ u_1)} (ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (CategoryTheory.Category.toCategoryStruct.{u_1, max u_2 (succ u_1)} (ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (ModuleCat.moduleCategory.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 (ModuleCat.of.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10)) (f : Quiver.Hom.{u_1, max u_2 (succ u_1)} (ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (CategoryTheory.CategoryStruct.toQuiver.{u_1, max u_2 (succ u_1)} (ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (CategoryTheory.Category.toCategoryStruct.{u_1, max u_2 (succ u_1)} (ModuleCat.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (ModuleCat.moduleCategory.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (motive : (Exists.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (fun (h : LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) => forall (x : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32), Eq.{succ u_1} M (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) h (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33 f) x)) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 (ModuleCat.of.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) g) x))) -> Prop) (x._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.57 : Exists.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (fun (h : LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) => forall (x : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32), Eq.{succ u_1} M (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) h (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33 f) x)) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 (ModuleCat.of.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) g) x))), (forall (l : LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (h : forall (x : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32), Eq.{succ u_1} M (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) l (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33 f) x)) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 (ModuleCat.of.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) g) x)), motive (Exists.intro.{succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (fun (h : LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) => forall (x : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32), Eq.{succ u_1} M (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) h (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33)) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 Y._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.33 f) x)) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (LinearMap.{u_2, u_2, u_1, u_1} R R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4))) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) => M) (LinearMap.instFunLike.{u_2, u_2, u_1, u_1} R R (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) M (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_1} (ModuleCat.carrier.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) (ModuleCat.isAddCommGroup.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32)) (AddCommGroup.toAddCommMonoid.{u_1} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7) (ModuleCat.isModule.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10 (RingHom.id.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (Ring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4)))) (ModuleCat.Hom.hom.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 X._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.32 (ModuleCat.of.{u_1, u_2} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.10) g) x)) l h)) -> (motive x._@.Mathlib.Algebra.Category.ModuleCat.Injective.3887543903._hygCtx._hyg.57)","typeFull":"∀ (R : Type u_2) (M : Type u_1) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {X Y : ModuleCat R}\n  (g : X ⟶ ModuleCat.of R M) (f : X ⟶ Y)\n  (motive : (∃ h, ∀ (x : ↑X), h ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x) → Prop)\n  (x : ∃ h, ∀ (x : ↑X), h ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x),\n  (∀ (l : ↑Y →ₗ[R] M) (h : ∀ (x : ↑X), l ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x), motive ⋯) → motive x","typeReadable":"∀ (R : Type u_2) (M : Type u_1) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {X Y : ModuleCat R}\n  (g : X ⟶ ModuleCat.of R M) (f : X ⟶ Y)\n  (motive : (∃ h, ∀ (x : ↑X), h ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x) → Prop)\n  (x : ∃ h, ∀ (x : ↑X), h ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x),\n  (∀ (l : ↑Y →ₗ[R] M) (h : ∀ (x : ↑X), l ((ModuleCat.Hom.hom f) x) = (ModuleCat.Hom.hom g) x), motive ⋯) → motive x","typeReferences":[["ModuleCat","isModule"],["ModuleCat","isAddCommGroup"],["Exists"],["LinearMap","instFunLike"],["ModuleCat","Hom","hom"],["Module"],["Exists","intro"],["ModuleCat","moduleCategory"],["AddCommGroup"],["ModuleCat","of"],["LinearMap"],["DFunLike","coe"],["CategoryTheory","Category","toCategoryStruct"],["Ring","toSemiring"],["Semiring","toNonAssocSemiring"],["CategoryTheory","CategoryStruct","toQuiver"],["RingHom","id"],["Quiver","Hom"],["AddCommGroup","toAddCommMonoid"],["Eq"],["ModuleCat","carrier"],["Ring"],["ModuleCat"]],"valueReferences":[["ModuleCat","isModule"],["ModuleCat","isAddCommGroup"],["LinearMap","instFunLike"],["ModuleCat","Hom","hom"],["ModuleCat","of"],["LinearMap"],["DFunLike","coe"],["Ring","toSemiring"],["Exists","casesOn"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddCommGroup","toAddCommMonoid"],["Eq"],["ModuleCat","carrier"]]},{"isProp":true,"kind":"theorem","name":["Module","injective_module_of_injective_object"],"typeFallback":"forall (R : Type.{u}) (M : Type.{v}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.4 : Ring.{u} R] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.7 : AddCommGroup.{v} M] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.10 : Module.{u, v} R M (Ring.toSemiring.{u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.7)] [inj : CategoryTheory.Injective.{v, max u (succ v)} (ModuleCat.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.4) (ModuleCat.moduleCategory.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.4) (ModuleCat.of.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.10)], Module.Injective.{u, v} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.3164413687._hygCtx._hyg.10","typeFull":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]\n  [inj : CategoryTheory.Injective (ModuleCat.of R M)], Module.Injective R M","typeReadable":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]\n  [inj : CategoryTheory.Injective (ModuleCat.of R M)], Module.Injective R M","typeReferences":[["Module","Injective"],["Module"],["CategoryTheory","Injective"],["AddCommGroup","toAddCommMonoid"],["ModuleCat","moduleCategory"],["ModuleCat","of"],["AddCommGroup"],["ModuleCat"],["Ring","toSemiring"],["Ring"]],"valueReferences":[["ModuleCat","isModule"],["ModuleCat","ofHom"],["LinearMap","instFunLike"],["Iff","mp"],["Exists","intro"],["ModuleCat","moduleCategory"],["CategoryTheory","Mono"],["ModuleCat","hom_ext_iff"],["CategoryTheory","Injective","factors"],["DFunLike","coe"],["CategoryTheory","ConcreteCategory","hom"],["ModuleCat","mono_iff_injective"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Quiver","Hom"],["ModuleCat","instConcreteCategoryLinearMapIdCarrier"],["Module","Injective","mk"],["Eq","ndrec"],["Eq"],["ModuleCat","carrier"],["ModuleCat"],["rfl"],["ModuleCat","isAddCommGroup"],["Exists"],["ModuleCat","Hom","hom"],["ModuleCat","of"],["LinearMap"],["CategoryTheory","Category","toCategoryStruct"],["Ring","toSemiring"],["Exists","casesOn"],["CategoryTheory","CategoryStruct","toQuiver"],["CategoryTheory","CategoryStruct","comp"],["Iff","mpr"],["AddCommGroup","toAddCommMonoid"],["Function","Injective"]]},{"isProp":true,"kind":"theorem","name":["ModuleCat","ulift_injective_of_injective"],"typeFallback":"forall (R : Type.{u}) (M : Type.{v}) [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4 : Ring.{u} R] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.7 : AddCommGroup.{v} M] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.10 : Module.{u, v} R M (Ring.toSemiring.{u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.7)] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.14 : Small.{v, u} R] [inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.17 : CategoryTheory.Injective.{v, max u (succ v)} (ModuleCat.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4) (ModuleCat.moduleCategory.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4) (ModuleCat.of.{v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4 M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.10)], CategoryTheory.Injective.{max v v', max u (succ (max v' v))} (ModuleCat.{max v' v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4) (ModuleCat.moduleCategory.{max v v', u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4) (ModuleCat.of.{max v' v, u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4 (ULift.{v', v} M) (ULift.addCommGroup.{v, v'} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.7) (ULift.module'.{u, v, v'} R M (Ring.toSemiring.{u} R inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{v} M inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Category.ModuleCat.Injective.436766509._hygCtx._hyg.10))","typeFull":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Small.{v, u} R]\n  [CategoryTheory.Injective (ModuleCat.of R M)], CategoryTheory.Injective (ModuleCat.of R (ULift.{v', v} M))","typeReadable":"∀ (R : Type u) (M : Type v) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Small.{v, u} R]\n  [CategoryTheory.Injective (ModuleCat.of R M)], CategoryTheory.Injective (ModuleCat.of R (ULift.{v', v} M))","typeReferences":[["Module"],["ULift"],["Small"],["CategoryTheory","Injective"],["ModuleCat","moduleCategory"],["AddCommGroup"],["ModuleCat","of"],["ULift","addCommGroup"],["ULift","module'"],["Ring","toSemiring"],["AddCommGroup","toAddCommMonoid"],["Ring"],["ModuleCat"]],"valueReferences":[["ULift"],["Module","injective_object_of_injective_module"],["Module","injective_module_of_injective_object"],["AddCommGroup","toAddCommMonoid"],["Module","ulift_injective_of_injective"],["ULift","module'"],["ULift","addCommGroup"],["Ring","toSemiring"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Topology.Basic.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:2af336dd42e972ef21b8d2b44585aee4a2926461f9bcb4703041cb5f3f9c7513
+size 16056943

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Field.ModEq.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["AddCommGroup","div_modEq_div"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3 : DivisionSemiring.{u_1} K] {a : K} {b : K} {c : K} {p : K}, (Ne.{succ u_1} K c (OfNat.ofNat.{u_1} K 0 (Zero.toOfNat0.{u_1} K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))))))) -> (Iff (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) p (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) a c) (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) b c)) (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))))) p c) a b))","typeFull":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a / c ≡ b / c [PMOD p] ↔ a ≡ b [PMOD p * c])","typeReadable":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a / c ≡ b / c [PMOD p] ↔ a ≡ b [PMOD p * c])","typeReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["DivisionSemiring"],["OfNat","ofNat"],["AddCommGroup","ModEq"],["HDiv","hDiv"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["Iff"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["Ne"],["Zero","toOfNat0"]],"valueReferences":[["Eq","trans"],["GroupWithZero","toDivInvMonoid"],["HMul","hMul"],["NonUnitalSemiring","toSemigroupWithZero"],["HDiv","hDiv"],["Semiring","toNonAssocSemiring"],["iff_self"],["funext"],["Semiring","toNonUnitalSemiring"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Exists"],["NonUnitalNonAssocSemiring","toDistrib"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DivisionSemiring","toSemiring"],["DivisionSemiring","toGroupWithZero"],["Nat"],["AddMonoidWithOne","toNatCast"],["AddMonoid","toNSMul"],["Iff"],["HSMul","hSMul"],["instHMul"],["Nat","cast"],["mul_assoc"],["AddCommMonoid","toAddMonoid"],["instHDiv"],["div_left_inj'"],["Semigroup","toMul"],["congrArg"],["AddCommGroup","ModEq"],["congr"],["_private","Mathlib","Algebra","Field","ModEq",0,"AddCommGroup","div_modEq_div","_simp_1_1"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["congrFun'"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["add_div'"],["Eq"],["propext"],["Distrib","toAdd"],["True"],["instHAdd"],["Distrib","toMul"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DivInvMonoid","toDiv"],["HAdd","hAdd"],["of_eq_true"],["AddCommMonoid","toAddCommSemigroup"],["nsmul_eq_mul"],["SemigroupWithZero","toSemigroup"]]},{"isProp":true,"kind":"theorem","name":["AddCommGroup","mul_modEq_mul_left"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3 : Semifield.{u_1} K] {a : K} {b : K} {c : K} {p : K}, (Ne.{succ u_1} K c (OfNat.ofNat.{u_1} K 0 (Zero.toOfNat0.{u_1} K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))))))) -> (Iff (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))) p (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))))) c a) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))))) c b)) (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))) (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))) p c) a b))","typeFull":"∀ {K : Type u_1} [inst : Semifield K] {a b c p : K}, c ≠ 0 → (c * a ≡ c * b [PMOD p] ↔ a ≡ b [PMOD p / c])","typeReadable":"∀ {K : Type u_1} [inst : Semifield K] {a b c p : K}, c ≠ 0 → (c * a ≡ c * b [PMOD p] ↔ a ≡ b [PMOD p / c])","typeReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["OfNat","ofNat"],["HDiv","hDiv"],["AddCommGroup","ModEq"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["Iff"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["Semifield"],["Ne"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"]],"valueReferences":[["Semifield","toCommSemiring"],["Eq","trans"],["NonUnitalNonAssocCommSemiring","toCommMagma"],["GroupWithZero","toDivInvMonoid"],["HMul","hMul"],["instHDiv"],["congrArg"],["HDiv","hDiv"],["AddCommGroup","ModEq"],["NonUnitalCommSemiring","toNonUnitalNonAssocCommSemiring"],["not_false_eq_true"],["Semiring","toNonAssocSemiring"],["iff_self"],["AddCommGroup","mul_modEq_mul_right","_simp_1"],["CommSemiring","toNonUnitalCommSemiring"],["congr"],["mul_comm"],["Zero","toOfNat0"],["congrFun'"],["Semifield","toDivisionSemiring"],["Eq"],["Not"],["NonUnitalNonAssocSemiring","toDistrib"],["True"],["CommMagma","toMul"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DivisionSemiring","toSemiring"],["DivisionSemiring","toGroupWithZero"],["OfNat","ofNat"],["DivInvMonoid","toDiv"],["of_eq_true"],["MulZeroClass","toZero"],["eq_false"],["Iff"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["False"],["instHMul"]]},{"isProp":true,"kind":"theorem","name":["AddCommGroup","mul_modEq_mul_left","_simp_1"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3 : Semifield.{u_1} K] {a : K} {b : K} {c : K} {p : K}, (Ne.{succ u_1} K c (OfNat.ofNat.{u_1} K 0 (Zero.toOfNat0.{u_1} K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))))))) -> (Eq.{1} Prop (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))) p (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))))) c a) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))))) c b)) (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))) (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K (Semifield.toDivisionSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.514332539._hygCtx._hyg.3))))) p c) a b))","typeFull":"∀ {K : Type u_1} [inst : Semifield K] {a b c p : K}, c ≠ 0 → (c * a ≡ c * b [PMOD p]) = (a ≡ b [PMOD p / c])","typeReadable":"∀ {K : Type u_1} [inst : Semifield K] {a b c p : K}, c ≠ 0 → (c * a ≡ c * b [PMOD p]) = (a ≡ b [PMOD p / c])","typeReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["OfNat","ofNat"],["HDiv","hDiv"],["AddCommGroup","ModEq"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["Semifield"],["Ne"],["Zero","toOfNat0"],["Semifield","toDivisionSemiring"],["Eq"]],"valueReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Distrib","toMul"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["AddCommGroup","ModEq"],["HDiv","hDiv"],["Semiring","toNonAssocSemiring"],["AddCommGroup","mul_modEq_mul_left"],["instHMul"],["Semifield","toDivisionSemiring"],["propext"]]},{"isProp":true,"kind":"theorem","name":["AddCommGroup","mul_modEq_mul_right","_simp_1"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3 : DivisionSemiring.{u_1} K] {a : K} {b : K} {c : K} {p : K}, (Ne.{succ u_1} K c (OfNat.ofNat.{u_1} K 0 (Zero.toOfNat0.{u_1} K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))))))) -> (Eq.{1} Prop (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))) p (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))))) a c) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))))) b c)) (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))) (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))) p c) a b))","typeFull":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a * c ≡ b * c [PMOD p]) = (a ≡ b [PMOD p / c])","typeReadable":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a * c ≡ b * c [PMOD p]) = (a ≡ b [PMOD p / c])","typeReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["DivisionSemiring"],["OfNat","ofNat"],["HDiv","hDiv"],["AddCommGroup","ModEq"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["Ne"],["Zero","toOfNat0"],["Eq"]],"valueReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["Distrib","toMul"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["AddCommGroup","ModEq"],["HDiv","hDiv"],["Semiring","toNonAssocSemiring"],["AddCommGroup","mul_modEq_mul_right"],["instHMul"],["propext"]]},{"isProp":true,"kind":"theorem","name":["_private","Mathlib","Algebra","Field","ModEq",0,"AddCommGroup","div_modEq_div","_simp_1_1"],"typeFallback":"forall {M : Type.{u_1}} [inst._@.Mathlib.Algebra.Group.ModEq.3041720194._hygCtx._hyg.3 : AddCommMonoid.{u_1} M] {a : M} {b : M} {p : M}, Eq.{1} Prop (AddCommGroup.ModEq.{u_1} M inst._@.Mathlib.Algebra.Group.ModEq.3041720194._hygCtx._hyg.3 p a b) (Exists.{1} Nat (fun (m : Nat) => Exists.{1} Nat (fun (n : Nat) => Eq.{succ u_1} M (HAdd.hAdd.{u_1, u_1, u_1} M M M (instHAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Group.ModEq.3041720194._hygCtx._hyg.3)))) (HSMul.hSMul.{0, u_1, u_1} Nat M M (instHSMul.{0, u_1} Nat M (AddMonoid.toNSMul.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Group.ModEq.3041720194._hygCtx._hyg.3))) m p) a) (HAdd.hAdd.{u_1, u_1, u_1} M M M (instHAdd.{u_1} M (AddCommMagma.toAdd.{u_1} M (AddCommSemigroup.toAddCommMagma.{u_1} M (AddCommMonoid.toAddCommSemigroup.{u_1} M inst._@.Mathlib.Algebra.Group.ModEq.3041720194._hygCtx._hyg.3)))) (HSMul.hSMul.{0, u_1, u_1} Nat M M (instHSMul.{0, u_1} Nat M (AddMonoid.toNSMul.{u_1} M (AddCommMonoid.toAddMonoid.{u_1} M inst._@.Mathlib.Algebra.Group.ModEq.3041720194._hygCtx._hyg.3))) n p) b))))","typeFull":"∀ {M : Type u_1} [inst : AddCommMonoid M] {a b p : M}, (a ≡ b [PMOD p]) = ∃ m n, m • p + a = n • p + b","typeReadable":"∀ {M : Type u_1} [inst : AddCommMonoid M] {a b p : M}, (a ≡ b [PMOD p]) = ∃ m n, m • p + a = n • p + b","typeReferences":[["Exists"],["instHAdd"],["AddCommMonoid","toAddMonoid"],["AddCommGroup","ModEq"],["HAdd","hAdd"],["AddCommMonoid"],["Nat"],["AddCommMonoid","toAddCommSemigroup"],["AddMonoid","toNSMul"],["HSMul","hSMul"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"]],"valueReferences":[["Exists"],["instHAdd"],["AddCommMonoid","toAddMonoid"],["AddCommGroup","ModEq"],["HAdd","hAdd"],["Nat"],["AddCommMonoid","toAddCommSemigroup"],["AddMonoid","toNSMul"],["HSMul","hSMul"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Eq"],["propext"],["AddCommGroup","modEq_iff_nsmul"]]},{"isProp":true,"kind":"theorem","name":["AddCommGroup","div_modEq_div","_simp_1"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3 : DivisionSemiring.{u_1} K] {a : K} {b : K} {c : K} {p : K}, (Ne.{succ u_1} K c (OfNat.ofNat.{u_1} K 0 (Zero.toOfNat0.{u_1} K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))))))) -> (Eq.{1} Prop (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) p (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) a c) (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) b c)) (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.2036670839._hygCtx._hyg.3)))))) p c) a b))","typeFull":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a / c ≡ b / c [PMOD p]) = (a ≡ b [PMOD p * c])","typeReadable":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a / c ≡ b / c [PMOD p]) = (a ≡ b [PMOD p * c])","typeReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["DivisionSemiring"],["OfNat","ofNat"],["AddCommGroup","ModEq"],["HDiv","hDiv"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["Ne"],["Zero","toOfNat0"],["Eq"]],"valueReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["Distrib","toMul"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["HMul","hMul"],["DivisionSemiring","toSemiring"],["DivisionSemiring","toGroupWithZero"],["instHDiv"],["AddCommGroup","div_modEq_div"],["DivInvMonoid","toDiv"],["AddCommGroup","ModEq"],["HDiv","hDiv"],["Semiring","toNonAssocSemiring"],["instHMul"],["propext"]]},{"isProp":true,"kind":"theorem","name":["AddCommGroup","mul_modEq_mul_right"],"typeFallback":"forall {K : Type.{u_1}} [inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3 : DivisionSemiring.{u_1} K] {a : K} {b : K} {c : K} {p : K}, (Ne.{succ u_1} K c (OfNat.ofNat.{u_1} K 0 (Zero.toOfNat0.{u_1} K (MulZeroClass.toZero.{u_1} K (NonUnitalNonAssocSemiring.toMulZeroClass.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))))))) -> (Iff (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))) p (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))))) a c) (HMul.hMul.{u_1, u_1, u_1} K K K (instHMul.{u_1} K (Distrib.toMul.{u_1} K (NonUnitalNonAssocSemiring.toDistrib.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))))) b c)) (AddCommGroup.ModEq.{u_1} K (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_1} K (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_1} K (Semiring.toNonAssocSemiring.{u_1} K (DivisionSemiring.toSemiring.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))) (HDiv.hDiv.{u_1, u_1, u_1} K K K (instHDiv.{u_1} K (DivInvMonoid.toDiv.{u_1} K (GroupWithZero.toDivInvMonoid.{u_1} K (DivisionSemiring.toGroupWithZero.{u_1} K inst._@.Mathlib.Algebra.Field.ModEq.1282437814._hygCtx._hyg.3)))) p c) a b))","typeFull":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a * c ≡ b * c [PMOD p] ↔ a ≡ b [PMOD p / c])","typeReadable":"∀ {K : Type u_1} [inst : DivisionSemiring K] {a b c p : K}, c ≠ 0 → (a * c ≡ b * c [PMOD p] ↔ a ≡ b [PMOD p / c])","typeReferences":[["NonUnitalNonAssocSemiring","toDistrib"],["GroupWithZero","toDivInvMonoid"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["HMul","hMul"],["DivisionSemiring","toGroupWithZero"],["DivisionSemiring","toSemiring"],["instHDiv"],["DivInvMonoid","toDiv"],["DivisionSemiring"],["OfNat","ofNat"],["HDiv","hDiv"],["AddCommGroup","ModEq"],["Semiring","toNonAssocSemiring"],["MulZeroClass","toZero"],["Iff"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["Ne"],["Zero","toOfNat0"]],"valueReferences":[["div_eq_mul_inv"],["MulOneClass","toMulOne"],["DivInvMonoid","toInv"],["GroupWithZero","toDivInvMonoid"],["HMul","hMul"],["instHDiv"],["congrArg"],["HDiv","hDiv"],["AddCommGroup","ModEq"],["div_inv_eq_mul"],["DivisionMonoid","toDivInvMonoid"],["MulOne","toMul"],["Semiring","toNonAssocSemiring"],["Monoid","toMulOneClass"],["Eq","symm"],["Eq"],["inv_ne_zero"],["propext"],["Inv","inv"],["InvOneClass","toInv"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Iff","rfl"],["DivisionSemiring","toSemiring"],["DivisionSemiring","toGroupWithZero"],["AddCommGroup","div_modEq_div"],["DivInvMonoid","toDiv"],["DivInvOneMonoid","toInvOneClass"],["DivInvMonoid","toMonoid"],["Iff"],["id"],["instHMul"],["Eq","mpr"],["DivisionMonoid","toDivInvOneMonoid"],["GroupWithZero","toDivisionMonoid"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.FreeMonoid.Symbols.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["FreeAddMonoid","symbols_of"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1920368186._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {m : α}, Eq.{succ u_1} (Finset.{u_1} α) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1920368186._hygCtx._hyg.3 (FreeAddMonoid.of.{u_1} α m)) (Singleton.singleton.{u_1, u_1} α (Finset.{u_1} α) (Finset.instSingleton.{u_1} α) m)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α}, (FreeAddMonoid.of m).symbols = {m}","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α}, (FreeAddMonoid.of m).symbols = {m}","typeReferences":[["Finset","instSingleton"],["Finset"],["Singleton","singleton"],["DecidableEq"],["FreeAddMonoid","symbols"],["Eq"],["FreeAddMonoid","of"]],"valueReferences":[["rfl"],["Finset"],["FreeAddMonoid","symbols"],["FreeAddMonoid","of"]]},{"isProp":true,"kind":"theorem","name":["FreeMonoid","symbols_one"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1717014673._hygCtx._hyg.3 : DecidableEq.{succ u_1} α], Eq.{succ u_1} (Finset.{u_1} α) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1717014673._hygCtx._hyg.3 (OfNat.ofNat.{u_1} (FreeMonoid.{u_1} α) 1 (One.toOfNat1.{u_1} (FreeMonoid.{u_1} α) (MulOne.toOne.{u_1} (FreeMonoid.{u_1} α) (MulOneClass.toMulOne.{u_1} (FreeMonoid.{u_1} α) (Monoid.toMulOneClass.{u_1} (FreeMonoid.{u_1} α) (RightCancelMonoid.toMonoid.{u_1} (FreeMonoid.{u_1} α) (CancelMonoid.toRightCancelMonoid.{u_1} (FreeMonoid.{u_1} α) (FreeMonoid.instCancelMonoid.{u_1} α))))))))) (EmptyCollection.emptyCollection.{u_1} (Finset.{u_1} α) (Finset.instEmptyCollection.{u_1} α))","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α], FreeMonoid.symbols 1 = ∅","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α], FreeMonoid.symbols 1 = ∅","typeReferences":[["MulOneClass","toMulOne"],["RightCancelMonoid","toMonoid"],["FreeMonoid","symbols"],["Finset"],["MulOne","toOne"],["DecidableEq"],["Finset","instEmptyCollection"],["EmptyCollection","emptyCollection"],["OfNat","ofNat"],["CancelMonoid","toRightCancelMonoid"],["FreeMonoid"],["One","toOfNat1"],["Monoid","toMulOneClass"],["FreeMonoid","instCancelMonoid"],["Eq"]],"valueReferences":[["MulOneClass","toMulOne"],["rfl"],["RightCancelMonoid","toMonoid"],["FreeMonoid"],["FreeMonoid","symbols"],["Finset"],["MulOne","toOne"],["One","toOfNat1"],["Monoid","toMulOneClass"],["FreeMonoid","instCancelMonoid"],["CancelMonoid","toRightCancelMonoid"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["FreeMonoid","symbols_mul"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {a : FreeMonoid.{u_1} α} {b : FreeMonoid.{u_1} α}, Eq.{succ u_1} (Finset.{u_1} α) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 (HMul.hMul.{u_1, u_1, u_1} (FreeMonoid.{u_1} α) (FreeMonoid.{u_1} α) (FreeMonoid.{u_1} α) (instHMul.{u_1} (FreeMonoid.{u_1} α) (MulOne.toMul.{u_1} (FreeMonoid.{u_1} α) (MulOneClass.toMulOne.{u_1} (FreeMonoid.{u_1} α) (Monoid.toMulOneClass.{u_1} (FreeMonoid.{u_1} α) (RightCancelMonoid.toMonoid.{u_1} (FreeMonoid.{u_1} α) (CancelMonoid.toRightCancelMonoid.{u_1} (FreeMonoid.{u_1} α) (FreeMonoid.instCancelMonoid.{u_1} α))))))) a b)) (Union.union.{u_1} (Finset.{u_1} α) (Finset.instUnion.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 a) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 b))","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {a b : FreeMonoid α}, (a * b).symbols = a.symbols ∪ b.symbols","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {a b : FreeMonoid α}, (a * b).symbols = a.symbols ∪ b.symbols","typeReferences":[["MulOneClass","toMulOne"],["RightCancelMonoid","toMonoid"],["FreeMonoid","symbols"],["Finset"],["DecidableEq"],["HMul","hMul"],["Union","union"],["Finset","instUnion"],["CancelMonoid","toRightCancelMonoid"],["FreeMonoid"],["MulOne","toMul"],["Monoid","toMulOneClass"],["FreeMonoid","instCancelMonoid"],["instHMul"],["Eq"]],"valueReferences":[["FreeMonoid"],["Equiv","instEquivLike"],["List","toFinset_append"],["EquivLike","toFunLike"],["FreeMonoid","toList"],["List"],["DFunLike","coe"],["Equiv"]]},{"isProp":true,"kind":"theorem","name":["FreeAddMonoid","symbols_add"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {a : FreeAddMonoid.{u_1} α} {b : FreeAddMonoid.{u_1} α}, Eq.{succ u_1} (Finset.{u_1} α) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 (HAdd.hAdd.{u_1, u_1, u_1} (FreeAddMonoid.{u_1} α) (FreeAddMonoid.{u_1} α) (FreeAddMonoid.{u_1} α) (instHAdd.{u_1} (FreeAddMonoid.{u_1} α) (AddZero.toAdd.{u_1} (FreeAddMonoid.{u_1} α) (AddZeroClass.toAddZero.{u_1} (FreeAddMonoid.{u_1} α) (AddMonoid.toAddZeroClass.{u_1} (FreeAddMonoid.{u_1} α) (AddRightCancelMonoid.toAddMonoid.{u_1} (FreeAddMonoid.{u_1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u_1} (FreeAddMonoid.{u_1} α) (FreeAddMonoid.instAddCancelMonoid.{u_1} α))))))) a b)) (Union.union.{u_1} (Finset.{u_1} α) (Finset.instUnion.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 a) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.531716370._hygCtx._hyg.3 b))","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {a b : FreeAddMonoid α}, (a + b).symbols = a.symbols ∪ b.symbols","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {a b : FreeAddMonoid α}, (a + b).symbols = a.symbols ∪ b.symbols","typeReferences":[["Finset"],["FreeAddMonoid","instAddCancelMonoid"],["instHAdd"],["DecidableEq"],["AddCancelMonoid","toAddRightCancelMonoid"],["Union","union"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["Finset","instUnion"],["FreeAddMonoid"],["HAdd","hAdd"],["FreeAddMonoid","symbols"],["Eq"],["AddRightCancelMonoid","toAddMonoid"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["FreeAddMonoid"],["Equiv","instEquivLike"],["List","toFinset_append"],["EquivLike","toFunLike"],["FreeAddMonoid","toList"],["List"],["DFunLike","coe"],["Equiv"]]},{"isProp":true,"kind":"theorem","name":["FreeMonoid","mem_symbols","_simp_2"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {m : α} {a : FreeMonoid.{u_1} α}, Eq.{1} Prop (Membership.mem.{u_1, u_1} α (Finset.{u_1} α) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} α) α (Finset.instSetLike.{u_1} α)) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 a) m) (Membership.mem.{u_1, u_1} α (FreeMonoid.{u_1} α) (FreeMonoid.instMembership.{u_1} α) a m)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeMonoid α}, (m ∈ a.symbols) = (m ∈ a)","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeMonoid α}, (m ∈ a.symbols) = (m ∈ a)","typeReferences":[["Finset","instSetLike"],["FreeMonoid"],["FreeMonoid","symbols"],["SetLike","instMembership"],["Finset"],["DecidableEq"],["Membership","mem"],["Eq"],["FreeMonoid","instMembership"]],"valueReferences":[["FreeMonoid"],["Finset","instSetLike"],["FreeMonoid","symbols"],["SetLike","instMembership"],["Finset"],["Membership","mem"],["FreeMonoid","instMembership"],["FreeMonoid","mem_symbols"],["propext"]]},{"isProp":true,"kind":"theorem","name":["FreeMonoid","symbols_of"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1920368186._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {m : α}, Eq.{succ u_1} (Finset.{u_1} α) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1920368186._hygCtx._hyg.3 (FreeMonoid.of.{u_1} α m)) (Singleton.singleton.{u_1, u_1} α (Finset.{u_1} α) (Finset.instSingleton.{u_1} α) m)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α}, (FreeMonoid.of m).symbols = {m}","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α}, (FreeMonoid.of m).symbols = {m}","typeReferences":[["FreeMonoid","of"],["FreeMonoid","symbols"],["Finset","instSingleton"],["Finset"],["Singleton","singleton"],["DecidableEq"],["Eq"]],"valueReferences":[["rfl"],["FreeMonoid","of"],["FreeMonoid","symbols"],["Finset"]]},{"isProp":false,"kind":"definition","name":["FreeMonoid","symbols"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 : DecidableEq.{succ u_1} α], (FreeMonoid.{u_1} α) -> (Finset.{u_1} α)","typeFull":"{α : Type u_1} → [DecidableEq α] → FreeMonoid α → Finset α","typeReadable":"{α : Type u_1} → [DecidableEq α] → FreeMonoid α → Finset α","typeReferences":[["FreeMonoid"],["Finset"],["DecidableEq"]],"valueReferences":[["List","toFinset"]]},{"isProp":true,"kind":"theorem","name":["FreeMonoid","mem_symbols"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {m : α} {a : FreeMonoid.{u_1} α}, Iff (Membership.mem.{u_1, u_1} α (Finset.{u_1} α) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} α) α (Finset.instSetLike.{u_1} α)) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 a) m) (Membership.mem.{u_1, u_1} α (FreeMonoid.{u_1} α) (FreeMonoid.instMembership.{u_1} α) a m)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeMonoid α}, m ∈ a.symbols ↔ m ∈ a","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeMonoid α}, m ∈ a.symbols ↔ m ∈ a","typeReferences":[["Finset","instSetLike"],["FreeMonoid"],["FreeMonoid","symbols"],["SetLike","instMembership"],["Finset"],["Iff"],["DecidableEq"],["Membership","mem"],["FreeMonoid","instMembership"]],"valueReferences":[["List","mem_toFinset"]]},{"isProp":true,"kind":"theorem","name":["FreeAddMonoid","symbols","eq_1"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] (a : FreeAddMonoid.{u_1} α), Eq.{succ u_1} (Finset.{u_1} α) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 a) (List.toFinset.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 a)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] (a : FreeAddMonoid α), a.symbols = List.toFinset a","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] (a : FreeAddMonoid α), a.symbols = List.toFinset a","typeReferences":[["FreeAddMonoid"],["List","toFinset"],["Finset"],["DecidableEq"],["FreeAddMonoid","symbols"],["Eq"]],"valueReferences":[["Finset"],["Eq","refl"],["FreeAddMonoid","symbols"]]},{"isProp":true,"kind":"theorem","name":["FreeAddMonoid","mem_symbols"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {m : α} {a : FreeAddMonoid.{u_1} α}, Iff (Membership.mem.{u_1, u_1} α (Finset.{u_1} α) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} α) α (Finset.instSetLike.{u_1} α)) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 a) m) (Membership.mem.{u_1, u_1} α (FreeAddMonoid.{u_1} α) (FreeAddMonoid.instMembership.{u_1} α) a m)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeAddMonoid α}, m ∈ a.symbols ↔ m ∈ a","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeAddMonoid α}, m ∈ a.symbols ↔ m ∈ a","typeReferences":[["FreeAddMonoid"],["Finset","instSetLike"],["SetLike","instMembership"],["Finset"],["FreeAddMonoid","instMembership"],["Iff"],["DecidableEq"],["Membership","mem"],["FreeAddMonoid","symbols"]],"valueReferences":[["List","mem_toFinset"]]},{"isProp":true,"kind":"theorem","name":["FreeMonoid","symbols","eq_1"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] (a : FreeMonoid.{u_1} α), Eq.{succ u_1} (Finset.{u_1} α) (FreeMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 a) (List.toFinset.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 a)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] (a : FreeMonoid α), a.symbols = List.toFinset a","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] (a : FreeMonoid α), a.symbols = List.toFinset a","typeReferences":[["FreeMonoid"],["List","toFinset"],["FreeMonoid","symbols"],["Finset"],["DecidableEq"],["Eq"]],"valueReferences":[["FreeMonoid","symbols"],["Finset"],["Eq","refl"]]},{"isProp":false,"kind":"definition","name":["FreeAddMonoid","symbols"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.739869967._hygCtx._hyg.3 : DecidableEq.{succ u_1} α], (FreeAddMonoid.{u_1} α) -> (Finset.{u_1} α)","typeFull":"{α : Type u_1} → [DecidableEq α] → FreeAddMonoid α → Finset α","typeReadable":"{α : Type u_1} → [DecidableEq α] → FreeAddMonoid α → Finset α","typeReferences":[["FreeAddMonoid"],["Finset"],["DecidableEq"]],"valueReferences":[["List","toFinset"]]},{"isProp":true,"kind":"theorem","name":["FreeAddMonoid","symbols_zero"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1717014673._hygCtx._hyg.3 : DecidableEq.{succ u_1} α], Eq.{succ u_1} (Finset.{u_1} α) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.1717014673._hygCtx._hyg.3 (OfNat.ofNat.{u_1} (FreeAddMonoid.{u_1} α) 0 (Zero.toOfNat0.{u_1} (FreeAddMonoid.{u_1} α) (AddZero.toZero.{u_1} (FreeAddMonoid.{u_1} α) (AddZeroClass.toAddZero.{u_1} (FreeAddMonoid.{u_1} α) (AddMonoid.toAddZeroClass.{u_1} (FreeAddMonoid.{u_1} α) (AddRightCancelMonoid.toAddMonoid.{u_1} (FreeAddMonoid.{u_1} α) (AddCancelMonoid.toAddRightCancelMonoid.{u_1} (FreeAddMonoid.{u_1} α) (FreeAddMonoid.instAddCancelMonoid.{u_1} α))))))))) (EmptyCollection.emptyCollection.{u_1} (Finset.{u_1} α) (Finset.instEmptyCollection.{u_1} α))","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α], FreeAddMonoid.symbols 0 = ∅","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α], FreeAddMonoid.symbols 0 = ∅","typeReferences":[["Finset"],["FreeAddMonoid","instAddCancelMonoid"],["DecidableEq"],["Finset","instEmptyCollection"],["AddCancelMonoid","toAddRightCancelMonoid"],["EmptyCollection","emptyCollection"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["FreeAddMonoid"],["FreeAddMonoid","symbols"],["Zero","toOfNat0"],["Eq"],["AddRightCancelMonoid","toAddMonoid"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["FreeAddMonoid"],["rfl"],["FreeAddMonoid","instAddCancelMonoid"],["Finset"],["Zero","toOfNat0"],["FreeAddMonoid","symbols"],["AddCancelMonoid","toAddRightCancelMonoid"],["AddRightCancelMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["OfNat","ofNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["FreeAddMonoid","mem_symbols","_simp_1"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 : DecidableEq.{succ u_1} α] {m : α} {a : FreeAddMonoid.{u_1} α}, Eq.{1} Prop (Membership.mem.{u_1, u_1} α (Finset.{u_1} α) (SetLike.instMembership.{u_1, u_1} (Finset.{u_1} α) α (Finset.instSetLike.{u_1} α)) (FreeAddMonoid.symbols.{u_1} α inst._@.Mathlib.Algebra.FreeMonoid.Symbols.2249724858._hygCtx._hyg.3 a) m) (Membership.mem.{u_1, u_1} α (FreeAddMonoid.{u_1} α) (FreeAddMonoid.instMembership.{u_1} α) a m)","typeFull":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeAddMonoid α}, (m ∈ a.symbols) = (m ∈ a)","typeReadable":"∀ {α : Type u_1} [inst : DecidableEq α] {m : α} {a : FreeAddMonoid α}, (m ∈ a.symbols) = (m ∈ a)","typeReferences":[["FreeAddMonoid"],["Finset","instSetLike"],["SetLike","instMembership"],["Finset"],["FreeAddMonoid","instMembership"],["DecidableEq"],["Membership","mem"],["FreeAddMonoid","symbols"],["Eq"]],"valueReferences":[["FreeAddMonoid"],["FreeAddMonoid","mem_symbols"],["Finset","instSetLike"],["SetLike","instMembership"],["Finset"],["FreeAddMonoid","instMembership"],["Membership","mem"],["FreeAddMonoid","symbols"],["propext"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Action.Option.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Option","instMulAction","_proof_1"],"typeFallback":"forall {M : Type.{u_2}} {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5 : Monoid.{u_2} M] [inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.8 : MulAction.{u_2, u_1} M α inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5] (a₁ : M) (a₂ : M) (b : Option.{u_1} α), Eq.{succ u_1} (Option.{u_1} α) (HSMul.hSMul.{u_2, u_1, u_1} M (Option.{u_1} α) (Option.{u_1} α) (instHSMul.{u_2, u_1} M (Option.{u_1} α) (Option.instSMul_mathlib.{u_2, u_1} M α (SemigroupAction.toSMul.{u_2, u_1} M α (Monoid.toSemigroup.{u_2} M inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5) (MulAction.toSemigroupAction.{u_2, u_1} M α inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.8)))) (HMul.hMul.{u_2, u_2, u_2} M M M (instHMul.{u_2} M (Semigroup.toMul.{u_2} M (Monoid.toSemigroup.{u_2} M inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5))) a₁ a₂) b) (HSMul.hSMul.{u_2, u_1, u_1} M (Option.{u_1} α) (Option.{u_1} α) (instHSMul.{u_2, u_1} M (Option.{u_1} α) (Option.instSMul_mathlib.{u_2, u_1} M α (SemigroupAction.toSMul.{u_2, u_1} M α (Monoid.toSemigroup.{u_2} M inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5) (MulAction.toSemigroupAction.{u_2, u_1} M α inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.8)))) a₁ (HSMul.hSMul.{u_2, u_1, u_1} M (Option.{u_1} α) (Option.{u_1} α) (instHSMul.{u_2, u_1} M (Option.{u_1} α) (Option.instSMul_mathlib.{u_2, u_1} M α (SemigroupAction.toSMul.{u_2, u_1} M α (Monoid.toSemigroup.{u_2} M inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5) (MulAction.toSemigroupAction.{u_2, u_1} M α inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.8)))) a₂ b))","typeFull":"∀ {M : Type u_2} {α : Type u_1} [inst : Monoid M] [inst_1 : MulAction M α] (a₁ a₂ : M) (b : Option α),\n  (a₁ * a₂) • b = a₁ • a₂ • b","typeReadable":"∀ {M : Type u_2} {α : Type u_1} [inst : Monoid M] [inst_1 : MulAction M α] (a₁ a₂ : M) (b : Option α),\n  (a₁ * a₂) • b = a₁ • a₂ • b","typeReferences":[["SemigroupAction","toSMul"],["HMul","hMul"],["Option","instSMul_mathlib"],["Semigroup","toMul"],["MulAction"],["Option"],["HSMul","hSMul"],["Monoid"],["instHSMul"],["instHMul"],["Monoid","toSemigroup"],["Eq"],["MulAction","toSemigroupAction"]],"valueReferences":[["rfl"],["congr_arg"],["SemigroupAction","toSMul"],["HMul","hMul"],["Option","some"],["Option","instSMul_mathlib"],["Semigroup","toMul"],["Option","casesOn"],["Option","none"],["Eq","refl"],["Option"],["HSMul","hSMul"],["Eq","symm"],["instHSMul"],["instHMul"],["Monoid","toSemigroup"],["Eq"],["Eq","ndrec"],["MulAction","toSemigroupAction"],["SemigroupAction","mul_smul"]]},{"isProp":true,"kind":"theorem","name":["Option","vadd_none"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2548798951._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α] (a : M), Eq.{succ u_3} (Option.{u_3} α) (HVAdd.hVAdd.{u_1, u_3, u_3} M (Option.{u_3} α) (Option.{u_3} α) (instHVAdd.{u_1, u_3} M (Option.{u_3} α) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2548798951._hygCtx._hyg.5)) a (Option.none.{u_3} α)) (Option.none.{u_3} α)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] (a : M), a +ᵥ none = none","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] (a : M), a +ᵥ none = none","typeReferences":[["VAdd"],["Option","none"],["instHVAdd"],["Option"],["Eq"],["Option","VAdd"],["HVAdd","hVAdd"]],"valueReferences":[["rfl"],["Option","none"],["instHVAdd"],["Option"],["Option","VAdd"],["HVAdd","hVAdd"]]},{"isProp":true,"kind":"theorem","name":["Option","instVAddAssocClassOfVAdd"],"typeFallback":"forall {M : Type.{u_1}} {N : Type.{u_2}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.9 : VAdd.{u_2, u_3} N α] [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.17 : VAdd.{u_1, u_2} M N] [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.21 : VAddAssocClass.{u_1, u_2, u_3} M N α inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.5], VAddAssocClass.{u_1, u_2, u_3} M N (Option.{u_3} α) inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.17 (Option.VAdd.{u_2, u_3} N α inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.9) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.5)","typeFull":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : VAdd M α] [inst_1 : VAdd N α] [inst_2 : VAdd M N]\n  [VAddAssocClass M N α], VAddAssocClass M N (Option α)","typeReadable":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : VAdd M α] [inst_1 : VAdd N α] [inst_2 : VAdd M N]\n  [VAddAssocClass M N α], VAddAssocClass M N (Option α)","typeReferences":[["VAdd"],["Option"],["Option","VAdd"],["VAddAssocClass"]],"valueReferences":[["rfl"],["instHVAdd"],["congr_arg"],["vadd_assoc"],["Option","some"],["Option","VAdd"],["HVAdd","hVAdd"],["Option","casesOn"],["Option","none"],["Eq","refl"],["Option"],["Eq","symm"],["Eq"],["Eq","ndrec"],["VAddAssocClass","mk"]]},{"isProp":false,"kind":"definition","name":["Option","VAdd"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α], VAdd.{u_1, u_3} M (Option.{u_3} α)","typeFull":"{M : Type u_1} → {α : Type u_3} → [VAdd M α] → VAdd M (Option α)","typeReadable":"{M : Type u_1} → {α : Type u_3} → [VAdd M α] → VAdd M (Option α)","typeReferences":[["VAdd"],["Option"]],"valueReferences":[["instHVAdd"],["Option"],["Option","map"],["HVAdd","hVAdd"],["VAdd","mk"]]},{"isProp":true,"kind":"theorem","name":["Option","smul_none"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2548798951._hygCtx._hyg.5 : SMul.{u_1, u_3} M α] (a : M), Eq.{succ u_3} (Option.{u_3} α) (HSMul.hSMul.{u_1, u_3, u_3} M (Option.{u_3} α) (Option.{u_3} α) (instHSMul.{u_1, u_3} M (Option.{u_3} α) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2548798951._hygCtx._hyg.5)) a (Option.none.{u_3} α)) (Option.none.{u_3} α)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] (a : M), a • none = none","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] (a : M), a • none = none","typeReferences":[["SMul"],["Option","none"],["Option"],["HSMul","hSMul"],["instHSMul"],["Eq"],["Option","instSMul_mathlib"]],"valueReferences":[["rfl"],["Option","none"],["Option"],["HSMul","hSMul"],["instHSMul"],["Option","instSMul_mathlib"]]},{"isProp":true,"kind":"theorem","name":["Option","vadd_some"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2490492355._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α] (a : M) (b : α), Eq.{succ u_3} (Option.{u_3} α) (HVAdd.hVAdd.{u_1, u_3, u_3} M (Option.{u_3} α) (Option.{u_3} α) (instHVAdd.{u_1, u_3} M (Option.{u_3} α) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2490492355._hygCtx._hyg.5)) a (Option.some.{u_3} α b)) (Option.some.{u_3} α (HVAdd.hVAdd.{u_1, u_3, u_3} M α α (instHVAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2490492355._hygCtx._hyg.5) a b))","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] (a : M) (b : α), a +ᵥ some b = some (a +ᵥ b)","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] (a : M) (b : α), a +ᵥ some b = some (a +ᵥ b)","typeReferences":[["VAdd"],["instHVAdd"],["Option"],["Option","some"],["Eq"],["Option","VAdd"],["HVAdd","hVAdd"]],"valueReferences":[["rfl"],["instHVAdd"],["Option"],["Option","some"],["Option","VAdd"],["HVAdd","hVAdd"]]},{"isProp":true,"kind":"theorem","name":["Option","VAdd","eq_1"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α], Eq.{max (succ u_1) (succ u_3)} (VAdd.{u_1, u_3} M (Option.{u_3} α)) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5) (VAdd.mk.{u_1, u_3} M (Option.{u_3} α) (fun (a : M) => Option.map.{u_3, u_3} α α (fun (x._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.33 : α) => HVAdd.hVAdd.{u_1, u_3, u_3} M α α (instHVAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5) a x._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.33)))","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α], Option.VAdd = { vadd := fun a => Option.map fun x => a +ᵥ x }","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α], Option.VAdd = { vadd := fun a => Option.map fun x => a +ᵥ x }","typeReferences":[["VAdd"],["instHVAdd"],["Option"],["Option","map"],["Eq"],["HVAdd","hVAdd"],["Option","VAdd"],["VAdd","mk"]],"valueReferences":[["VAdd"],["Option"],["Eq","refl"],["Option","VAdd"]]},{"isProp":true,"kind":"theorem","name":["Option","instSMul_mathlib","eq_1"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5 : SMul.{u_1, u_3} M α], Eq.{max (succ u_1) (succ u_3)} (SMul.{u_1, u_3} M (Option.{u_3} α)) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5) (SMul.mk.{u_1, u_3} M (Option.{u_3} α) (fun (a : M) => Option.map.{u_3, u_3} α α (fun (x._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.33 : α) => HSMul.hSMul.{u_1, u_3, u_3} M α α (instHSMul.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5) a x._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.33)))","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α],\n  Option.instSMul_mathlib = { smul := fun a => Option.map fun x => a • x }","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α],\n  Option.instSMul_mathlib = { smul := fun a => Option.map fun x => a • x }","typeReferences":[["SMul","mk"],["SMul"],["Option"],["HSMul","hSMul"],["instHSMul"],["Option","map"],["Eq"],["Option","instSMul_mathlib"]],"valueReferences":[["SMul"],["Option"],["Eq","refl"],["Option","instSMul_mathlib"]]},{"isProp":true,"kind":"theorem","name":["Option","instMulAction","_proof_2"],"typeFallback":"forall {M : Type.{u_2}} {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5 : Monoid.{u_2} M] [inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.8 : MulAction.{u_2, u_1} M α inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5] (b : Option.{u_1} α), Eq.{succ u_1} (Option.{u_1} α) (HSMul.hSMul.{u_2, u_1, u_1} M (Option.{u_1} α) (Option.{u_1} α) (instHSMul.{u_2, u_1} M (Option.{u_1} α) (Option.instSMul_mathlib.{u_2, u_1} M α (SemigroupAction.toSMul.{u_2, u_1} M α (Monoid.toSemigroup.{u_2} M inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5) (MulAction.toSemigroupAction.{u_2, u_1} M α inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.8)))) (OfNat.ofNat.{u_2} M 1 (One.toOfNat1.{u_2} M (MulOne.toOne.{u_2} M (MulOneClass.toMulOne.{u_2} M (Monoid.toMulOneClass.{u_2} M inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5))))) b) b","typeFull":"∀ {M : Type u_2} {α : Type u_1} [inst : Monoid M] [inst_1 : MulAction M α] (b : Option α), 1 • b = b","typeReadable":"∀ {M : Type u_2} {α : Type u_1} [inst : Monoid M] [inst_1 : MulAction M α] (b : Option α), 1 • b = b","typeReferences":[["MulOneClass","toMulOne"],["MulOne","toOne"],["SemigroupAction","toSMul"],["OfNat","ofNat"],["Option","instSMul_mathlib"],["MulAction"],["One","toOfNat1"],["Option"],["Monoid","toMulOneClass"],["HSMul","hSMul"],["Monoid"],["instHSMul"],["Monoid","toSemigroup"],["Eq"],["MulAction","toSemigroupAction"]],"valueReferences":[["rfl"],["MulOneClass","toMulOne"],["MulOne","toOne"],["congr_arg"],["SemigroupAction","toSMul"],["Option","some"],["OfNat","ofNat"],["Option","instSMul_mathlib"],["Option","casesOn"],["Option","none"],["One","toOfNat1"],["Eq","refl"],["Option"],["one_smul"],["Monoid","toMulOneClass"],["HSMul","hSMul"],["Eq","symm"],["instHSMul"],["Monoid","toSemigroup"],["Eq","ndrec"],["Eq"],["MulAction","toSemigroupAction"]]},{"isProp":true,"kind":"theorem","name":["Option","smul_def"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.5 : SMul.{u_1, u_3} M α] (a : M) (x : Option.{u_3} α), Eq.{succ u_3} (Option.{u_3} α) (HSMul.hSMul.{u_1, u_3, u_3} M (Option.{u_3} α) (Option.{u_3} α) (instHSMul.{u_1, u_3} M (Option.{u_3} α) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.5)) a x) (Option.map.{u_3, u_3} α α (fun (x._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.26 : α) => HSMul.hSMul.{u_1, u_3, u_3} M α α (instHSMul.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.5) a x._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.26) x)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] (a : M) (x : Option α), a • x = Option.map (fun x => a • x) x","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] (a : M) (x : Option α), a • x = Option.map (fun x => a • x) x","typeReferences":[["SMul"],["Option"],["HSMul","hSMul"],["instHSMul"],["Option","map"],["Eq"],["Option","instSMul_mathlib"]],"valueReferences":[["rfl"],["Option"],["HSMul","hSMul"],["instHSMul"],["Option","instSMul_mathlib"]]},{"isProp":true,"kind":"theorem","name":["Option","instIsCentralScalar"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.5 : SMul.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.17 : SMul.{u_1, u_3} (MulOpposite.{u_1} M) α] [inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.24 : IsCentralScalar.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.17], IsCentralScalar.{u_1, u_3} M (Option.{u_3} α) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.5) (Option.instSMul_mathlib.{u_1, u_3} (MulOpposite.{u_1} M) α inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.17)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] [inst_1 : SMul Mᵐᵒᵖ α] [IsCentralScalar M α],\n  IsCentralScalar M (Option α)","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] [inst_1 : SMul Mᵐᵒᵖ α] [IsCentralScalar M α],\n  IsCentralScalar M (Option α)","typeReferences":[["MulOpposite"],["SMul"],["IsCentralScalar"],["Option"],["Option","instSMul_mathlib"]],"valueReferences":[["rfl"],["congr_arg"],["Option","some"],["Option","instSMul_mathlib"],["Option","casesOn"],["MulOpposite"],["Option","none"],["Eq","refl"],["Option"],["MulOpposite","op"],["HSMul","hSMul"],["Eq","symm"],["IsCentralScalar","mk"],["instHSMul"],["Eq"],["Eq","ndrec"],["IsCentralScalar","op_smul_eq_smul"]]},{"isProp":true,"kind":"theorem","name":["Option","instSMulCommClass"],"typeFallback":"forall {M : Type.{u_1}} {N : Type.{u_2}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.5 : SMul.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.9 : SMul.{u_2, u_3} N α] [inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.17 : SMulCommClass.{u_1, u_2, u_3} M N α inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.9], SMulCommClass.{u_1, u_2, u_3} M N (Option.{u_3} α) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.5) (Option.instSMul_mathlib.{u_2, u_3} N α inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.9)","typeFull":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : SMul M α] [inst_1 : SMul N α] [SMulCommClass M N α],\n  SMulCommClass M N (Option α)","typeReadable":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : SMul M α] [inst_1 : SMul N α] [SMulCommClass M N α],\n  SMulCommClass M N (Option α)","typeReferences":[["SMulCommClass"],["SMul"],["Option"],["Option","instSMul_mathlib"]],"valueReferences":[["SMulCommClass","mk"],["Option"],["HSMul","hSMul"],["instHSMul"],["Function","Commute","option_map"],["SMulCommClass","smul_comm"],["Option","instSMul_mathlib"]]},{"isProp":true,"kind":"theorem","name":["Option","instIsScalarTowerOfSMul"],"typeFallback":"forall {M : Type.{u_1}} {N : Type.{u_2}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.5 : SMul.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.9 : SMul.{u_2, u_3} N α] [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.17 : SMul.{u_1, u_2} M N] [inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.21 : IsScalarTower.{u_1, u_2, u_3} M N α inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.5], IsScalarTower.{u_1, u_2, u_3} M N (Option.{u_3} α) inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.17 (Option.instSMul_mathlib.{u_2, u_3} N α inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.9) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2697542075._hygCtx._hyg.5)","typeFull":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : SMul M α] [inst_1 : SMul N α] [inst_2 : SMul M N]\n  [IsScalarTower M N α], IsScalarTower M N (Option α)","typeReadable":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : SMul M α] [inst_1 : SMul N α] [inst_2 : SMul M N]\n  [IsScalarTower M N α], IsScalarTower M N (Option α)","typeReferences":[["SMul"],["IsScalarTower"],["Option"],["Option","instSMul_mathlib"]],"valueReferences":[["rfl"],["congr_arg"],["Option","some"],["IsScalarTower","mk"],["Option","instSMul_mathlib"],["Option","casesOn"],["Option","none"],["Eq","refl"],["Option"],["HSMul","hSMul"],["Eq","symm"],["smul_assoc"],["instHSMul"],["Eq"],["Eq","ndrec"]]},{"isProp":true,"kind":"theorem","name":["Option","smul_some"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2490492355._hygCtx._hyg.5 : SMul.{u_1, u_3} M α] (a : M) (b : α), Eq.{succ u_3} (Option.{u_3} α) (HSMul.hSMul.{u_1, u_3, u_3} M (Option.{u_3} α) (Option.{u_3} α) (instHSMul.{u_1, u_3} M (Option.{u_3} α) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2490492355._hygCtx._hyg.5)) a (Option.some.{u_3} α b)) (Option.some.{u_3} α (HSMul.hSMul.{u_1, u_3, u_3} M α α (instHSMul.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2490492355._hygCtx._hyg.5) a b))","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] (a : M) (b : α), a • some b = some (a • b)","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] (a : M) (b : α), a • some b = some (a • b)","typeReferences":[["SMul"],["Option"],["HSMul","hSMul"],["instHSMul"],["Option","some"],["Eq"],["Option","instSMul_mathlib"]],"valueReferences":[["rfl"],["Option"],["HSMul","hSMul"],["instHSMul"],["Option","some"],["Option","instSMul_mathlib"]]},{"isProp":true,"kind":"theorem","name":["Option","vadd_def"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α] (a : M) (x : Option.{u_3} α), Eq.{succ u_3} (Option.{u_3} α) (HVAdd.hVAdd.{u_1, u_3, u_3} M (Option.{u_3} α) (Option.{u_3} α) (instHVAdd.{u_1, u_3} M (Option.{u_3} α) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.5)) a x) (Option.map.{u_3, u_3} α α (fun (x._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.26 : α) => HVAdd.hVAdd.{u_1, u_3, u_3} M α α (instHVAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.5) a x._@.Mathlib.Algebra.Group.Action.Option.1925582909._hygCtx._hyg.26) x)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] (a : M) (x : Option α), a +ᵥ x = Option.map (fun x => a +ᵥ x) x","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] (a : M) (x : Option α), a +ᵥ x = Option.map (fun x => a +ᵥ x) x","typeReferences":[["VAdd"],["instHVAdd"],["Option"],["Option","map"],["Eq"],["Option","VAdd"],["HVAdd","hVAdd"]],"valueReferences":[["rfl"],["instHVAdd"],["Option"],["Option","VAdd"],["HVAdd","hVAdd"]]},{"isProp":true,"kind":"theorem","name":["Option","instFaithfulSMul"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.5 : SMul.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.17 : FaithfulSMul.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.5], FaithfulSMul.{u_1, u_3} M (Option.{u_3} α) (Option.instSMul_mathlib.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.5)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] [FaithfulSMul M α], FaithfulSMul M (Option α)","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : SMul M α] [FaithfulSMul M α], FaithfulSMul M (Option α)","typeReferences":[["SMul"],["Option"],["FaithfulSMul"],["Option","instSMul_mathlib"]],"valueReferences":[["Option"],["eq_of_heq"],["HSMul","hSMul"],["instHSMul"],["Option","some"],["Eq"],["FaithfulSMul","eq_of_smul_eq_smul"],["FaithfulSMul","mk"],["Option","some","noConfusion"],["Option","instSMul_mathlib"]]},{"isProp":true,"kind":"theorem","name":["Option","instIsCentralVAdd"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.17 : VAdd.{u_1, u_3} (AddOpposite.{u_1} M) α] [inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.24 : IsCentralVAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.17], IsCentralVAdd.{u_1, u_3} M (Option.{u_3} α) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.5) (Option.VAdd.{u_1, u_3} (AddOpposite.{u_1} M) α inst._@.Mathlib.Algebra.Group.Action.Option.1836316326._hygCtx._hyg.17)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] [inst_1 : VAdd Mᵃᵒᵖ α] [IsCentralVAdd M α], IsCentralVAdd M (Option α)","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] [inst_1 : VAdd Mᵃᵒᵖ α] [IsCentralVAdd M α], IsCentralVAdd M (Option α)","typeReferences":[["VAdd"],["AddOpposite"],["Option"],["IsCentralVAdd"],["Option","VAdd"]],"valueReferences":[["rfl"],["instHVAdd"],["AddOpposite"],["congr_arg"],["Option","some"],["Option","VAdd"],["HVAdd","hVAdd"],["Option","casesOn"],["IsCentralVAdd","op_vadd_eq_vadd"],["IsCentralVAdd","mk"],["Option","none"],["Eq","refl"],["Option"],["Eq","symm"],["Eq"],["AddOpposite","op"],["Eq","ndrec"]]},{"isProp":true,"kind":"theorem","name":["Option","instVAddCommClass"],"typeFallback":"forall {M : Type.{u_1}} {N : Type.{u_2}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.9 : VAdd.{u_2, u_3} N α] [inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.17 : VAddCommClass.{u_1, u_2, u_3} M N α inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.9], VAddCommClass.{u_1, u_2, u_3} M N (Option.{u_3} α) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.5) (Option.VAdd.{u_2, u_3} N α inst._@.Mathlib.Algebra.Group.Action.Option.1193137464._hygCtx._hyg.9)","typeFull":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : VAdd M α] [inst_1 : VAdd N α] [VAddCommClass M N α],\n  VAddCommClass M N (Option α)","typeReadable":"∀ {M : Type u_1} {N : Type u_2} {α : Type u_3} [inst : VAdd M α] [inst_1 : VAdd N α] [VAddCommClass M N α],\n  VAddCommClass M N (Option α)","typeReferences":[["VAddCommClass"],["VAdd"],["Option"],["Option","VAdd"]],"valueReferences":[["instHVAdd"],["Option"],["VAddCommClass","mk"],["Function","Commute","option_map"],["HVAdd","hVAdd"],["Option","VAdd"],["VAddCommClass","vadd_comm"]]},{"isProp":false,"kind":"definition","name":["Option","instSMul_mathlib"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.3634251640._hygCtx._hyg.5 : SMul.{u_1, u_3} M α], SMul.{u_1, u_3} M (Option.{u_3} α)","typeFull":"{M : Type u_1} → {α : Type u_3} → [SMul M α] → SMul M (Option α)","typeReadable":"{M : Type u_1} → {α : Type u_3} → [SMul M α] → SMul M (Option α)","typeReferences":[["SMul"],["Option"]],"valueReferences":[["SMul","mk"],["Option"],["HSMul","hSMul"],["instHSMul"],["Option","map"]]},{"isProp":true,"kind":"theorem","name":["Option","instFaithfulVAdd"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.5 : VAdd.{u_1, u_3} M α] [inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.17 : FaithfulVAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.5], FaithfulVAdd.{u_1, u_3} M (Option.{u_3} α) (Option.VAdd.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.2015994326._hygCtx._hyg.5)","typeFull":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] [FaithfulVAdd M α], FaithfulVAdd M (Option α)","typeReadable":"∀ {M : Type u_1} {α : Type u_3} [inst : VAdd M α] [FaithfulVAdd M α], FaithfulVAdd M (Option α)","typeReferences":[["VAdd"],["Option"],["Option","VAdd"],["FaithfulVAdd"]],"valueReferences":[["instHVAdd"],["Option"],["eq_of_heq"],["FaithfulVAdd","eq_of_vadd_eq_vadd"],["Option","some"],["Eq"],["FaithfulVAdd","mk"],["HVAdd","hVAdd"],["Option","some","noConfusion"],["Option","VAdd"]]},{"isProp":false,"kind":"definition","name":["Option","instMulAction"],"typeFallback":"forall {M : Type.{u_1}} {α : Type.{u_3}} [inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5 : Monoid.{u_1} M] [inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.8 : MulAction.{u_1, u_3} M α inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5], MulAction.{u_1, u_3} M (Option.{u_3} α) inst._@.Mathlib.Algebra.Group.Action.Option.4004681244._hygCtx._hyg.5","typeFull":"{M : Type u_1} → {α : Type u_3} → [inst : Monoid M] → [MulAction M α] → MulAction M (Option α)","typeReadable":"{M : Type u_1} → {α : Type u_3} → [inst : Monoid M] → [MulAction M α] → MulAction M (Option α)","typeReferences":[["MulAction"],["Option"],["Monoid"]],"valueReferences":[["Option","instMulAction","_proof_1"],["SemigroupAction","mk"],["Option"],["SemigroupAction","toSMul"],["Monoid","toSemigroup"],["MulAction","toSemigroupAction"],["Option","instMulAction","_proof_2"],["Option","instSMul_mathlib"],["MulAction","mk"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.TypeTags.Finite.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["instInfiniteMultiplicative"],"typeFallback":"forall {α : Type.{u}} [h : Infinite.{succ u} α], Infinite.{succ u} (Multiplicative.{u} α)","typeFull":"∀ {α : Type u} [h : Infinite α], Infinite (Multiplicative α)","typeReadable":"∀ {α : Type u} [h : Infinite α], Infinite (Multiplicative α)","typeReferences":[["Multiplicative"],["Infinite"]],"valueReferences":[]},{"isProp":true,"kind":"theorem","name":["Fintype","card_multiplicative"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Group.TypeTags.Finite.2049878251._hygCtx._hyg.4 : Fintype.{u_1} α], Eq.{1} Nat (Fintype.card.{u_1} (Multiplicative.{u_1} α) (Multiplicative.fintype.{u_1} α inst._@.Mathlib.Algebra.Group.TypeTags.Finite.2049878251._hygCtx._hyg.4)) (Fintype.card.{u_1} α inst._@.Mathlib.Algebra.Group.TypeTags.Finite.2049878251._hygCtx._hyg.4)","typeFull":"∀ (α : Type u_1) [inst : Fintype α], Fintype.card (Multiplicative α) = Fintype.card α","typeReadable":"∀ (α : Type u_1) [inst : Fintype α], Fintype.card (Multiplicative α) = Fintype.card α","typeReferences":[["Fintype","card"],["Nat"],["Multiplicative","fintype"],["Multiplicative"],["Eq"],["Fintype"]],"valueReferences":[["Equiv","bijective"],["Finset","univ"],["Fintype","ofBijective","_proof_1"],["Equiv","instEquivLike"],["Function","Embedding","mk"],["EquivLike","toFunLike"],["Finset","card_map"],["Multiplicative"],["DFunLike","coe"],["Multiplicative","ofAdd"],["Equiv"]]},{"isProp":true,"kind":"theorem","name":["Fintype","card_additive"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Group.TypeTags.Finite.3004192662._hygCtx._hyg.4 : Fintype.{u_1} α], Eq.{1} Nat (Fintype.card.{u_1} (Additive.{u_1} α) (Additive.fintype.{u_1} α inst._@.Mathlib.Algebra.Group.TypeTags.Finite.3004192662._hygCtx._hyg.4)) (Fintype.card.{u_1} α inst._@.Mathlib.Algebra.Group.TypeTags.Finite.3004192662._hygCtx._hyg.4)","typeFull":"∀ (α : Type u_1) [inst : Fintype α], Fintype.card (Additive α) = Fintype.card α","typeReadable":"∀ (α : Type u_1) [inst : Fintype α], Fintype.card (Additive α) = Fintype.card α","typeReferences":[["Fintype","card"],["Nat"],["Additive","fintype"],["Eq"],["Fintype"],["Additive"]],"valueReferences":[["Equiv","bijective"],["Finset","univ"],["Fintype","ofBijective","_proof_1"],["Equiv","instEquivLike"],["Function","Embedding","mk"],["EquivLike","toFunLike"],["Finset","card_map"],["Additive","ofMul"],["DFunLike","coe"],["Additive"],["Equiv"]]},{"isProp":true,"kind":"theorem","name":["instInfiniteAdditive"],"typeFallback":"forall {α : Type.{u}} [h : Infinite.{succ u} α], Infinite.{succ u} (Additive.{u} α)","typeFull":"∀ {α : Type u} [h : Infinite α], Infinite (Additive α)","typeReadable":"∀ {α : Type u} [h : Infinite α], Infinite (Additive α)","typeReferences":[["Additive"],["Infinite"]],"valueReferences":[]},{"isProp":true,"kind":"theorem","name":["instFiniteAdditive"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Group.TypeTags.Finite.4189393846._hygCtx._hyg.3 : Finite.{succ u} α], Finite.{succ u} (Additive.{u} α)","typeFull":"∀ {α : Type u} [Finite α], Finite (Additive α)","typeReadable":"∀ {α : Type u} [Finite α], Finite (Additive α)","typeReferences":[["Finite"],["Additive"]],"valueReferences":[["Equiv","refl"],["Finite","of_equiv"],["Additive"]]},{"isProp":true,"kind":"theorem","name":["instFiniteMultiplicative"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Group.TypeTags.Finite.3740827541._hygCtx._hyg.3 : Finite.{succ u} α], Finite.{succ u} (Multiplicative.{u} α)","typeFull":"∀ {α : Type u} [Finite α], Finite (Multiplicative α)","typeReadable":"∀ {α : Type u} [Finite α], Finite (Multiplicative α)","typeReferences":[["Multiplicative"],["Finite"]],"valueReferences":[["Equiv","refl"],["Multiplicative"],["Finite","of_equiv"]]},{"isProp":false,"kind":"definition","name":["Additive","fintype"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Group.TypeTags.Finite.1764317704._hygCtx._hyg.5 : Fintype.{u} α], Fintype.{u} (Additive.{u} α)","typeFull":"{α : Type u} → [Fintype α] → Fintype (Additive α)","typeReadable":"{α : Type u} → [Fintype α] → Fintype (Additive α)","typeReferences":[["Fintype"],["Additive"]],"valueReferences":[["Additive","ofMul"],["Additive"],["Fintype","ofEquiv"]]},{"isProp":false,"kind":"definition","name":["Multiplicative","fintype"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Group.TypeTags.Finite.1764317705._hygCtx._hyg.5 : Fintype.{u} α], Fintype.{u} (Multiplicative.{u} α)","typeFull":"{α : Type u} → [Fintype α] → Fintype (Multiplicative α)","typeReadable":"{α : Type u} → [Fintype α] → Fintype (Multiplicative α)","typeReferences":[["Multiplicative"],["Fintype"]],"valueReferences":[["Multiplicative"],["Fintype","ofEquiv"],["Multiplicative","ofAdd"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Int.sym.json

@@ -0,0 +1 @@
+[]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["MulZeroMemClass","isCancelMulZero"],"typeFallback":"forall {M₀ : Type.{u_1}} [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.3 : Mul.{u_1} M₀] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.6 : Zero.{u_1} M₀] {S : Type.{u_2}} [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.10 : SetLike.{u_2, u_1} S M₀] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.14 : MulMemClass.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.10] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.18 : ZeroMemClass.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.6 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.10] (s : S) [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.23 : IsCancelMulZero.{u_1} M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.6], IsCancelMulZero.{u_1} (Subtype.{succ u_1} M₀ (fun (x : M₀) => Membership.mem.{u_1, u_2} M₀ S (SetLike.instMembership.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.10) s x)) (MulMemClass.mul.{u_1, u_2} M₀ S inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.10 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.14 s) (ZeroMemClass.zero.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.10 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.6 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.3779628978._hygCtx._hyg.18 s)","typeFull":"∀ {M₀ : Type u_1} [inst : Mul M₀] [inst_1 : Zero M₀] {S : Type u_2} [inst_2 : SetLike S M₀] [inst_3 : MulMemClass S M₀]\n  [inst_4 : ZeroMemClass S M₀] (s : S) [IsCancelMulZero M₀], IsCancelMulZero ↥s","typeReadable":"∀ {M₀ : Type u_1} [inst : Mul M₀] [inst_1 : Zero M₀] {S : Type u_2} [inst_2 : SetLike S M₀] [inst_3 : MulMemClass S M₀]\n  [inst_4 : ZeroMemClass S M₀] (s : S) [IsCancelMulZero M₀], IsCancelMulZero ↥s","typeReferences":[["MulMemClass","mul"],["SetLike","instMembership"],["Subtype"],["Membership","mem"],["Mul"],["MulMemClass"],["ZeroMemClass","zero"],["SetLike"],["Zero"],["IsCancelMulZero"],["ZeroMemClass"]],"valueReferences":[["IsCancelMulZero","toIsRightCancelMulZero"],["MulMemClass","mul"],["SetLike","instMembership"],["Subtype"],["MulZeroMemClass","isLeftCancelMulZero"],["Membership","mem"],["ZeroMemClass","zero"],["IsCancelMulZero","mk"],["IsCancelMulZero","toIsLeftCancelMulZero"],["MulZeroMemClass","isRightCancelMulZero"]]},{"isProp":true,"kind":"theorem","name":["MulZeroMemClass","isLeftCancelMulZero"],"typeFallback":"forall {M₀ : Type.{u_1}} [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.3 : Mul.{u_1} M₀] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.6 : Zero.{u_1} M₀] {S : Type.{u_2}} [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.10 : SetLike.{u_2, u_1} S M₀] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.14 : MulMemClass.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.10] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.18 : ZeroMemClass.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.6 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.10] (s : S) [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.23 : IsLeftCancelMulZero.{u_1} M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.6], IsLeftCancelMulZero.{u_1} (Subtype.{succ u_1} M₀ (fun (x : M₀) => Membership.mem.{u_1, u_2} M₀ S (SetLike.instMembership.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.10) s x)) (MulMemClass.mul.{u_1, u_2} M₀ S inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.10 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.14 s) (ZeroMemClass.zero.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.10 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.6 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.1090387697._hygCtx._hyg.18 s)","typeFull":"∀ {M₀ : Type u_1} [inst : Mul M₀] [inst_1 : Zero M₀] {S : Type u_2} [inst_2 : SetLike S M₀] [inst_3 : MulMemClass S M₀]\n  [inst_4 : ZeroMemClass S M₀] (s : S) [IsLeftCancelMulZero M₀], IsLeftCancelMulZero ↥s","typeReadable":"∀ {M₀ : Type u_1} [inst : Mul M₀] [inst_1 : Zero M₀] {S : Type u_2} [inst_2 : SetLike S M₀] [inst_3 : MulMemClass S M₀]\n  [inst_4 : ZeroMemClass S M₀] (s : S) [IsLeftCancelMulZero M₀], IsLeftCancelMulZero ↥s","typeReferences":[["MulMemClass","mul"],["SetLike","instMembership"],["Subtype"],["Membership","mem"],["Mul"],["MulMemClass"],["ZeroMemClass","zero"],["IsLeftCancelMulZero"],["SetLike"],["Zero"],["ZeroMemClass"]],"valueReferences":[["rfl"],["Subtype"],["SetLike","instMembership"],["Function","Injective","isLeftCancelMulZero"],["Membership","mem"],["HMul","hMul"],["Subtype","val"],["OfNat","ofNat"],["MulMemClass","mul"],["Subtype","coe_injective"],["instHMul"],["ZeroMemClass","zero"],["Zero","toOfNat0"]]},{"isProp":true,"kind":"theorem","name":["MulZeroMemClass","isRightCancelMulZero"],"typeFallback":"forall {M₀ : Type.{u_1}} [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.3 : Mul.{u_1} M₀] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.6 : Zero.{u_1} M₀] {S : Type.{u_2}} [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.10 : SetLike.{u_2, u_1} S M₀] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.14 : MulMemClass.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.10] [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.18 : ZeroMemClass.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.6 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.10] (s : S) [inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.23 : IsRightCancelMulZero.{u_1} M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.6], IsRightCancelMulZero.{u_1} (Subtype.{succ u_1} M₀ (fun (x : M₀) => Membership.mem.{u_1, u_2} M₀ S (SetLike.instMembership.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.10) s x)) (MulMemClass.mul.{u_1, u_2} M₀ S inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.3 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.10 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.14 s) (ZeroMemClass.zero.{u_2, u_1} S M₀ inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.10 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.6 inst._@.Mathlib.Algebra.GroupWithZero.Submonoid.CancelMulZero.942518414._hygCtx._hyg.18 s)","typeFull":"∀ {M₀ : Type u_1} [inst : Mul M₀] [inst_1 : Zero M₀] {S : Type u_2} [inst_2 : SetLike S M₀] [inst_3 : MulMemClass S M₀]\n  [inst_4 : ZeroMemClass S M₀] (s : S) [IsRightCancelMulZero M₀], IsRightCancelMulZero ↥s","typeReadable":"∀ {M₀ : Type u_1} [inst : Mul M₀] [inst_1 : Zero M₀] {S : Type u_2} [inst_2 : SetLike S M₀] [inst_3 : MulMemClass S M₀]\n  [inst_4 : ZeroMemClass S M₀] (s : S) [IsRightCancelMulZero M₀], IsRightCancelMulZero ↥s","typeReferences":[["MulMemClass","mul"],["SetLike","instMembership"],["Subtype"],["Membership","mem"],["Mul"],["MulMemClass"],["ZeroMemClass","zero"],["SetLike"],["Zero"],["IsRightCancelMulZero"],["ZeroMemClass"]],"valueReferences":[["rfl"],["Subtype"],["SetLike","instMembership"],["Membership","mem"],["HMul","hMul"],["Function","Injective","isRightCancelMulZero"],["Subtype","val"],["OfNat","ofNat"],["MulMemClass","mul"],["Subtype","coe_injective"],["instHMul"],["ZeroMemClass","zero"],["Zero","toOfNat0"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.ShortComplex.Abelian.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:9ab823fdd579132a2ebac6bf524973cfef3a38558c208d6e50bba183ca102127
+size 35398017

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Shrink.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Shrink","linearEquiv_symm_apply"],"typeFallback":"forall (R : Type.{u_1}) (α : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 : Small.{v, u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 : Module.{u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10] (a._@._internal._hyg.0 : α), Eq.{succ v} (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (DFunLike.coe.{max (succ v) (succ u_2), succ u_2, succ v} (LinearEquiv.{u_1, u_1, u_2, v} R R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13)) α (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : α) => Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (EquivLike.toFunLike.{max (succ v) (succ u_2), succ u_2, succ v} (LinearEquiv.{u_1, u_1, u_2, v} R R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13)) α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (LinearEquiv.instEquivLike.{u_1, u_1, u_2, v} R R α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7))) (LinearEquiv.symm.{u_1, u_1, v, u_2} R R (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (Shrink.linearEquiv.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13)) a._@._internal._hyg.0) (DFunLike.coe.{max (succ v) (succ u_2), succ u_2, succ v} (Equiv.{succ u_2, succ v} α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4)) α (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : α) => Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (EquivLike.toFunLike.{max (succ v) (succ u_2), succ u_2, succ v} (Equiv.{succ u_2, succ v} α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4)) α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (Equiv.instEquivLike.{succ u_2, succ v} α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4))) (equivShrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) a._@._internal._hyg.0)","typeFull":"∀ (R : Type u_1) (α : Type u_2) [inst : Small.{v, u_2} α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid α]\n  [inst_3 : Module R α] (a : α), (Shrink.linearEquiv R α).symm a = (equivShrink α) a","typeReadable":"∀ (R : Type u_1) (α : Type u_2) [inst : Small.{v, u_2} α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid α]\n  [inst_3 : Module R α] (a : α), (Shrink.linearEquiv R α).symm a = (equivShrink α) a","typeReferences":[["Equiv","instEquivLike"],["Module"],["Small"],["LinearEquiv"],["LinearEquiv","symm"],["Shrink"],["DFunLike","coe"],["Equiv"],["Shrink","instModule"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["equivShrink"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["Eq"],["Shrink","instAddCommMonoid"],["Shrink","linearEquiv"],["Semiring"]],"valueReferences":[["LinearEquiv"],["Shrink"],["DFunLike","coe"],["LinearEquiv","symm"],["Shrink","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["Shrink","instAddCommMonoid"],["Shrink","linearEquiv"]]},{"isProp":false,"kind":"definition","name":["Shrink","linearEquiv"],"typeFallback":"forall (R : Type.{u_1}) (α : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 : Small.{v, u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 : Module.{u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10], LinearEquiv.{u_1, u_1, v, u_2} R R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13","typeFull":"(R : Type u_1) →\n  (α : Type u_2) →\n    [inst : Small.{v, u_2} α] →\n      [inst_1 : Semiring R] → [inst_2 : AddCommMonoid α] → [inst_3 : Module R α] → Shrink.{v, u_2} α ≃ₗ[R] α","typeReadable":"(R : Type u_1) →\n  (α : Type u_2) →\n    [inst : Small.{v, u_2} α] →\n      [inst_1 : Semiring R] → [inst_2 : AddCommMonoid α] → [inst_3 : Module R α] → Shrink.{v, u_2} α ≃ₗ[R] α","typeReferences":[["Shrink","instModule"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Module"],["Small"],["RingHomInvPair","ids"],["LinearEquiv"],["Shrink","instAddCommMonoid"],["Shrink"],["Semiring"]],"valueReferences":[["equivShrink"],["Equiv","symm"],["Equiv","linearEquiv"],["Shrink"]]},{"isProp":false,"kind":"definition","name":["Shrink","instModule"],"typeFallback":"forall {R : Type.{u_1}} {α : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.4 : Small.{v, u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.7 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.10 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.13 : Module.{u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.10], Module.{u_1, v} R (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.7 (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.955123615._hygCtx._hyg.10)","typeFull":"{R : Type u_1} →\n  {α : Type u_2} →\n    [inst : Small.{v, u_2} α] →\n      [inst_1 : Semiring R] → [inst_2 : AddCommMonoid α] → [Module R α] → Module R (Shrink.{v, u_2} α)","typeReadable":"{R : Type u_1} →\n  {α : Type u_2} →\n    [inst : Small.{v, u_2} α] →\n      [inst_1 : Semiring R] → [inst_2 : AddCommMonoid α] → [Module R α] → Module R (Shrink.{v, u_2} α)","typeReferences":[["AddCommMonoid"],["Module"],["Small"],["Shrink","instAddCommMonoid"],["Shrink"],["Semiring"]],"valueReferences":[["Equiv","module"],["equivShrink"],["Equiv","symm"],["Shrink"]]},{"isProp":true,"kind":"theorem","name":["Shrink","linearEquiv_apply"],"typeFallback":"forall (R : Type.{u_1}) (α : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 : Small.{v, u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 : Semiring.{u_1} R] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 : Module.{u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10] (a._@._internal._hyg.0 : Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4), Eq.{succ u_2} α (DFunLike.coe.{max (succ v) (succ u_2), succ v, succ u_2} (LinearEquiv.{u_1, u_1, v, u_2} R R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) => α) (EquivLike.toFunLike.{max (succ v) (succ u_2), succ v, succ u_2} (LinearEquiv.{u_1, u_1, v, u_2} R R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α (LinearEquiv.instEquivLike.{u_1, u_1, v, u_2} R R (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 (Shrink.instAddCommMonoid.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 (Shrink.instModule.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7))) (Shrink.linearEquiv.{v, u_1, u_2} R α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.13) a._@._internal._hyg.0) (DFunLike.coe.{max (succ v) (succ u_2), succ v, succ u_2} (Equiv.{succ v, succ u_2} (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α) (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) => α) (EquivLike.toFunLike.{max (succ v) (succ u_2), succ v, succ u_2} (Equiv.{succ v, succ u_2} (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α) (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α (Equiv.instEquivLike.{succ v, succ u_2} (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) α)) (Equiv.symm.{succ u_2, succ v} α (Shrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4) (equivShrink.{v, u_2} α inst._@.Mathlib.Algebra.Module.Shrink.2994524416._hygCtx._hyg.4)) a._@._internal._hyg.0)","typeFull":"∀ (R : Type u_1) (α : Type u_2) [inst : Small.{v, u_2} α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid α]\n  [inst_3 : Module R α] (a : Shrink.{v, u_2} α), (Shrink.linearEquiv R α) a = (equivShrink α).symm a","typeReadable":"∀ (R : Type u_1) (α : Type u_2) [inst : Small.{v, u_2} α] [inst_1 : Semiring R] [inst_2 : AddCommMonoid α]\n  [inst_3 : Module R α] (a : Shrink.{v, u_2} α), (Shrink.linearEquiv R α) a = (equivShrink α).symm a","typeReferences":[["Equiv","instEquivLike"],["Module"],["Small"],["LinearEquiv"],["Shrink"],["DFunLike","coe"],["Equiv"],["Shrink","instModule"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["equivShrink"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Equiv","symm"],["LinearEquiv","instEquivLike"],["Eq"],["Shrink","instAddCommMonoid"],["Shrink","linearEquiv"],["Semiring"]],"valueReferences":[["Shrink","instModule"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["Eq","refl"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["Shrink","instAddCommMonoid"],["Shrink"],["DFunLike","coe"],["Shrink","linearEquiv"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.Torsion.Field.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["DivisionSemiring","to_moduleIsTorsionFree"],"typeFallback":"forall {𝕜 : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.4 : DivisionSemiring.{u_1} 𝕜] [inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.7 : AddCommMonoid.{u_2} M] [inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.10 : Module.{u_1, u_2} 𝕜 M (DivisionSemiring.toSemiring.{u_1} 𝕜 inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.7], Module.IsTorsionFree.{u_1, u_2} 𝕜 M (DivisionSemiring.toSemiring.{u_1} 𝕜 inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.4) inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Module.Torsion.Field.1964321063._hygCtx._hyg.10","typeFull":"∀ {𝕜 : Type u_1} {M : Type u_2} [inst : DivisionSemiring 𝕜] [inst_1 : AddCommMonoid M] [inst_2 : Module 𝕜 M],\n  Module.IsTorsionFree 𝕜 M","typeReadable":"∀ {𝕜 : Type u_1} {M : Type u_2} [inst : DivisionSemiring 𝕜] [inst_1 : AddCommMonoid M] [inst_2 : Module 𝕜 M],\n  Module.IsTorsionFree 𝕜 M","typeReferences":[["Module","IsTorsionFree"],["AddCommMonoid"],["Module"],["DivisionSemiring","toSemiring"],["DivisionSemiring"]],"valueReferences":[["IsRegular","ne_zero"],["Eq","trans"],["Eq","mp"],["MonoidWithZero","toMulZeroOneClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["Module","IsTorsionFree","mk"],["congrArg"],["not_false_eq_true"],["Semiring","toNonAssocSemiring"],["congr"],["inv_smul_smul₀"],["GroupWithZero","toMonoidWithZero"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["instHSMul"],["Zero","toOfNat0"],["Eq"],["GroupWithZero","toNontrivial"],["DistribSMul","toSMulZeroClass"],["Not"],["Inv","inv"],["InvOneClass","toInv"],["True"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["DivisionSemiring","toSemiring"],["DivisionSemiring","toGroupWithZero"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Module","toDistribMulAction"],["DivInvOneMonoid","toInvOneClass"],["MulZeroOneClass","toMulZeroClass"],["of_eq_true"],["MulZeroClass","toZero"],["eq_false"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["id"],["False"],["AddZero","toZero"],["DivisionMonoid","toDivInvOneMonoid"],["AddMonoid","toAddZeroClass"],["GroupWithZero","toDivisionMonoid"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Notation.sym.json

@@ -0,0 +1 @@
+[{"isProp":false,"kind":"definition","name":["PosPart","recOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (PosPart.{u_1} α) -> Sort.{u}} (t : PosPart.{u_1} α), (forall (posPart : α -> α), motive (PosPart.mk.{u_1} α posPart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : PosPart α → Sort u} → (t : PosPart α) → ((posPart : α → α) → motive { posPart := posPart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : PosPart α → Sort u} → (t : PosPart α) → ((posPart : α → α) → motive { posPart := posPart }) → motive t","typeReferences":[["PosPart","mk"],["PosPart"]],"valueReferences":[["PosPart","rec"]]},{"isProp":false,"kind":"definition","name":["PosPart","ctorIdx"],"typeFallback":"forall {α : Type.{u_1}}, (PosPart.{u_1} α) -> Nat","typeFull":"{α : Type u_1} → PosPart α → Nat","typeReadable":"{α : Type u_1} → PosPart α → Nat","typeReferences":[["Nat"],["PosPart"]],"valueReferences":[]},{"isProp":false,"kind":"definition","name":["NegPart","ctorIdx"],"typeFallback":"forall {α : Type.{u_1}}, (NegPart.{u_1} α) -> Nat","typeFull":"{α : Type u_1} → NegPart α → Nat","typeReadable":"{α : Type u_1} → NegPart α → Nat","typeReferences":[["Nat"],["NegPart"]],"valueReferences":[]},{"isProp":false,"kind":"inductive","name":["PosPart"],"typeFallback":"Type.{u_1} -> Type.{u_1}","typeFull":"Type u_1 → Type u_1","typeReadable":"Type u_1 → Type u_1","typeReferences":[],"valueReferences":null},{"isProp":false,"kind":"recursor","name":["NegPart","rec"],"typeFallback":"forall {α : Type.{u_1}} {motive : (NegPart.{u_1} α) -> Sort.{u}}, (forall (negPart : α -> α), motive (NegPart.mk.{u_1} α negPart)) -> (forall (t : NegPart.{u_1} α), motive t)","typeFull":"{α : Type u_1} →\n  {motive : NegPart α → Sort u} → ((negPart : α → α) → motive { negPart := negPart }) → (t : NegPart α) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : NegPart α → Sort u} → ((negPart : α → α) → motive { negPart := negPart }) → (t : NegPart α) → motive t","typeReferences":[["NegPart","mk"],["NegPart"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["NegPart","mk","_flat_ctor"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (NegPart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → NegPart α","typeReadable":"{α : Type u_1} → (α → α) → NegPart α","typeReferences":[["NegPart"]],"valueReferences":[["NegPart","mk"]]},{"isProp":false,"kind":"recursor","name":["PosPart","rec"],"typeFallback":"forall {α : Type.{u_1}} {motive : (PosPart.{u_1} α) -> Sort.{u}}, (forall (posPart : α -> α), motive (PosPart.mk.{u_1} α posPart)) -> (forall (t : PosPart.{u_1} α), motive t)","typeFull":"{α : Type u_1} →\n  {motive : PosPart α → Sort u} → ((posPart : α → α) → motive { posPart := posPart }) → (t : PosPart α) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : PosPart α → Sort u} → ((posPart : α → α) → motive { posPart := posPart }) → (t : PosPart α) → motive t","typeReferences":[["PosPart","mk"],["PosPart"]],"valueReferences":null},{"isProp":false,"kind":"constructor","name":["LeOnePart","mk"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (LeOnePart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → LeOnePart α","typeReadable":"{α : Type u_1} → (α → α) → LeOnePart α","typeReferences":[["LeOnePart"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["OneLePart","recOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (OneLePart.{u_1} α) -> Sort.{u}} (t : OneLePart.{u_1} α), (forall (oneLePart : α -> α), motive (OneLePart.mk.{u_1} α oneLePart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : OneLePart α → Sort u} →\n    (t : OneLePart α) → ((oneLePart : α → α) → motive { oneLePart := oneLePart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : OneLePart α → Sort u} →\n    (t : OneLePart α) → ((oneLePart : α → α) → motive { oneLePart := oneLePart }) → motive t","typeReferences":[["OneLePart","mk"],["OneLePart"]],"valueReferences":[["OneLePart","rec"]]},{"isProp":false,"kind":"definition","name":["LeOnePart","casesOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (LeOnePart.{u_1} α) -> Sort.{u}} (t : LeOnePart.{u_1} α), (forall (leOnePart : α -> α), motive (LeOnePart.mk.{u_1} α leOnePart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : LeOnePart α → Sort u} →\n    (t : LeOnePart α) → ((leOnePart : α → α) → motive { leOnePart := leOnePart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : LeOnePart α → Sort u} →\n    (t : LeOnePart α) → ((leOnePart : α → α) → motive { leOnePart := leOnePart }) → motive t","typeReferences":[["LeOnePart"],["LeOnePart","mk"]],"valueReferences":[["LeOnePart","rec"]]},{"isProp":false,"kind":"definition","name":["term_⁻"],"typeFallback":"Lean.TrailingParserDescr","typeFull":"Lean.TrailingParserDescr","typeReadable":"Lean.TrailingParserDescr","typeReferences":[["Lean","TrailingParserDescr"]],"valueReferences":[["Nat"],["Lean","Name","mkStr1"],["instOfNatNat"],["Lean","ParserDescr","trailingNode"],["Lean","ParserDescr","symbol"],["OfNat","ofNat"]]},{"isProp":false,"kind":"inductive","name":["NegPart"],"typeFallback":"Type.{u_1} -> Type.{u_1}","typeFull":"Type u_1 → Type u_1","typeReadable":"Type u_1 → Type u_1","typeReferences":[],"valueReferences":null},{"isProp":false,"kind":"definition","name":["PosPart","mk","_flat_ctor"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (PosPart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → PosPart α","typeReadable":"{α : Type u_1} → (α → α) → PosPart α","typeReferences":[["PosPart"]],"valueReferences":[["PosPart","mk"]]},{"isProp":false,"kind":"definition","name":["term_⁺"],"typeFallback":"Lean.TrailingParserDescr","typeFull":"Lean.TrailingParserDescr","typeReadable":"Lean.TrailingParserDescr","typeReferences":[["Lean","TrailingParserDescr"]],"valueReferences":[["Nat"],["Lean","Name","mkStr1"],["instOfNatNat"],["Lean","ParserDescr","trailingNode"],["Lean","ParserDescr","symbol"],["OfNat","ofNat"]]},{"isProp":false,"kind":"definition","name":["NegPart","recOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (NegPart.{u_1} α) -> Sort.{u}} (t : NegPart.{u_1} α), (forall (negPart : α -> α), motive (NegPart.mk.{u_1} α negPart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : NegPart α → Sort u} → (t : NegPart α) → ((negPart : α → α) → motive { negPart := negPart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : NegPart α → Sort u} → (t : NegPart α) → ((negPart : α → α) → motive { negPart := negPart }) → motive t","typeReferences":[["NegPart","mk"],["NegPart"]],"valueReferences":[["NegPart","rec"]]},{"isProp":false,"kind":"definition","name":["LeOnePart","noConfusionType"],"typeFallback":"Sort.{u} -> (forall {α : Type.{u_1}}, (LeOnePart.{u_1} α) -> (forall {α' : Type.{u_1}}, (LeOnePart.{u_1} α') -> Sort.{u}))","typeFull":"Sort u → {α : Type u_1} → LeOnePart α → {α' : Type u_1} → LeOnePart α' → Sort u","typeReadable":"Sort u → {α : Type u_1} → LeOnePart α → {α' : Type u_1} → LeOnePart α' → Sort u","typeReferences":[["LeOnePart"]],"valueReferences":[["LeOnePart","casesOn"],["HEq"]]},{"isProp":false,"kind":"definition","name":["OneLePart","ctorIdx"],"typeFallback":"forall {α : Type.{u_1}}, (OneLePart.{u_1} α) -> Nat","typeFull":"{α : Type u_1} → OneLePart α → Nat","typeReadable":"{α : Type u_1} → OneLePart α → Nat","typeReferences":[["Nat"],["OneLePart"]],"valueReferences":[]},{"isProp":false,"kind":"definition","name":["term_⁻ᵐ"],"typeFallback":"Lean.TrailingParserDescr","typeFull":"Lean.TrailingParserDescr","typeReadable":"Lean.TrailingParserDescr","typeReferences":[["Lean","TrailingParserDescr"]],"valueReferences":[["Nat"],["Lean","Name","mkStr1"],["instOfNatNat"],["Lean","ParserDescr","trailingNode"],["Lean","ParserDescr","symbol"],["OfNat","ofNat"]]},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___unexpand_LeOnePart_leOnePart_1"],"typeFallback":"Lean.PrettyPrinter.Unexpander","typeFull":"Lean.PrettyPrinter.Unexpander","typeReadable":"Lean.PrettyPrinter.Unexpander","typeReferences":[["Lean","PrettyPrinter","Unexpander"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Bool","false"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","MonadQuotation","toMonadRef"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["List","cons"],["Bool","true"],["Unit","unit"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","PrettyPrinter","instMonadQuotationUnexpandM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["Bool","or"],["cond"],["Unit"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Lean","Syntax","atom"],["Lean","withRef"],["Bool"],["Applicative","toPure"],["Lean","PrettyPrinter","UnexpandM"],["ReaderT","instMonadExceptOf"],["EStateM"],["Lean","Syntax","isOfKind"],["Lean","Syntax","matchesNull"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Eq"],["Lean","Syntax","node2"],["List","nil"],["Bind","bind"],["EStateM","instMonadExceptOfOfBacktrackable"],["Lean","Name","mkStr1"],["ite"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"constructor","name":["NegPart","mk"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (NegPart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → NegPart α","typeReadable":"{α : Type u_1} → (α → α) → NegPart α","typeReferences":[["NegPart"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["NegPart","noConfusionType"],"typeFallback":"Sort.{u} -> (forall {α : Type.{u_1}}, (NegPart.{u_1} α) -> (forall {α' : Type.{u_1}}, (NegPart.{u_1} α') -> Sort.{u}))","typeFull":"Sort u → {α : Type u_1} → NegPart α → {α' : Type u_1} → NegPart α' → Sort u","typeReadable":"Sort u → {α : Type u_1} → NegPart α → {α' : Type u_1} → NegPart α' → Sort u","typeReferences":[["NegPart"]],"valueReferences":[["HEq"],["NegPart","casesOn"]]},{"isProp":false,"kind":"definition","name":["NegPart","noConfusion"],"typeFallback":"forall {P : Sort.{u}} {α : Type.{u_1}} {t : NegPart.{u_1} α} {α' : Type.{u_1}} {t' : NegPart.{u_1} α'}, (Eq.{succ (succ u_1)} Type.{u_1} α α') -> (HEq.{succ u_1} (NegPart.{u_1} α) t (NegPart.{u_1} α') t') -> (NegPart.noConfusionType.{u, u_1} P α t α' t')","typeFull":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : NegPart α} → {α' : Type u_1} → {t' : NegPart α'} → α = α' → t ≍ t' → NegPart.noConfusionType P t t'","typeReadable":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : NegPart α} → {α' : Type u_1} → {t' : NegPart α'} → α = α' → t ≍ t' → NegPart.noConfusionType P t t'","typeReferences":[["HEq"],["NegPart"],["NegPart","noConfusionType"],["Eq"]],"valueReferences":[["HEq","refl"],["eq_of_heq"],["NegPart","casesOn"],["HEq"],["NegPart"],["NegPart","noConfusionType"],["Eq","ndrec"]]},{"isProp":false,"kind":"inductive","name":["OneLePart"],"typeFallback":"Type.{u_1} -> Type.{u_1}","typeFull":"Type u_1 → Type u_1","typeReadable":"Type u_1 → Type u_1","typeReferences":[],"valueReferences":null},{"isProp":false,"kind":"definition","name":["OneLePart","oneLePart"],"typeFallback":"forall {α : Type.{u_1}} [self : OneLePart.{u_1} α], α -> α","typeFull":"{α : Type u_1} → [self : OneLePart α] → α → α","typeReadable":"{α : Type u_1} → [self : OneLePart α] → α → α","typeReferences":[["OneLePart"]],"valueReferences":[]},{"isProp":false,"kind":"definition","name":["OneLePart","mk","_flat_ctor"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (OneLePart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → OneLePart α","typeReadable":"{α : Type u_1} → (α → α) → OneLePart α","typeReferences":[["OneLePart"]],"valueReferences":[["OneLePart","mk"]]},{"isProp":false,"kind":"definition","name":["NegPart","casesOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (NegPart.{u_1} α) -> Sort.{u}} (t : NegPart.{u_1} α), (forall (negPart : α -> α), motive (NegPart.mk.{u_1} α negPart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : NegPart α → Sort u} → (t : NegPart α) → ((negPart : α → α) → motive { negPart := negPart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : NegPart α → Sort u} → (t : NegPart α) → ((negPart : α → α) → motive { negPart := negPart }) → motive t","typeReferences":[["NegPart","mk"],["NegPart"]],"valueReferences":[["NegPart","rec"]]},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___unexpand_PosPart_posPart_1"],"typeFallback":"Lean.PrettyPrinter.Unexpander","typeFull":"Lean.PrettyPrinter.Unexpander","typeReadable":"Lean.PrettyPrinter.Unexpander","typeReferences":[["Lean","PrettyPrinter","Unexpander"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Bool","false"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","MonadQuotation","toMonadRef"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["List","cons"],["Bool","true"],["Unit","unit"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","PrettyPrinter","instMonadQuotationUnexpandM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["Bool","or"],["cond"],["Unit"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Lean","Syntax","atom"],["Lean","withRef"],["Bool"],["Applicative","toPure"],["Lean","PrettyPrinter","UnexpandM"],["ReaderT","instMonadExceptOf"],["EStateM"],["Lean","Syntax","isOfKind"],["Lean","Syntax","matchesNull"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Eq"],["Lean","Syntax","node2"],["List","nil"],["Bind","bind"],["EStateM","instMonadExceptOfOfBacktrackable"],["Lean","Name","mkStr1"],["ite"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___macroRules_term_⁻ᵐ_1"],"typeFallback":"Lean.Macro","typeFull":"Lean.Macro","typeReadable":"Lean.Macro","typeReferences":[["Lean","Macro"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Lean","Macro","State"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","Syntax","ident"],["String"],["Lean","Macro","Context"],["Lean","Macro","Exception","unsupportedSyntax"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["Lean","Syntax","Preresolved"],["List","cons"],["Bool","true"],["Lean","Syntax","Preresolved","decl"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","Macro","instMonadQuotationMacroM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Bool"],["Applicative","toPure"],["ReaderT","instMonadExceptOf"],["EStateM"],["String","toRawSubstring'"],["Lean","Syntax","isOfKind"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Lean","addMacroScope"],["Lean","MacroM"],["Eq"],["Lean","Name","mkStr2"],["Lean","Syntax","node2"],["EStateM","instMonadExceptOfOfBacktrackable"],["Bind","bind"],["List","nil"],["Lean","Name","mkStr1"],["ite"],["Lean","Syntax","node1"],["Lean","Macro","instMonadRefMacroM"],["Lean","Macro","Exception"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"definition","name":["term_⁺ᵐ"],"typeFallback":"Lean.TrailingParserDescr","typeFull":"Lean.TrailingParserDescr","typeReadable":"Lean.TrailingParserDescr","typeReferences":[["Lean","TrailingParserDescr"]],"valueReferences":[["Nat"],["Lean","Name","mkStr1"],["instOfNatNat"],["Lean","ParserDescr","trailingNode"],["Lean","ParserDescr","symbol"],["OfNat","ofNat"]]},{"isProp":false,"kind":"recursor","name":["LeOnePart","rec"],"typeFallback":"forall {α : Type.{u_1}} {motive : (LeOnePart.{u_1} α) -> Sort.{u}}, (forall (leOnePart : α -> α), motive (LeOnePart.mk.{u_1} α leOnePart)) -> (forall (t : LeOnePart.{u_1} α), motive t)","typeFull":"{α : Type u_1} →\n  {motive : LeOnePart α → Sort u} →\n    ((leOnePart : α → α) → motive { leOnePart := leOnePart }) → (t : LeOnePart α) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : LeOnePart α → Sort u} →\n    ((leOnePart : α → α) → motive { leOnePart := leOnePart }) → (t : LeOnePart α) → motive t","typeReferences":[["LeOnePart"],["LeOnePart","mk"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___macroRules_term_⁺ᵐ_1"],"typeFallback":"Lean.Macro","typeFull":"Lean.Macro","typeReadable":"Lean.Macro","typeReferences":[["Lean","Macro"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Lean","Macro","State"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","Syntax","ident"],["String"],["Lean","Macro","Context"],["Lean","Macro","Exception","unsupportedSyntax"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["Lean","Syntax","Preresolved"],["List","cons"],["Bool","true"],["Lean","Syntax","Preresolved","decl"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","Macro","instMonadQuotationMacroM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Bool"],["Applicative","toPure"],["ReaderT","instMonadExceptOf"],["EStateM"],["String","toRawSubstring'"],["Lean","Syntax","isOfKind"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Lean","addMacroScope"],["Lean","MacroM"],["Eq"],["Lean","Name","mkStr2"],["Lean","Syntax","node2"],["EStateM","instMonadExceptOfOfBacktrackable"],["Bind","bind"],["List","nil"],["Lean","Name","mkStr1"],["ite"],["Lean","Syntax","node1"],["Lean","Macro","instMonadRefMacroM"],["Lean","Macro","Exception"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___unexpand_OneLePart_oneLePart_1"],"typeFallback":"Lean.PrettyPrinter.Unexpander","typeFull":"Lean.PrettyPrinter.Unexpander","typeReadable":"Lean.PrettyPrinter.Unexpander","typeReferences":[["Lean","PrettyPrinter","Unexpander"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Bool","false"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","MonadQuotation","toMonadRef"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["List","cons"],["Bool","true"],["Unit","unit"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","PrettyPrinter","instMonadQuotationUnexpandM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["Bool","or"],["cond"],["Unit"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Lean","Syntax","atom"],["Lean","withRef"],["Bool"],["Applicative","toPure"],["Lean","PrettyPrinter","UnexpandM"],["ReaderT","instMonadExceptOf"],["EStateM"],["Lean","Syntax","isOfKind"],["Lean","Syntax","matchesNull"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Eq"],["Lean","Syntax","node2"],["List","nil"],["Bind","bind"],["EStateM","instMonadExceptOfOfBacktrackable"],["Lean","Name","mkStr1"],["ite"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"definition","name":["OneLePart","casesOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (OneLePart.{u_1} α) -> Sort.{u}} (t : OneLePart.{u_1} α), (forall (oneLePart : α -> α), motive (OneLePart.mk.{u_1} α oneLePart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : OneLePart α → Sort u} →\n    (t : OneLePart α) → ((oneLePart : α → α) → motive { oneLePart := oneLePart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : OneLePart α → Sort u} →\n    (t : OneLePart α) → ((oneLePart : α → α) → motive { oneLePart := oneLePart }) → motive t","typeReferences":[["OneLePart","mk"],["OneLePart"]],"valueReferences":[["OneLePart","rec"]]},{"isProp":false,"kind":"definition","name":["LeOnePart","mk","noConfusion"],"typeFallback":"forall {α : Type.{u_1}} {P : Sort.{u}} {leOnePart : α -> α} {leOnePart' : α -> α}, (Eq.{succ u_1} (LeOnePart.{u_1} α) (LeOnePart.mk.{u_1} α leOnePart) (LeOnePart.mk.{u_1} α leOnePart')) -> ((HEq.{succ u_1} (α -> α) leOnePart (α -> α) leOnePart') -> P) -> P","typeFull":"{α : Type u_1} →\n  {P : Sort u} →\n    {leOnePart leOnePart' : α → α} →\n      { leOnePart := leOnePart } = { leOnePart := leOnePart' } → (leOnePart ≍ leOnePart' → P) → P","typeReadable":"{α : Type u_1} →\n  {P : Sort u} →\n    {leOnePart leOnePart' : α → α} →\n      { leOnePart := leOnePart } = { leOnePart := leOnePart' } → (leOnePart ≍ leOnePart' → P) → P","typeReferences":[["LeOnePart"],["HEq"],["LeOnePart","mk"],["Eq"]],"valueReferences":[["LeOnePart"],["Eq","refl"],["LeOnePart","noConfusion"],["id"],["LeOnePart","mk"],["heq_of_eq"]]},{"isProp":false,"kind":"definition","name":["NegPart","negPart"],"typeFallback":"forall {α : Type.{u_1}} [self : NegPart.{u_1} α], α -> α","typeFull":"{α : Type u_1} → [self : NegPart α] → α → α","typeReadable":"{α : Type u_1} → [self : NegPart α] → α → α","typeReferences":[["NegPart"]],"valueReferences":[]},{"isProp":false,"kind":"constructor","name":["OneLePart","mk"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (OneLePart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → OneLePart α","typeReadable":"{α : Type u_1} → (α → α) → OneLePart α","typeReferences":[["OneLePart"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["PosPart","noConfusion"],"typeFallback":"forall {P : Sort.{u}} {α : Type.{u_1}} {t : PosPart.{u_1} α} {α' : Type.{u_1}} {t' : PosPart.{u_1} α'}, (Eq.{succ (succ u_1)} Type.{u_1} α α') -> (HEq.{succ u_1} (PosPart.{u_1} α) t (PosPart.{u_1} α') t') -> (PosPart.noConfusionType.{u, u_1} P α t α' t')","typeFull":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : PosPart α} → {α' : Type u_1} → {t' : PosPart α'} → α = α' → t ≍ t' → PosPart.noConfusionType P t t'","typeReadable":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : PosPart α} → {α' : Type u_1} → {t' : PosPart α'} → α = α' → t ≍ t' → PosPart.noConfusionType P t t'","typeReferences":[["HEq"],["Eq"],["PosPart"],["PosPart","noConfusionType"]],"valueReferences":[["PosPart","casesOn"],["HEq","refl"],["eq_of_heq"],["HEq"],["PosPart"],["Eq","ndrec"],["PosPart","noConfusionType"]]},{"isProp":false,"kind":"definition","name":["LeOnePart","ctorIdx"],"typeFallback":"forall {α : Type.{u_1}}, (LeOnePart.{u_1} α) -> Nat","typeFull":"{α : Type u_1} → LeOnePart α → Nat","typeReadable":"{α : Type u_1} → LeOnePart α → Nat","typeReferences":[["Nat"],["LeOnePart"]],"valueReferences":[]},{"isProp":false,"kind":"definition","name":["LeOnePart","noConfusion"],"typeFallback":"forall {P : Sort.{u}} {α : Type.{u_1}} {t : LeOnePart.{u_1} α} {α' : Type.{u_1}} {t' : LeOnePart.{u_1} α'}, (Eq.{succ (succ u_1)} Type.{u_1} α α') -> (HEq.{succ u_1} (LeOnePart.{u_1} α) t (LeOnePart.{u_1} α') t') -> (LeOnePart.noConfusionType.{u, u_1} P α t α' t')","typeFull":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : LeOnePart α} → {α' : Type u_1} → {t' : LeOnePart α'} → α = α' → t ≍ t' → LeOnePart.noConfusionType P t t'","typeReadable":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : LeOnePart α} → {α' : Type u_1} → {t' : LeOnePart α'} → α = α' → t ≍ t' → LeOnePart.noConfusionType P t t'","typeReferences":[["LeOnePart"],["LeOnePart","noConfusionType"],["HEq"],["Eq"]],"valueReferences":[["LeOnePart","casesOn"],["LeOnePart"],["HEq","refl"],["LeOnePart","noConfusionType"],["eq_of_heq"],["HEq"],["Eq","ndrec"]]},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___unexpand_NegPart_negPart_1"],"typeFallback":"Lean.PrettyPrinter.Unexpander","typeFull":"Lean.PrettyPrinter.Unexpander","typeReadable":"Lean.PrettyPrinter.Unexpander","typeReferences":[["Lean","PrettyPrinter","Unexpander"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Bool","false"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","MonadQuotation","toMonadRef"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["List","cons"],["Bool","true"],["Unit","unit"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","PrettyPrinter","instMonadQuotationUnexpandM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["Bool","or"],["cond"],["Unit"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Lean","Syntax","atom"],["Lean","withRef"],["Bool"],["Applicative","toPure"],["Lean","PrettyPrinter","UnexpandM"],["ReaderT","instMonadExceptOf"],["EStateM"],["Lean","Syntax","isOfKind"],["Lean","Syntax","matchesNull"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Eq"],["Lean","Syntax","node2"],["List","nil"],["Bind","bind"],["EStateM","instMonadExceptOfOfBacktrackable"],["Lean","Name","mkStr1"],["ite"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"definition","name":["OneLePart","mk","noConfusion"],"typeFallback":"forall {α : Type.{u_1}} {P : Sort.{u}} {oneLePart : α -> α} {oneLePart' : α -> α}, (Eq.{succ u_1} (OneLePart.{u_1} α) (OneLePart.mk.{u_1} α oneLePart) (OneLePart.mk.{u_1} α oneLePart')) -> ((HEq.{succ u_1} (α -> α) oneLePart (α -> α) oneLePart') -> P) -> P","typeFull":"{α : Type u_1} →\n  {P : Sort u} →\n    {oneLePart oneLePart' : α → α} →\n      { oneLePart := oneLePart } = { oneLePart := oneLePart' } → (oneLePart ≍ oneLePart' → P) → P","typeReadable":"{α : Type u_1} →\n  {P : Sort u} →\n    {oneLePart oneLePart' : α → α} →\n      { oneLePart := oneLePart } = { oneLePart := oneLePart' } → (oneLePart ≍ oneLePart' → P) → P","typeReferences":[["OneLePart","mk"],["HEq"],["Eq"],["OneLePart"]],"valueReferences":[["OneLePart","mk"],["Eq","refl"],["id"],["heq_of_eq"],["OneLePart","noConfusion"],["OneLePart"]]},{"isProp":false,"kind":"recursor","name":["OneLePart","rec"],"typeFallback":"forall {α : Type.{u_1}} {motive : (OneLePart.{u_1} α) -> Sort.{u}}, (forall (oneLePart : α -> α), motive (OneLePart.mk.{u_1} α oneLePart)) -> (forall (t : OneLePart.{u_1} α), motive t)","typeFull":"{α : Type u_1} →\n  {motive : OneLePart α → Sort u} →\n    ((oneLePart : α → α) → motive { oneLePart := oneLePart }) → (t : OneLePart α) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : OneLePart α → Sort u} →\n    ((oneLePart : α → α) → motive { oneLePart := oneLePart }) → (t : OneLePart α) → motive t","typeReferences":[["OneLePart","mk"],["OneLePart"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["LeOnePart","mk","_flat_ctor"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (LeOnePart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → LeOnePart α","typeReadable":"{α : Type u_1} → (α → α) → LeOnePart α","typeReferences":[["LeOnePart"]],"valueReferences":[["LeOnePart","mk"]]},{"isProp":false,"kind":"definition","name":["PosPart","casesOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (PosPart.{u_1} α) -> Sort.{u}} (t : PosPart.{u_1} α), (forall (posPart : α -> α), motive (PosPart.mk.{u_1} α posPart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : PosPart α → Sort u} → (t : PosPart α) → ((posPart : α → α) → motive { posPart := posPart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : PosPart α → Sort u} → (t : PosPart α) → ((posPart : α → α) → motive { posPart := posPart }) → motive t","typeReferences":[["PosPart","mk"],["PosPart"]],"valueReferences":[["PosPart","rec"]]},{"isProp":false,"kind":"definition","name":["LeOnePart","leOnePart"],"typeFallback":"forall {α : Type.{u_1}} [self : LeOnePart.{u_1} α], α -> α","typeFull":"{α : Type u_1} → [self : LeOnePart α] → α → α","typeReadable":"{α : Type u_1} → [self : LeOnePart α] → α → α","typeReferences":[["LeOnePart"]],"valueReferences":[]},{"isProp":false,"kind":"definition","name":["OneLePart","noConfusionType"],"typeFallback":"Sort.{u} -> (forall {α : Type.{u_1}}, (OneLePart.{u_1} α) -> (forall {α' : Type.{u_1}}, (OneLePart.{u_1} α') -> Sort.{u}))","typeFull":"Sort u → {α : Type u_1} → OneLePart α → {α' : Type u_1} → OneLePart α' → Sort u","typeReadable":"Sort u → {α : Type u_1} → OneLePart α → {α' : Type u_1} → OneLePart α' → Sort u","typeReferences":[["OneLePart"]],"valueReferences":[["HEq"],["OneLePart","casesOn"]]},{"isProp":false,"kind":"definition","name":["PosPart","mk","noConfusion"],"typeFallback":"forall {α : Type.{u_1}} {P : Sort.{u}} {posPart : α -> α} {posPart' : α -> α}, (Eq.{succ u_1} (PosPart.{u_1} α) (PosPart.mk.{u_1} α posPart) (PosPart.mk.{u_1} α posPart')) -> ((HEq.{succ u_1} (α -> α) posPart (α -> α) posPart') -> P) -> P","typeFull":"{α : Type u_1} →\n  {P : Sort u} →\n    {posPart posPart' : α → α} → { posPart := posPart } = { posPart := posPart' } → (posPart ≍ posPart' → P) → P","typeReadable":"{α : Type u_1} →\n  {P : Sort u} →\n    {posPart posPart' : α → α} → { posPart := posPart } = { posPart := posPart' } → (posPart ≍ posPart' → P) → P","typeReferences":[["HEq"],["PosPart","mk"],["PosPart"],["Eq"]],"valueReferences":[["Eq","refl"],["id"],["PosPart","mk"],["PosPart","noConfusion"],["heq_of_eq"],["PosPart"]]},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___macroRules_term_⁺_1"],"typeFallback":"Lean.Macro","typeFull":"Lean.Macro","typeReadable":"Lean.Macro","typeReferences":[["Lean","Macro"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Lean","Macro","State"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","Syntax","ident"],["String"],["Lean","Macro","Context"],["Lean","Macro","Exception","unsupportedSyntax"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["Lean","Syntax","Preresolved"],["List","cons"],["Bool","true"],["Lean","Syntax","Preresolved","decl"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","Macro","instMonadQuotationMacroM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Bool"],["Applicative","toPure"],["ReaderT","instMonadExceptOf"],["EStateM"],["String","toRawSubstring'"],["Lean","Syntax","isOfKind"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Lean","addMacroScope"],["Lean","MacroM"],["Eq"],["Lean","Name","mkStr2"],["Lean","Syntax","node2"],["EStateM","instMonadExceptOfOfBacktrackable"],["Bind","bind"],["List","nil"],["Lean","Name","mkStr1"],["ite"],["Lean","Syntax","node1"],["Lean","Macro","instMonadRefMacroM"],["Lean","Macro","Exception"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"definition","name":["OneLePart","noConfusion"],"typeFallback":"forall {P : Sort.{u}} {α : Type.{u_1}} {t : OneLePart.{u_1} α} {α' : Type.{u_1}} {t' : OneLePart.{u_1} α'}, (Eq.{succ (succ u_1)} Type.{u_1} α α') -> (HEq.{succ u_1} (OneLePart.{u_1} α) t (OneLePart.{u_1} α') t') -> (OneLePart.noConfusionType.{u, u_1} P α t α' t')","typeFull":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : OneLePart α} → {α' : Type u_1} → {t' : OneLePart α'} → α = α' → t ≍ t' → OneLePart.noConfusionType P t t'","typeReadable":"{P : Sort u} →\n  {α : Type u_1} →\n    {t : OneLePart α} → {α' : Type u_1} → {t' : OneLePart α'} → α = α' → t ≍ t' → OneLePart.noConfusionType P t t'","typeReferences":[["OneLePart","noConfusionType"],["HEq"],["Eq"],["OneLePart"]],"valueReferences":[["OneLePart","noConfusionType"],["HEq","refl"],["eq_of_heq"],["HEq"],["OneLePart","casesOn"],["Eq","ndrec"],["OneLePart"]]},{"isProp":false,"kind":"constructor","name":["PosPart","mk"],"typeFallback":"forall {α : Type.{u_1}}, (α -> α) -> (PosPart.{u_1} α)","typeFull":"{α : Type u_1} → (α → α) → PosPart α","typeReadable":"{α : Type u_1} → (α → α) → PosPart α","typeReferences":[["PosPart"]],"valueReferences":null},{"isProp":false,"kind":"definition","name":["PosPart","noConfusionType"],"typeFallback":"Sort.{u} -> (forall {α : Type.{u_1}}, (PosPart.{u_1} α) -> (forall {α' : Type.{u_1}}, (PosPart.{u_1} α') -> Sort.{u}))","typeFull":"Sort u → {α : Type u_1} → PosPart α → {α' : Type u_1} → PosPart α' → Sort u","typeReadable":"Sort u → {α : Type u_1} → PosPart α → {α' : Type u_1} → PosPart α' → Sort u","typeReferences":[["PosPart"]],"valueReferences":[["PosPart","casesOn"],["HEq"]]},{"isProp":false,"kind":"definition","name":["_aux_Mathlib_Algebra_Notation___macroRules_term_⁻_1"],"typeFallback":"Lean.Macro","typeFull":"Lean.Macro","typeReadable":"Lean.Macro","typeReferences":[["Lean","Macro"]],"valueReferences":[["Lean","Name"],["Lean","TSyntax","raw"],["Lean","Macro","State"],["Lean","MonadQuotation","getCurrMacroScope"],["Lean","MacroScope"],["Lean","SourceInfo"],["Lean","Syntax","ident"],["String"],["Lean","Macro","Context"],["Lean","Macro","Exception","unsupportedSyntax"],["Lean","MonadRef","mkInfoFromRefPos"],["ReaderT","instApplicativeOfMonad"],["Lean","Syntax","Preresolved"],["List","cons"],["Bool","true"],["Lean","Syntax","Preresolved","decl"],["MonadExcept","throw"],["Lean","Name","mkStr4"],["Lean","SyntaxNodeKind"],["Lean","TSyntax","mk"],["EStateM","instMonad"],["Lean","Macro","instMonadQuotationMacroM"],["instMonadExceptOfMonadExceptOf"],["Lean","Syntax"],["instDecidableEqBool"],["Nat"],["Monad","toBind"],["Bool"],["Applicative","toPure"],["ReaderT","instMonadExceptOf"],["EStateM"],["String","toRawSubstring'"],["Lean","Syntax","isOfKind"],["PUnit"],["instOfNatNat"],["Lean","MonadQuotation","getContext"],["Lean","addMacroScope"],["Lean","MacroM"],["Eq"],["Lean","Name","mkStr2"],["Lean","Syntax","node2"],["EStateM","instMonadExceptOfOfBacktrackable"],["Bind","bind"],["List","nil"],["Lean","Name","mkStr1"],["ite"],["Lean","Syntax","node1"],["Lean","Macro","instMonadRefMacroM"],["Lean","Macro","Exception"],["ReaderT","instMonad"],["OfNat","ofNat"],["EStateM","nonBacktrackable"],["Lean","Syntax","getArg"],["Pure","pure"]]},{"isProp":false,"kind":"definition","name":["NegPart","mk","noConfusion"],"typeFallback":"forall {α : Type.{u_1}} {P : Sort.{u}} {negPart : �� -> α} {negPart' : α -> α}, (Eq.{succ u_1} (NegPart.{u_1} α) (NegPart.mk.{u_1} α negPart) (NegPart.mk.{u_1} α negPart')) -> ((HEq.{succ u_1} (α -> α) negPart (α -> α) negPart') -> P) -> P","typeFull":"{α : Type u_1} →\n  {P : Sort u} →\n    {negPart negPart' : α → α} → { negPart := negPart } = { negPart := negPart' } → (negPart ≍ negPart' → P) → P","typeReadable":"{α : Type u_1} →\n  {P : Sort u} →\n    {negPart negPart' : α → α} → { negPart := negPart } = { negPart := negPart' } → (negPart ≍ negPart' → P) → P","typeReferences":[["HEq"],["NegPart","mk"],["NegPart"],["Eq"]],"valueReferences":[["Eq","refl"],["NegPart","mk"],["id"],["NegPart","noConfusion"],["NegPart"],["heq_of_eq"]]},{"isProp":false,"kind":"definition","name":["PosPart","posPart"],"typeFallback":"forall {α : Type.{u_1}} [self : PosPart.{u_1} α], α -> α","typeFull":"{α : Type u_1} → [self : PosPart α] → α → α","typeReadable":"{α : Type u_1} → [self : PosPart α] → α → α","typeReferences":[["PosPart"]],"valueReferences":[]},{"isProp":false,"kind":"definition","name":["LeOnePart","recOn"],"typeFallback":"forall {α : Type.{u_1}} {motive : (LeOnePart.{u_1} α) -> Sort.{u}} (t : LeOnePart.{u_1} α), (forall (leOnePart : α -> α), motive (LeOnePart.mk.{u_1} α leOnePart)) -> (motive t)","typeFull":"{α : Type u_1} →\n  {motive : LeOnePart α → Sort u} →\n    (t : LeOnePart α) → ((leOnePart : α → α) → motive { leOnePart := leOnePart }) → motive t","typeReadable":"{α : Type u_1} →\n  {motive : LeOnePart α → Sort u} →\n    (t : LeOnePart α) → ((leOnePart : α → α) → motive { leOnePart := leOnePart }) → motive t","typeReferences":[["LeOnePart"],["LeOnePart","mk"]],"valueReferences":[["LeOnePart","rec"]]},{"isProp":false,"kind":"inductive","name":["LeOnePart"],"typeFallback":"Type.{u_1} -> Type.{u_1}","typeFull":"Type u_1 → Type u_1","typeReadable":"Type u_1 → Type u_1","typeReferences":[],"valueReferences":null}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Module.HahnEmbedding.sym.json

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:bd016e82902695a0d94cf406a18c530b69c490ee7b4bffeead1fb1b69dc23e0c
+size 71007724

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Monoid.NatCast.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["zero_lt_two"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 2","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 2","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["one_le_two"],["LT","lt","trans_le"],["instOfNatAtLeastTwo"],["zero_lt_one"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["Nat","instNeZeroSucc"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["instOfNatNat"],["AddMonoidWithOne","toOne"],["Zero","toOfNat0"],["Preorder","toLE"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["one_lt_two"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.18 : AddLeftStrictMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3))) (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4081984041._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1]\n  [AddLeftStrictMono α], 1 < 2","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1]\n  [AddLeftStrictMono α], 1 < 2","typeReferences":[["PartialOrder","toPreorder"],["AddLeftStrictMono"],["instOfNatAtLeastTwo"],["Preorder","toLT"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["LT","lt"],["NeZero"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["PartialOrder"],["AddMonoidWithOne","toOne"],["Preorder","toLE"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddSemigroup","toAdd"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["congrArg"],["Nat","instNeZeroSucc"],["instOfNatNat"],["Eq","symm"],["Eq"],["AddSemigroup","toAdd"],["instHAdd"],["instOfNatAtLeastTwo"],["OfNat","ofNat"],["LT","lt"],["HAdd","hAdd"],["Nat"],["lt_add_one"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["id"],["Eq","mpr"],["one_add_one_eq_two"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["four_pos"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 4 (instOfNatAtLeastTwo.{u_1} α 4 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 4","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 4","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["zero_lt_four"]]},{"isProp":true,"kind":"theorem","name":["one_le_two'"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.6 : LE.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.6] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.12 : AddRightMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.3))) inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.6], LE.le.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.6 (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.3))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3379666876._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : LE α] [ZeroLEOneClass α] [AddRightMono α], 1 ≤ 2","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : LE α] [ZeroLEOneClass α] [AddRightMono α], 1 ≤ 2","typeReferences":[["instOfNatAtLeastTwo"],["LE"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["AddRightMono"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["LE","le"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"],["AddSemigroup","toAdd"]],"valueReferences":[["Trans","trans"],["AddMonoidWithOne","toAddMonoid"],["Nat","instNeZeroSucc"],["instOfNatNat"],["Eq","symm"],["Zero","toOfNat0"],["Eq"],["AddSemigroup","toAdd"],["instTransEq"],["instHAdd"],["zero_le_one"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["OfNat","ofNat"],["HAdd","hAdd"],["zero_add"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["LE","le"],["one_add_one_eq_two"],["add_le_add_left"],["instTransEq_1"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_three","_simp_1"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6))], Eq.{1} Prop (LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 3 (instOfNatAtLeastTwo.{u_1} α 3 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) True","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  (0 < 3) = True","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  (0 < 3) = True","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["Nat","instNeZeroSucc"],["NeZero"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["True"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["Preorder","toLT"],["instOfNatAtLeastTwo"],["eq_true"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["Nat","instNeZeroSucc"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["Zero","toOfNat0"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["zero_lt_three"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_four","_simp_1"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6))], Eq.{1} Prop (LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 4 (instOfNatAtLeastTwo.{u_1} α 4 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))) True","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  (0 < 4) = True","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  (0 < 4) = True","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["Nat","instNeZeroSucc"],["NeZero"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["True"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["Preorder","toLT"],["instOfNatAtLeastTwo"],["eq_true"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["Nat","instNeZeroSucc"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["zero_lt_four"],["Zero","toOfNat0"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["ZeroLEOneClass","neZero","two"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.6))], NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1549619166._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  NeZero 2","typeReadable":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  NeZero 2","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["NeZero"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["PartialOrder"],["AddMonoidWithOne","toOne"],["Preorder","toLE"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddSemigroup","toAdd"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["zero_lt_two"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["Nat","instNeZeroSucc"],["Nat"],["LT","lt","ne'"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["Zero","toOfNat0"],["NeZero","mk"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["lt_add_one"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.3 : One.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.6 : AddZeroClass.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.9 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.12 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.6)) inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.3 (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.9))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.15 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.3))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.21 : AddLeftStrictMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.6)) (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.9))] (a : α), LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.9)) a (HAdd.hAdd.{u_1, u_1, u_1} α α α (instHAdd.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.6))) a (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1156345328._hygCtx._hyg.3)))","typeFull":"∀ {α : Type u_1} [inst : One α] [inst_1 : AddZeroClass α] [inst_2 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1]\n  [AddLeftStrictMono α] (a : α), a < a + 1","typeReadable":"∀ {α : Type u_1} [inst : One α] [inst_1 : AddZeroClass α] [inst_2 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1]\n  [AddLeftStrictMono α] (a : α), a < a + 1","typeReferences":[["PartialOrder","toPreorder"],["AddZeroClass"],["instHAdd"],["AddLeftStrictMono"],["Preorder","toLT"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["OfNat","ofNat"],["ZeroLEOneClass"],["HAdd","hAdd"],["LT","lt"],["NeZero"],["One","toOfNat1"],["PartialOrder"],["One"],["Preorder","toLE"],["AddZero","toZero"]],"valueReferences":[["lt_add_of_pos_right"],["PartialOrder","toPreorder"],["One","toOfNat1"],["Preorder","toLT"],["zero_lt_one"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["zero_le_three"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.6 : Preorder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.3) (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.12 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.6)], LE.le.{u_1} α (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.6) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 3 (instOfNatAtLeastTwo.{u_1} α 3 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.4243974995._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : Preorder α] [ZeroLEOneClass α] [AddLeftMono α], 0 ≤ 3","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : Preorder α] [ZeroLEOneClass α] [AddLeftMono α], 0 ≤ 3","typeReferences":[["AddLeftMono"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["Nat"],["Preorder"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["LE","le"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"],["AddSemigroup","toAdd"]],"valueReferences":[["AddMonoidWithOne","toAddMonoid"],["congrArg"],["Nat","instNeZeroSucc"],["zero_le_two"],["instOfNatNat"],["Eq","symm"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddSemigroup","toAdd"],["add_nonneg"],["instHAdd"],["zero_le_one"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["LE","le"],["AddMonoidWithOne","toOne"],["id"],["Eq","mpr"],["AddZero","toZero"],["two_add_one_eq_three"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_le_four"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.6 : Preorder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.3) (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.12 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.6)], LE.le.{u_1} α (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.6) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 4 (instOfNatAtLeastTwo.{u_1} α 4 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2360619316._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : Preorder α] [ZeroLEOneClass α] [AddLeftMono α], 0 ≤ 4","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : Preorder α] [ZeroLEOneClass α] [AddLeftMono α], 0 ≤ 4","typeReferences":[["AddLeftMono"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["Nat"],["Preorder"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["LE","le"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"],["AddSemigroup","toAdd"]],"valueReferences":[["AddMonoidWithOne","toAddMonoid"],["congrArg"],["Nat","instNeZeroSucc"],["three_add_one_eq_four"],["instOfNatNat"],["Eq","symm"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddSemigroup","toAdd"],["add_nonneg"],["instHAdd"],["zero_le_three"],["zero_le_one"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["LE","le"],["AddMonoidWithOne","toOne"],["id"],["Eq","mpr"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["lt_one_add"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.3 : One.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.6 : AddZeroClass.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.9 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.12 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.6)) inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.3 (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.9))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.15 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.3))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.21 : AddRightStrictMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.6)) (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.9))] (a : α), LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.9)) a (HAdd.hAdd.{u_1, u_1, u_1} α α α (instHAdd.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} �� inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.6))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3708908048._hygCtx._hyg.3)) a)","typeFull":"∀ {α : Type u_1} [inst : One α] [inst_1 : AddZeroClass α] [inst_2 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1]\n  [AddRightStrictMono α] (a : α), a < 1 + a","typeReadable":"∀ {α : Type u_1} [inst : One α] [inst_1 : AddZeroClass α] [inst_2 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1]\n  [AddRightStrictMono α] (a : α), a < 1 + a","typeReferences":[["PartialOrder","toPreorder"],["AddZeroClass"],["AddRightStrictMono"],["instHAdd"],["Preorder","toLT"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["OfNat","ofNat"],["ZeroLEOneClass"],["HAdd","hAdd"],["LT","lt"],["NeZero"],["One","toOfNat1"],["PartialOrder"],["One"],["Preorder","toLE"],["AddZero","toZero"]],"valueReferences":[["lt_add_of_pos_left"],["PartialOrder","toPreorder"],["One","toOfNat1"],["Preorder","toLT"],["zero_lt_one"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["one_le_two"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.6 : LE.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.3) inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.6] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.12 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.3))) inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.6], LE.le.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.6 (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.3))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.84535035._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : LE α] [ZeroLEOneClass α] [AddLeftMono α], 1 ≤ 2","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : LE α] [ZeroLEOneClass α] [AddLeftMono α], 1 ≤ 2","typeReferences":[["AddLeftMono"],["instOfNatAtLeastTwo"],["LE"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["LE","le"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"],["AddSemigroup","toAdd"]],"valueReferences":[["Trans","trans"],["AddMonoidWithOne","toAddMonoid"],["add_le_add_right"],["Nat","instNeZeroSucc"],["instOfNatNat"],["Eq","symm"],["Zero","toOfNat0"],["Eq"],["AddSemigroup","toAdd"],["instTransEq"],["instHAdd"],["zero_le_one"],["instOfNatAtLeastTwo"],["add_zero"],["AddZeroClass","toAddZero"],["AddZero","toAdd"],["OfNat","ofNat"],["HAdd","hAdd"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["LE","le"],["one_add_one_eq_two"],["instTransEq_1"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["two_pos"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 2","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 2","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["zero_lt_two"]]},{"isProp":true,"kind":"theorem","name":["ZeroLEOneClass","neZero","three"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.6))], NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 3 (instOfNatAtLeastTwo.{u_1} α 3 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1219813011._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))","typeFull":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  NeZero 3","typeReadable":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  NeZero 3","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["NeZero"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["PartialOrder"],["AddMonoidWithOne","toOne"],["Preorder","toLE"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddSemigroup","toAdd"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["Nat","instNeZeroSucc"],["Nat"],["LT","lt","ne'"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["Zero","toOfNat0"],["NeZero","mk"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["zero_lt_three"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_three"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 3 (instOfNatAtLeastTwo.{u_1} α 3 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 3","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 3","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["congrArg"],["Nat","instNeZeroSucc"],["instOfNatNat"],["Eq","symm"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddSemigroup","toAdd"],["zero_lt_two"],["instHAdd"],["zero_le_one"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["lt_add_of_lt_of_nonneg"],["LT","lt"],["HAdd","hAdd"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["id"],["Eq","mpr"],["AddZero","toZero"],["two_add_one_eq_three"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_four'"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 4 (instOfNatAtLeastTwo.{u_1} α 4 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1579489717._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))","typeFull":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 4","typeReadable":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 4","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["zero_lt_four"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_four"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 4 (instOfNatAtLeastTwo.{u_1} α 4 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.547678994._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 4","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 4","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["congrArg"],["Nat","instNeZeroSucc"],["three_add_one_eq_four"],["instOfNatNat"],["Eq","symm"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddSemigroup","toAdd"],["instHAdd"],["zero_le_one"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["lt_add_of_lt_of_nonneg"],["LT","lt"],["HAdd","hAdd"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["id"],["Eq","mpr"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["zero_lt_three"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_three'"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 3 (instOfNatAtLeastTwo.{u_1} α 3 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2934838091._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))","typeFull":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 3","typeReadable":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 3","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["zero_lt_three"]]},{"isProp":true,"kind":"theorem","name":["zero_le_two"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.6 : Preorder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.3) (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.12 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.6)], LE.le.{u_1} α (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.6) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.2166042573._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : Preorder α] [ZeroLEOneClass α] [AddLeftMono α], 0 ≤ 2","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : Preorder α] [ZeroLEOneClass α] [AddLeftMono α], 0 ≤ 2","typeReferences":[["AddLeftMono"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["Nat"],["Preorder"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["LE","le"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"],["AddSemigroup","toAdd"]],"valueReferences":[["AddMonoidWithOne","toAddMonoid"],["congrArg"],["Nat","instNeZeroSucc"],["instOfNatNat"],["Eq","symm"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddSemigroup","toAdd"],["add_nonneg"],["instHAdd"],["zero_le_one"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["HAdd","hAdd"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["LE","le"],["AddMonoidWithOne","toOne"],["id"],["one_add_one_eq_two"],["Eq","mpr"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_two","_simp_1"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6))], Eq.{1} Prop (LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3260382110._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) True","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  (0 < 2) = True","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  (0 < 2) = True","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["Nat","instNeZeroSucc"],["NeZero"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["Eq"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["True"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["zero_lt_two"],["Preorder","toLT"],["instOfNatAtLeastTwo"],["eq_true"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["Nat","instNeZeroSucc"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["Zero","toOfNat0"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["three_pos"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 3 (instOfNatAtLeastTwo.{u_1} α 3 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.1213290486._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))","typeFull":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 3","typeReadable":"∀ {α : Type u_1} [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 3","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["zero_lt_three"]]},{"isProp":true,"kind":"theorem","name":["ZeroLEOneClass","neZero","four"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.6))], NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 4 (instOfNatAtLeastTwo.{u_1} α 4 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.553726029._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))))","typeFull":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  NeZero 4","typeReadable":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  NeZero 4","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["ZeroLEOneClass"],["Nat","instNeZeroSucc"],["NeZero"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["instOfNatNat"],["AddMonoid","toAddSemigroup"],["PartialOrder"],["AddMonoidWithOne","toOne"],["Preorder","toLE"],["AddMonoidWithOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddSemigroup","toAdd"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["PartialOrder","toPreorder"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["AddMonoidWithOne","toAddMonoid"],["OfNat","ofNat"],["Nat","instNeZeroSucc"],["Nat"],["LT","lt","ne'"],["AddMonoidWithOne","toNatCast"],["instOfNatNat"],["zero_lt_four"],["Zero","toOfNat0"],["NeZero","mk"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["zero_lt_two'"],"typeFallback":"forall (α : Type.{u_1}) [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3 : AddMonoidWithOne.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.9 : ZeroLEOneClass.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3)))) (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.12 : NeZero.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} α 1 (One.toOfNat1.{u_1} α (AddMonoidWithOne.toOne.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3)))] [inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.18 : AddLeftMono.{u_1} α (AddSemigroup.toAdd.{u_1} α (AddMonoid.toAddSemigroup.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.6))], LT.lt.{u_1} α (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddMonoidWithOne.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3)))))) (OfNat.ofNat.{u_1} α 2 (instOfNatAtLeastTwo.{u_1} α 2 (AddMonoidWithOne.toNatCast.{u_1} α inst._@.Mathlib.Algebra.Order.Monoid.NatCast.3973041923._hygCtx._hyg.3) (Nat.instAtLeastTwoHAddOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (Nat.instNeZeroSucc (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))","typeFull":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 2","typeReadable":"∀ (α : Type u_1) [inst : AddMonoidWithOne α] [inst_1 : PartialOrder α] [ZeroLEOneClass α] [NeZero 1] [AddLeftMono α],\n  0 < 2","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Preorder","toLT"],["AddMonoidWithOne","toAddMonoid"],["NeZero"],["Nat","instNeZeroSucc"],["instOfNatNat"],["PartialOrder"],["Zero","toOfNat0"],["Preorder","toLE"],["AddMonoidWithOne"],["AddSemigroup","toAdd"],["instOfNatAtLeastTwo"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["ZeroLEOneClass"],["LT","lt"],["Nat"],["AddMonoidWithOne","toNatCast"],["One","toOfNat1"],["AddMonoid","toAddSemigroup"],["AddMonoidWithOne","toOne"],["AddZero","toZero"],["Nat","instAtLeastTwoHAddOfNat"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["zero_lt_two"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Monoid.OrderDual.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["OrderDual","isOrderedAddMonoid"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.3 : AddCommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.9 : IsOrderedAddMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.6], IsOrderedAddMonoid.{u} (OrderDual.{u} α) (OrderDual.instAddCommMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.3) (OrderDual.instPreorder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.6)","typeFull":"∀ {α : Type u} [inst : AddCommMonoid α] [inst_1 : Preorder α] [IsOrderedAddMonoid α], IsOrderedAddMonoid αᵒᵈ","typeReadable":"∀ {α : Type u} [inst : AddCommMonoid α] [inst_1 : Preorder α] [IsOrderedAddMonoid α], IsOrderedAddMonoid αᵒᵈ","typeReferences":[["OrderDual","instPreorder"],["OrderDual"],["Preorder"],["AddCommMonoid"],["OrderDual","instAddCommMonoid"],["IsOrderedAddMonoid"]],"valueReferences":[["IsOrderedAddMonoid","mk"],["OrderDual"],["IsOrderedMonoid","_proof_1","_to_additive_1"],["OrderDual","instAdd"],["OrderDual","instAddCommMonoid"],["IsOrderedAddMonoid","toAddLeftMono"],["AddCommMonoid","toAddMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["OrderDual","addRightMono"],["OrderDual","instPreorder"],["AddCommMonoid","toAddCommSemigroup"],["LE","le"],["add_le_add_left"],["Preorder","toLE"],["covariant_swap_add_of_covariant_add"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["OrderDual","isOrderedMonoid"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.3 : CommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.9 : IsOrderedMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.6], IsOrderedMonoid.{u} (OrderDual.{u} α) (OrderDual.instCommMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.3) (OrderDual.instPreorder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.4051453974._hygCtx._hyg.6)","typeFull":"∀ {α : Type u} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedMonoid α], IsOrderedMonoid αᵒᵈ","typeReadable":"∀ {α : Type u} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedMonoid α], IsOrderedMonoid αᵒᵈ","typeReferences":[["OrderDual","instPreorder"],["OrderDual"],["Preorder"],["OrderDual","instCommMonoid"],["IsOrderedMonoid"],["CommMonoid"]],"valueReferences":[["MulOneClass","toMulOne"],["OrderDual"],["CommMonoid","toMonoid"],["covariant_swap_mul_of_covariant_mul"],["mul_le_mul_left"],["OrderDual","mulRightMono"],["OrderDual","instMul"],["IsOrderedMonoid","_proof_1"],["OrderDual","instPreorder"],["MulOne","toMul"],["OrderDual","instCommMonoid"],["CommMonoid","toCommSemigroup"],["LE","le"],["Monoid","toMulOneClass"],["IsOrderedMonoid","mk"],["IsOrderedMonoid","toMulLeftMono"],["Preorder","toLE"]]},{"isProp":true,"kind":"theorem","name":["OrderDual","isOrderedAddCancelMonoid"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.3 : AddCommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.9 : IsOrderedCancelAddMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.6], IsOrderedCancelAddMonoid.{u} (OrderDual.{u} α) (OrderDual.instAddCommMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.3) (OrderDual.instPreorder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.6)","typeFull":"∀ {α : Type u} [inst : AddCommMonoid α] [inst_1 : Preorder α] [IsOrderedCancelAddMonoid α], IsOrderedCancelAddMonoid αᵒᵈ","typeReadable":"∀ {α : Type u} [inst : AddCommMonoid α] [inst_1 : Preorder α] [IsOrderedCancelAddMonoid α], IsOrderedCancelAddMonoid αᵒᵈ","typeReferences":[["OrderDual","instPreorder"],["OrderDual"],["Preorder"],["AddCommMonoid"],["OrderDual","instAddCommMonoid"],["IsOrderedCancelAddMonoid"]],"valueReferences":[["OrderDual"],["IsOrderedCancelAddMonoid","mk"],["le_of_add_le_add_left"],["OrderDual","instAddCommMonoid"],["IsOrderedCancelMonoid","_proof_1","_to_additive_1"],["OrderDual","isOrderedAddMonoid"],["AddCommMonoid","toAddMonoid"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["OrderDual","addLeftReflectLE"],["OrderDual","instPreorder"],["AddMonoid","toAddSemigroup"],["IsOrderedCancelAddMonoid","toAddLeftReflectLE"],["IsOrderedCancelAddMonoid","toIsOrderedAddMonoid"],["Preorder","toLE"],["AddSemigroup","toAdd"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["OrderDual","isOrderedCancelMonoid"],"typeFallback":"forall {α : Type.{u}} [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.3 : CommMonoid.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.6 : Preorder.{u} α] [inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.9 : IsOrderedCancelMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.3 inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.6], IsOrderedCancelMonoid.{u} (OrderDual.{u} α) (OrderDual.instCommMonoid.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.3) (OrderDual.instPreorder.{u} α inst._@.Mathlib.Algebra.Order.Monoid.OrderDual.2396638665._hygCtx._hyg.6)","typeFull":"∀ {α : Type u} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedCancelMonoid α], IsOrderedCancelMonoid αᵒᵈ","typeReadable":"∀ {α : Type u} [inst : CommMonoid α] [inst_1 : Preorder α] [IsOrderedCancelMonoid α], IsOrderedCancelMonoid αᵒᵈ","typeReferences":[["OrderDual","instPreorder"],["OrderDual"],["Preorder"],["OrderDual","instCommMonoid"],["IsOrderedCancelMonoid"],["CommMonoid"]],"valueReferences":[["MulOneClass","toMulOne"],["OrderDual"],["OrderDual","mulLeftReflectLE"],["CommMonoid","toMonoid"],["IsOrderedCancelMonoid","_proof_1"],["OrderDual","isOrderedMonoid"],["Semigroup","toMul"],["IsOrderedCancelMonoid","mk"],["OrderDual","instPreorder"],["MulOne","toMul"],["OrderDual","instCommMonoid"],["IsOrderedCancelMonoid","toMulLeftReflectLE"],["Monoid","toMulOneClass"],["Monoid","toSemigroup"],["le_of_mul_le_mul_left'"],["Preorder","toLE"],["IsOrderedCancelMonoid","toIsOrderedMonoid"]]}]

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Ring.Finset.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["Nat","cast_finsetSup"],"typeFallback":"forall {ι : Type.{u_1}} {R : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7 : LinearOrder.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.10 : IsStrictOrderedRing.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4 (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))))] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.15 : OrderBot.{u_2} R (Preorder.toLE.{u_2} R (PartialOrder.toPreorder.{u_2} R (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))))))] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.18 : CanonicallyOrderedAdd.{u_2} R (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4)))) (Preorder.toLE.{u_2} R (PartialOrder.toPreorder.{u_2} R (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))))))] (s : Finset.{u_1} ι) (f : ι -> Nat), Eq.{succ u_2} R (Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4)))) (Finset.sup.{0, u_1} Nat ι (Lattice.toSemilatticeSup.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)) Nat.instOrderBot s f)) (Finset.sup.{u_2, u_1} R ι (Lattice.toSemilatticeSup.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))) inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.15 s (fun (i : ι) => Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4)))) (f i)))","typeFull":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R]\n  [inst_3 : OrderBot R] [CanonicallyOrderedAdd R] (s : Finset ι) (f : ι → ℕ), ↑(s.sup f) = s.sup fun i => ↑(f i)","typeReadable":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R]\n  [inst_3 : OrderBot R] [CanonicallyOrderedAdd R] (s : Finset ι) (f : ι → ℕ), ↑(s.sup f) = s.sup fun i => ↑(f i)","typeReferences":[["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["Finset"],["Nat","cast"],["CanonicallyOrderedAdd"],["instDistribLatticeOfLinearOrder"],["Semiring","toNonAssocSemiring"],["Finset","sup"],["Nat","instOrderBot"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Preorder","toLE"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["OrderBot"],["SemilatticeInf","toPartialOrder"],["Distrib","toAdd"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["NonUnitalNonAssocSemiring","toDistrib"],["instDistribLatticeNat"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearOrder"],["Nat"],["DistribLattice","toLattice"],["AddMonoidWithOne","toNatCast"],["Semiring"]],"valueReferences":[["Lattice","toSemilatticeSup"],["Finset","comp_sup_eq_sup_comp"],["Nat","cast"],["PartialOrder","toPreorder"],["Eq","trans"],["SemilatticeSup","toPartialOrder"],["AddMonoidWithOne","toAddMonoid"],["congrArg"],["instDistribLatticeOfLinearOrder"],["Semiring","toNonAssocSemiring"],["congr"],["Nat","cast_max"],["Nat","instOrderBot"],["Zero","toOfNat0"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["OrderBot","toBot"],["Eq"],["Preorder","toLE"],["NonAssocSemiring","toAddCommMonoidWithOne"],["bot_eq_zero'"],["True"],["instDistribLatticeNat"],["AddZeroClass","toAddZero"],["Bot","bot"],["OfNat","ofNat"],["eq_self"],["Nat"],["AddMonoidWithOne","toNatCast"],["DistribLattice","toLattice"],["of_eq_true"],["Nat","cast_zero"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Nat","cast_finsetInf'"],"typeFallback":"forall {ι : Type.{u_1}} {R : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.7 : LinearOrder.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.10 : IsStrictOrderedRing.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4 (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.7))))] {s : Finset.{u_1} ι} (f : ι -> Nat) (hs : Finset.Nonempty.{u_1} ι s), Eq.{succ u_2} R (Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4)))) (Finset.inf'.{0, u_1} Nat ι (Lattice.toSemilatticeInf.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)) s hs f)) (Finset.inf'.{u_2, u_1} R ι (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.7))) s hs (fun (i : ι) => Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4)))) (f i)))","typeFull":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), ↑(s.inf' hs f) = s.inf' hs fun i => ↑(f i)","typeReadable":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), ↑(s.inf' hs f) = s.inf' hs fun i => ↑(f i)","typeReferences":[["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Finset"],["Nat","cast"],["instDistribLatticeNat"],["LinearOrder"],["instDistribLatticeOfLinearOrder"],["Nat"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["AddMonoidWithOne","toNatCast"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Finset","Nonempty"],["Finset","inf'"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["instDistribLatticeOfLinearOrder"],["Nat"],["Semiring","toNonAssocSemiring"],["AddMonoidWithOne","toNatCast"],["Nat","cast"],["DistribLattice","toLattice"],["Lattice","toSemilatticeInf"],["instDistribLatticeNat"],["Nat","cast_min"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Finset","comp_inf'_eq_inf'_comp"],["NonAssocSemiring","toAddCommMonoidWithOne"]]},{"isProp":true,"kind":"theorem","name":["Nat","cast_finsetSup'","_simp_1"],"typeFallback":"forall {ι : Type.{u_1}} {R : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.7 : LinearOrder.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.10 : IsStrictOrderedRing.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4 (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.7))))] {s : Finset.{u_1} ι} (f : ι -> Nat) (hs : Finset.Nonempty.{u_1} ι s), Eq.{succ u_2} R (Finset.sup'.{u_2, u_1} R ι (Lattice.toSemilatticeSup.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.7))) s hs (fun (i : ι) => Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4)))) (f i))) (Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4)))) (Finset.sup'.{0, u_1} Nat ι (Lattice.toSemilatticeSup.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)) s hs f))","typeFull":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), (s.sup' hs fun i => ↑(f i)) = ↑(s.sup' hs f)","typeReadable":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), (s.sup' hs fun i => ↑(f i)) = ↑(s.sup' hs f)","typeReferences":[["Lattice","toSemilatticeSup"],["Nat","cast"],["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Finset"],["Finset","sup'"],["instDistribLatticeNat"],["LinearOrder"],["instDistribLatticeOfLinearOrder"],["Nat"],["Semiring","toNonAssocSemiring"],["AddMonoidWithOne","toNatCast"],["DistribLattice","toLattice"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Finset","Nonempty"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["Lattice","toSemilatticeSup"],["Nat","cast"],["Finset","sup'"],["instDistribLatticeNat"],["Nat","cast_finsetSup'"],["instDistribLatticeOfLinearOrder"],["Nat"],["AddMonoidWithOne","toNatCast"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["Eq","symm"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"]]},{"isProp":true,"kind":"theorem","name":["Nat","cast_finsetSup","_simp_1"],"typeFallback":"forall {ι : Type.{u_1}} {R : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7 : LinearOrder.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.10 : IsStrictOrderedRing.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4 (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))))] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.15 : OrderBot.{u_2} R (Preorder.toLE.{u_2} R (PartialOrder.toPreorder.{u_2} R (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))))))] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.18 : CanonicallyOrderedAdd.{u_2} R (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4)))) (Preorder.toLE.{u_2} R (PartialOrder.toPreorder.{u_2} R (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))))))] (s : Finset.{u_1} ι) (f : ι -> Nat), Eq.{succ u_2} R (Finset.sup.{u_2, u_1} R ι (Lattice.toSemilatticeSup.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.7))) inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.15 s (fun (i : ι) => Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4)))) (f i))) (Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1246991123._hygCtx._hyg.4)))) (Finset.sup.{0, u_1} Nat ι (Lattice.toSemilatticeSup.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)) Nat.instOrderBot s f))","typeFull":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R]\n  [inst_3 : OrderBot R] [CanonicallyOrderedAdd R] (s : Finset ι) (f : ι → ℕ), (s.sup fun i => ↑(f i)) = ↑(s.sup f)","typeReadable":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R]\n  [inst_3 : OrderBot R] [CanonicallyOrderedAdd R] (s : Finset ι) (f : ι → ℕ), (s.sup fun i => ↑(f i)) = ↑(s.sup f)","typeReferences":[["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["Finset"],["Nat","cast"],["CanonicallyOrderedAdd"],["instDistribLatticeOfLinearOrder"],["Semiring","toNonAssocSemiring"],["Finset","sup"],["Nat","instOrderBot"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Preorder","toLE"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["OrderBot"],["SemilatticeInf","toPartialOrder"],["Distrib","toAdd"],["Lattice","toSemilatticeInf"],["IsStrictOrderedRing"],["NonUnitalNonAssocSemiring","toDistrib"],["instDistribLatticeNat"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["LinearOrder"],["Nat"],["DistribLattice","toLattice"],["AddMonoidWithOne","toNatCast"],["Semiring"]],"valueReferences":[["Lattice","toSemilatticeSup"],["Nat","cast"],["instDistribLatticeNat"],["Nat","cast_finsetSup"],["instDistribLatticeOfLinearOrder"],["Nat"],["AddMonoidWithOne","toNatCast"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["Eq","symm"],["Finset","sup"],["Nat","instOrderBot"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"]]},{"isProp":true,"kind":"theorem","name":["Finset","sup_mul₀"],"typeFallback":"forall {R : Type.{u_1}} {ι : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.4 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.7 : NonUnitalNonAssocSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.10 : CanonicallyOrderedAdd.{u_1} R (Distrib.toAdd.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.7)) (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.4))))))] [inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.13 : OrderBot.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.4))))))] (s : Finset.{u_2} ι) (f : ι -> R) (a : R), Eq.{succ u_1} R (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.7))) (Finset.sup.{u_1, u_2} R ι (Lattice.toSemilatticeSup.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.13 s f) a) (Finset.sup.{u_1, u_2} R ι (Lattice.toSemilatticeSup.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.13 s (fun (x._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.32 : ι) => HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.7))) (f x._@.Mathlib.Algebra.Order.Ring.Finset.2841431177._hygCtx._hyg.32) a))","typeFull":"∀ {R : Type u_1} {ι : Type u_2} [inst : LinearOrder R] [inst_1 : NonUnitalNonAssocSemiring R] [CanonicallyOrderedAdd R]\n  [inst_3 : OrderBot R] (s : Finset ι) (f : ι → R) (a : R), s.sup f * a = s.sup fun x => f x * a","typeReadable":"∀ {R : Type u_1} {ι : Type u_2} [inst : LinearOrder R] [inst_1 : NonUnitalNonAssocSemiring R] [CanonicallyOrderedAdd R]\n  [inst_3 : OrderBot R] (s : Finset ι) (f : ι → R) (a : R), s.sup f * a = s.sup fun x => f x * a","typeReferences":[["Lattice","toSemilatticeSup"],["Distrib","toAdd"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["Finset"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["LinearOrder"],["HMul","hMul"],["CanonicallyOrderedAdd"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Finset","sup"],["instHMul"],["Eq"],["Preorder","toLE"],["NonUnitalNonAssocSemiring"],["OrderBot"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["Finset"],["Finset","instInsert"],["Eq","trans"],["Finset","instEmptyCollection"],["SemilatticeSup","toPartialOrder"],["Classical","propDecidable"],["HMul","hMul"],["AddCommMonoid","toAddMonoid"],["EmptyCollection","emptyCollection"],["max_mul"],["congrArg"],["instDistribLatticeOfLinearOrder"],["Finset","sup_insert"],["congr"],["Eq","symm"],["Finset","sup"],["congrFun'"],["Zero","toOfNat0"],["OrderBot","toBot"],["Preorder","toLE"],["Eq"],["SemilatticeInf","toPartialOrder"],["bot_eq_zero'"],["Lattice","toSemilatticeInf"],["True"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Insert","insert"],["CanonicallyOrderedAdd","toMulRightMono"],["MulZeroClass","zero_mul"],["AddZeroClass","toAddZero"],["Bot","bot"],["OfNat","ofNat"],["eq_self"],["Max","max"],["DistribLattice","toLattice"],["of_eq_true"],["MulZeroClass","toZero"],["Finset","sup_empty"],["SemilatticeSup","toMax"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["AddZero","toZero"],["Finset","induction"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Nat","cast_finsetSup'"],"typeFallback":"forall {ι : Type.{u_1}} {R : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.7 : LinearOrder.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.10 : IsStrictOrderedRing.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4 (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.7))))] {s : Finset.{u_1} ι} (f : ι -> Nat) (hs : Finset.Nonempty.{u_1} ι s), Eq.{succ u_2} R (Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4)))) (Finset.sup'.{0, u_1} Nat ι (Lattice.toSemilatticeSup.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)) s hs f)) (Finset.sup'.{u_2, u_1} R ι (Lattice.toSemilatticeSup.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.7))) s hs (fun (i : ι) => Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.1175832110._hygCtx._hyg.4)))) (f i)))","typeFull":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), ↑(s.sup' hs f) = s.sup' hs fun i => ↑(f i)","typeReadable":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), ↑(s.sup' hs f) = s.sup' hs fun i => ↑(f i)","typeReferences":[["Lattice","toSemilatticeSup"],["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Finset"],["Nat","cast"],["Finset","sup'"],["instDistribLatticeNat"],["LinearOrder"],["instDistribLatticeOfLinearOrder"],["Nat"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["AddMonoidWithOne","toNatCast"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Finset","Nonempty"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["instDistribLatticeOfLinearOrder"],["Lattice","toSemilatticeSup"],["Nat"],["Semiring","toNonAssocSemiring"],["AddMonoidWithOne","toNatCast"],["Nat","cast"],["DistribLattice","toLattice"],["instDistribLatticeNat"],["Finset","comp_sup'_eq_sup'_comp"],["Nat","cast_max"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"]]},{"isProp":true,"kind":"theorem","name":["Nat","cast_finsetInf'","_simp_1"],"typeFallback":"forall {ι : Type.{u_1}} {R : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4 : Semiring.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.7 : LinearOrder.{u_2} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.10 : IsStrictOrderedRing.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4 (SemilatticeInf.toPartialOrder.{u_2} R (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.7))))] {s : Finset.{u_1} ι} (f : ι -> Nat) (hs : Finset.Nonempty.{u_1} ι s), Eq.{succ u_2} R (Finset.inf'.{u_2, u_1} R ι (Lattice.toSemilatticeInf.{u_2} R (DistribLattice.toLattice.{u_2} R (instDistribLatticeOfLinearOrder.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.7))) s hs (fun (i : ι) => Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4)))) (f i))) (Nat.cast.{u_2} R (AddMonoidWithOne.toNatCast.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R inst._@.Mathlib.Algebra.Order.Ring.Finset.3252849472._hygCtx._hyg.4)))) (Finset.inf'.{0, u_1} Nat ι (Lattice.toSemilatticeInf.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)) s hs f))","typeFull":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), (s.inf' hs fun i => ↑(f i)) = ↑(s.inf' hs f)","typeReadable":"∀ {ι : Type u_1} {R : Type u_2} [inst : Semiring R] [inst_1 : LinearOrder R] [IsStrictOrderedRing R] {s : Finset ι}\n  (f : ι → ℕ) (hs : s.Nonempty), (s.inf' hs fun i => ↑(f i)) = ↑(s.inf' hs f)","typeReferences":[["IsStrictOrderedRing"],["Lattice","toSemilatticeInf"],["Finset"],["Nat","cast"],["instDistribLatticeNat"],["LinearOrder"],["instDistribLatticeOfLinearOrder"],["Nat"],["Semiring","toNonAssocSemiring"],["AddMonoidWithOne","toNatCast"],["DistribLattice","toLattice"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Finset","Nonempty"],["Finset","inf'"],["Semiring"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["Nat","cast"],["Lattice","toSemilatticeInf"],["instDistribLatticeNat"],["instDistribLatticeOfLinearOrder"],["Nat"],["AddMonoidWithOne","toNatCast"],["Semiring","toNonAssocSemiring"],["DistribLattice","toLattice"],["Eq","symm"],["Nat","cast_finsetInf'"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["Finset","inf'"]]},{"isProp":true,"kind":"theorem","name":["Finset","mul_sup₀"],"typeFallback":"forall {R : Type.{u_1}} {ι : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.4 : LinearOrder.{u_1} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.7 : NonUnitalNonAssocSemiring.{u_1} R] [inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.10 : CanonicallyOrderedAdd.{u_1} R (Distrib.toAdd.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.7)) (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.4))))))] [inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.13 : OrderBot.{u_1} R (Preorder.toLE.{u_1} R (PartialOrder.toPreorder.{u_1} R (SemilatticeInf.toPartialOrder.{u_1} R (Lattice.toSemilatticeInf.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.4))))))] (s : Finset.{u_2} ι) (f : ι -> R) (a : R), Eq.{succ u_1} R (HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.7))) a (Finset.sup.{u_1, u_2} R ι (Lattice.toSemilatticeSup.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.13 s f)) (Finset.sup.{u_1, u_2} R ι (Lattice.toSemilatticeSup.{u_1} R (DistribLattice.toLattice.{u_1} R (instDistribLatticeOfLinearOrder.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.4))) inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.13 s (fun (x._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.32 : ι) => HMul.hMul.{u_1, u_1, u_1} R R R (instHMul.{u_1} R (Distrib.toMul.{u_1} R (NonUnitalNonAssocSemiring.toDistrib.{u_1} R inst._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.7))) a (f x._@.Mathlib.Algebra.Order.Ring.Finset.2704877024._hygCtx._hyg.32)))","typeFull":"∀ {R : Type u_1} {ι : Type u_2} [inst : LinearOrder R] [inst_1 : NonUnitalNonAssocSemiring R] [CanonicallyOrderedAdd R]\n  [inst_3 : OrderBot R] (s : Finset ι) (f : ι → R) (a : R), a * s.sup f = s.sup fun x => a * f x","typeReadable":"∀ {R : Type u_1} {ι : Type u_2} [inst : LinearOrder R] [inst_1 : NonUnitalNonAssocSemiring R] [CanonicallyOrderedAdd R]\n  [inst_3 : OrderBot R] (s : Finset ι) (f : ι → R) (a : R), a * s.sup f = s.sup fun x => a * f x","typeReferences":[["Lattice","toSemilatticeSup"],["Distrib","toAdd"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["Finset"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["LinearOrder"],["HMul","hMul"],["CanonicallyOrderedAdd"],["instDistribLatticeOfLinearOrder"],["DistribLattice","toLattice"],["Finset","sup"],["instHMul"],["Eq"],["Preorder","toLE"],["NonUnitalNonAssocSemiring"],["OrderBot"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["Finset"],["Finset","instInsert"],["Eq","trans"],["Finset","instEmptyCollection"],["SemilatticeSup","toPartialOrder"],["Classical","propDecidable"],["HMul","hMul"],["CanonicallyOrderedAdd","toMulLeftMono"],["AddCommMonoid","toAddMonoid"],["EmptyCollection","emptyCollection"],["mul_max"],["congrArg"],["instDistribLatticeOfLinearOrder"],["Finset","sup_insert"],["congr"],["Eq","symm"],["Finset","sup"],["Zero","toOfNat0"],["OrderBot","toBot"],["Preorder","toLE"],["Eq"],["SemilatticeInf","toPartialOrder"],["bot_eq_zero'"],["Lattice","toSemilatticeInf"],["True"],["NonUnitalNonAssocSemiring","toDistrib"],["Distrib","toMul"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["Insert","insert"],["MulZeroClass","mul_zero"],["AddZeroClass","toAddZero"],["Bot","bot"],["OfNat","ofNat"],["eq_self"],["Max","max"],["DistribLattice","toLattice"],["of_eq_true"],["MulZeroClass","toZero"],["Finset","sup_empty"],["SemilatticeSup","toMax"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["instHMul"],["AddZero","toZero"],["Finset","induction"],["AddMonoid","toAddZeroClass"]]}]