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@@ -285,3 +285,10 @@ data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.Continuou
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong.sym.json filter=lfs diff=lfs merge=lfs -text
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.Distribution.ContDiffMapSupportedIn.sym.json filter=lfs diff=lfs merge=lfs -text
 data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.LinearAlgebra.ExteriorPower.Pairing.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Monoidal.Functor.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Topology.Gluing.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Topology.Sheaves.Over.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.LinearAlgebra.CliffordAlgebra.Even.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.NonUnital.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Geometry.Euclidean.Projection.sym.json filter=lfs diff=lfs merge=lfs -text
+data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.CategoryTheory.Bicategory.Functor.Lax.sym.json filter=lfs diff=lfs merge=lfs -text

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Algebra.Rat.sym.json

@@ -0,0 +1 @@
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[inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.11 : DivisionRing.{u_3} S] [inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.14 : CharZero.{u_3} S (AddGroupWithOne.toAddMonoidWithOne.{u_3} S (Ring.toAddGroupWithOne.{u_3} S (DivisionRing.toRing.{u_3} S inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.11)))] [inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.17 : FunLike.{succ u_1, succ u_2, succ u_3} F R S] [inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.22 : RingHomClass.{u_1, u_2, u_3} F R S (Semiring.toNonAssocSemiring.{u_2} R (DivisionSemiring.toSemiring.{u_2} R (DivisionRing.toDivisionSemiring.{u_2} R inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.5))) (Semiring.toNonAssocSemiring.{u_3} S (DivisionSemiring.toSemiring.{u_3} S (DivisionRing.toDivisionSemiring.{u_3} S inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.11))) inst._@.Mathlib.Algebra.Algebra.Rat.4046424363._hygCtx._hyg.17], 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{R : Type.{u_2}} {S : Type.{u_3}} [inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.11 : DivisionRing.{u_3} S] [inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.14 : CharZero.{u_3} S (AddGroupWithOne.toAddMonoidWithOne.{u_3} S (Ring.toAddGroupWithOne.{u_3} S (DivisionRing.toRing.{u_3} S inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.11)))] [inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.17 : SMul.{u_2, u_3} R S] [inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.21 : SMulCommClass.{u_2, u_3, u_3} R S S inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.17 (SMulZeroClass.toSMul.{u_3, u_3} S S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddGroupWithOne.toAddMonoidWithOne.{u_3} S (Ring.toAddGroupWithOne.{u_3} S (DivisionRing.toRing.{u_3} S inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.11))))))) 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inst._@.Mathlib.Algebra.Algebra.Rat.1193137465._hygCtx._hyg.17","typeFull":"∀ {R : Type u_2} {S : Type u_3} [inst : DivisionRing S] [inst_1 : CharZero S] [inst_2 : SMul R S] [SMulCommClass R S S],\n  SMulCommClass ℚ R S","typeReadable":"∀ {R : Type u_2} {S : Type u_3} [inst : DivisionRing S] [inst_1 : CharZero S] [inst_2 : SMul R S] [SMulCommClass R S S],\n  SMulCommClass ℚ R 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{R : Type.{u_2}} {S : Type.{u_3}} [inst._@.Mathlib.Algebra.Algebra.Rat.4034160367._hygCtx._hyg.11 : DivisionSemiring.{u_3} S] [inst._@.Mathlib.Algebra.Algebra.Rat.4034160367._hygCtx._hyg.14 : CharZero.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S (DivisionSemiring.toSemiring.{u_3} S inst._@.Mathlib.Algebra.Algebra.Rat.4034160367._hygCtx._hyg.11))))] [inst._@.Mathlib.Algebra.Algebra.Rat.4034160367._hygCtx._hyg.17 : SMul.{u_2, u_3} R S] [inst._@.Mathlib.Algebra.Algebra.Rat.4034160367._hygCtx._hyg.21 : SMulCommClass.{u_3, u_2, u_3} S R S (SMulZeroClass.toSMul.{u_3, u_3} S S (AddZero.toZero.{u_3} S (AddZeroClass.toAddZero.{u_3} S (AddMonoid.toAddZeroClass.{u_3} S (AddMonoidWithOne.toAddMonoid.{u_3} S (AddCommMonoidWithOne.toAddMonoidWithOne.{u_3} S (NonAssocSemiring.toAddCommMonoidWithOne.{u_3} S (Semiring.toNonAssocSemiring.{u_3} S (DivisionSemiring.toSemiring.{u_3} S 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{R : Type.{u_2}} [inst._@.Mathlib.Algebra.Algebra.Rat.2174015899._hygCtx._hyg.5 : DivisionSemiring.{u_2} R] [inst._@.Mathlib.Algebra.Algebra.Rat.2174015899._hygCtx._hyg.8 : CharZero.{u_2} R (AddCommMonoidWithOne.toAddMonoidWithOne.{u_2} R (NonAssocSemiring.toAddCommMonoidWithOne.{u_2} R (Semiring.toNonAssocSemiring.{u_2} R (DivisionSemiring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Algebra.Rat.2174015899._hygCtx._hyg.5))))], Algebra.{0, u_2} NNRat R instCommSemiringNNRat (DivisionSemiring.toSemiring.{u_2} R inst._@.Mathlib.Algebra.Algebra.Rat.2174015899._hygCtx._hyg.5)","typeFull":"{R : Type u_2} → [inst : DivisionSemiring R] → [CharZero R] → Algebra ℚ≥0 R","typeReadable":"{R : Type u_2} → [inst : DivisionSemiring R] → [CharZero R] → Algebra ℚ≥0 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[inst._@.Mathlib.Algebra.Algebra.Rat.1868678812._hygCtx._hyg.11 : DivisionRing.{u_3} S] [inst._@.Mathlib.Algebra.Algebra.Rat.1868678812._hygCtx._hyg.14 : CharZero.{u_3} S (AddGroupWithOne.toAddMonoidWithOne.{u_3} S (Ring.toAddGroupWithOne.{u_3} S (DivisionRing.toRing.{u_3} S inst._@.Mathlib.Algebra.Algebra.Rat.1868678812._hygCtx._hyg.11)))] [inst._@.Mathlib.Algebra.Algebra.Rat.1868678812._hygCtx._hyg.17 : EquivLike.{succ u_1, succ u_2, succ u_3} F R S] [inst._@.Mathlib.Algebra.Algebra.Rat.1868678812._hygCtx._hyg.22 : RingEquivClass.{u_1, u_2, u_3} F R S (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 (DivisionRing.toRing.{u_2} R inst._@.Mathlib.Algebra.Algebra.Rat.1868678812._hygCtx._hyg.5)))))) (Distrib.toAdd.{u_2} R (NonUnitalNonAssocSemiring.toDistrib.{u_2} R (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u_2} R 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S","typeReferences":[["Rat","semiring"],["Distrib","toAdd"],["Ring","toNonAssocRing"],["NonUnitalNonAssocSemiring","toDistrib"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DivisionRing","toRing"],["Distrib","toMul"],["AddGroupWithOne","toAddMonoidWithOne"],["DivisionSemiring","toSemiring"],["DivisionRing","toRatAlgebra"],["LinearEquivClass"],["Rat","commSemiring"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Ring","toAddGroupWithOne"],["DivisionRing","toDivisionSemiring"],["Algebra","toModule"],["Rat"],["RingEquivClass"],["DivisionRing"],["CharZero"],["EquivLike"],["NonAssocRing","toNonUnitalNonAssocRing"]],"valueReferences":[["RingHom"],["Ring","toNonAssocRing"],["Eq","trans"],["HMul","hMul"],["SMulZeroClass","toSMul"],["NonUnitalRingHomClass","toMulHomClass"],["RingHom","instRingHomClass"],["DivisionRing","toRatAlgebra"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Semiring","toNonAssocSemiring"],["RingEquivClass","toRingHomClass"],["RingHom","id"],["RingEquivClass","toAddEquivClass"],["NonAssocRing","toNonUnitalNonAssocRing"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toDistrib"],["outParam"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["DivisionSemiring","toSemiring"],["AddZeroClass","toAddZero"],["DivisionRing","toRatCast"],["HSMul","hSMul"],["map_mul"],["Rat"],["RingHomInvPair","ids"],["instHMul"],["map_ratCast"],["SemilinearEquivClass","mk"],["AddZero","toZero"],["Rat","instDivisionRing"],["algebraMap"],["AddMonoid","toAddZeroClass"],["Rat","semiring"],["RingEquivClass","toNonUnitalRingHomClass"],["RingHom","instFunLike"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["congrArg"],["DivisionRing","toDivisionSemiring"],["Algebra","toModule"],["congr"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["Rat","cast"],["Algebra","toSMul"],["instHSMul"],["congrFun'"],["Eq"],["Distrib","toAdd"],["eq_ratCast"],["True"],["CommSemiring","toSemiring"],["Distrib","toMul"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DivisionRing","toRing"],["Semiring","toMonoidWithZero"],["Rat","commSemiring"],["eq_self"],["Module","toDistribMulAction"],["of_eq_true"],["Algebra","smul_def"]]},{"isProp":true,"kind":"theorem","name":["RingHom","map_rat_algebraMap"],"typeFallback":"forall 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Field.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Module.sym.json

@@ -0,0 +1 @@
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{α : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Interval.Finset.SuccPred.2114247926._hygCtx._hyg.4 : LinearOrder.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.SuccPred.2114247926._hygCtx._hyg.7 : One.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.SuccPred.2114247926._hygCtx._hyg.10 : LocallyFiniteOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α inst._@.Mathlib.Algebra.Order.Interval.Finset.SuccPred.2114247926._hygCtx._hyg.4)))))] [inst._@.Mathlib.Algebra.Order.Interval.Finset.SuccPred.2114247926._hygCtx._hyg.13 : Add.{u_2} α] [inst._@.Mathlib.Algebra.Order.Interval.Finset.SuccPred.2114247926._hygCtx._hyg.16 : SuccAddOrder.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α (DistribLattice.toLattice.{u_2} α (instDistribLatticeOfLinearOrder.{u_2} α 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∑ i ∈ Finset.range (n - 1), (f (i + 1) - f i) • ∑ i ∈ Finset.range (i + 1), g i","typeReferences":[["instAddNat"],["Module"],["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["Ring","toAddGroupWithOne"],["instOfNatNat"],["SubNegMonoid","toSub"],["MonoidWithZero","toMonoid"],["HSub","hSub"],["instHSMul"],["Finset","sum"],["AddGroup","toSubNegMonoid"],["Eq"],["DistribSMul","toSMulZeroClass"],["Finset","range"],["instHAdd"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddCommGroup"],["AddZeroClass","toAddZero"],["OfNat","ofNat"],["Ring","toSemiring"],["HAdd","hAdd"],["Nat"],["Module","toDistribMulAction"],["AddGroupWithOne","toAddGroup"],["instSubNat"],["SubNegMonoid","toAddMonoid"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["instHSub"],["AddZero","toZero"],["Ring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["instAddNat"],["SubtractionMonoid","toSubNegZeroMonoid"],["Finset"],["Eq","trans"],["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["sub_zero"],["Nat","instAddCommMonoid"],["Ring","toAddGroupWithOne"],["Nat","instOrderedSub"],["SubNegMonoid","toSub"],["HSub","hSub"],["Finset","sum"],["Finset","sum_range_zero"],["Nat","pos_of_ne_zero"],["AddGroup","toSubNegMonoid"],["DistribSMul","toSMulZeroClass"],["sub_self"],["Nat","instPartialOrder"],["DistribMulAction","toDistribSMul"],["AddZeroClass","toAddZero"],["Ring","toSemiring"],["Nat","instCanonicallyOrderedAdd"],["Finset","sum_Ico_by_parts"],["Nat"],["Eq","refl"],["HSMul","hSMul"],["NegZeroClass","toZero"],["id"],["AddCommGroup","toAddCommMonoid"],["Finset","range_eq_Ico"],["Finset","Ico"],["Eq","mpr"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["smul_zero"],["Finset","instEmptyCollection"],["SubtractionCommMonoid","toSubtractionMonoid"],["SubNegZeroMonoid","toSubNegMonoid"],["AddCommMonoid","toAddMonoid"],["EmptyCollection","emptyCollection"],["SubNegZeroMonoid","toNegZeroClass"],["Nat","instPreorder"],["congrArg"],["Finset","sum_congr"],["instOfNatNat"],["congr"],["MonoidWithZero","toMonoid"],["instHSMul"],["Zero","toOfNat0"],["congrFun'"],["Eq"],["Finset","range"],["True"],["instHAdd"],["Semiring","toMonoidWithZero"],["Nat","instLocallyFiniteOrder"],["OfNat","ofNat"],["HAdd","hAdd"],["eq_self"],["Module","toDistribMulAction"],["AddGroupWithOne","toAddGroup"],["AddCommGroup","toDivisionAddCommMonoid"],["instSubNat"],["SubNegMonoid","toAddMonoid"],["of_eq_true"],["zero_tsub"],["instDecidableEqNat"],["instHSub"],["dite"]]},{"isProp":true,"kind":"theorem","name":["Finset","sum_Ico_by_parts"],"typeFallback":"forall {R : Type.{u_1}} {M : Type.{u_2}} [inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.4 : Ring.{u_1} R] [inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.7 : AddCommGroup.{u_2} M] [inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.10 : Module.{u_1, u_2} R M (Ring.toSemiring.{u_1} R inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.4) (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.7)] (f : Nat -> R) (g : Nat -> M) {m : Nat} {n : Nat}, (LT.lt.{0} Nat instLTNat m n) -> (Eq.{succ u_2} M (Finset.sum.{0, u_2} Nat M (AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.7) (Finset.Ico.{0} Nat Nat.instPreorder Nat.instLocallyFiniteOrder m n) (fun (i : Nat) => HSMul.hSMul.{u_1, u_2, u_2} R M M (instHSMul.{u_1, u_2} R M (SMulZeroClass.toSMul.{u_1, u_2} R M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M 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(AddCommGroup.toAddCommMonoid.{u_2} M inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.7) inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.10))))) (f i) (g i))) (HSub.hSub.{u_2, u_2, u_2} M M M (instHSub.{u_2} M (SubNegMonoid.toSub.{u_2} M (AddGroup.toSubNegMonoid.{u_2} M (AddCommGroup.toAddGroup.{u_2} M inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.7)))) (HSub.hSub.{u_2, u_2, u_2} M M M (instHSub.{u_2} M (SubNegMonoid.toSub.{u_2} M (AddGroup.toSubNegMonoid.{u_2} M (AddCommGroup.toAddGroup.{u_2} M inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.7)))) (HSMul.hSMul.{u_1, u_2, u_2} R M M (instHSMul.{u_1, u_2} R M (SMulZeroClass.toSMul.{u_1, u_2} R M (AddZero.toZero.{u_2} M (AddZeroClass.toAddZero.{u_2} M (AddMonoid.toAddZeroClass.{u_2} M (SubNegMonoid.toAddMonoid.{u_2} M (AddGroup.toSubNegMonoid.{u_2} M (AddCommGroup.toAddGroup.{u_2} M inst._@.Mathlib.Algebra.BigOperators.Module.1653832331._hygCtx._hyg.7)))))) 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.BigOperators.Option.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Category.ModuleCat.Descent.sym.json

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f)","typeReferences":[["CommRing","toRing"],["CategoryTheory","Limits","PreservesFiniteLimits"],["RingHom"],["CommRing","toCommSemiring"],["Semiring","toNonAssocSemiring"],["ModuleCat","extendScalars"],["CommSemiring","toSemiring"],["ModuleCat","moduleCategory"],["CommRing"],["ModuleCat"],["RingHom","Flat"]],"valueReferences":[["ModuleCat","restrictScalars"],["ModuleCat","instReflectsIsomorphismsRestrictScalars"],["ModuleCat","moduleCategory"],["ModuleCat","abelian"],["CategoryTheory","Limits","preservesFiniteLimits_of_reflects_of_preserves"],["ModuleCat","preservesFiniteLimits_tensorLeft_of_ringHomFlat"],["ModuleCat","instIsRightAdjointRestrictScalars"],["CategoryTheory","Limits","PreservesLimits","preservesFiniteLimits"],["CommRing","toRing"],["CategoryTheory","Abelian","hasFiniteLimits"],["ModuleCat","extendScalars"],["CategoryTheory","Limits","reflectsFiniteLimits_of_reflectsIsomorphisms"],["CategoryTheory","Functor","instPreservesLimitsOfSizeOfIsRightAdjoint"],["ModuleCat"]]},{"isProp":false,"kind":"definition","name":["comonadicExtendScalars"],"typeFallback":"forall 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.DirectSum.Finsupp.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Field.ZMod.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Irreducible.Defs.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Pointwise.Finset.Interval.sym.json

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b)","typeReferences":[["LocallyFiniteOrderBot"],["PartialOrder","toPreorder"],["Finset"],["AddRightStrictMono"],["Add"],["instHAdd"],["DecidableEq"],["AddLeftStrictMono"],["Preorder","toLT"],["Finset","instHasSubset"],["Finset","Iio"],["Finset","Iic"],["HAdd","hAdd"],["HasSubset","Subset"],["PartialOrder"],["Finset","add"]],"valueReferences":[["Finset","instSetLike"],["PartialOrder","toPreorder"],["Finset"],["Eq","trans"],["Iff","mp"],["Finset","coe_Iio"],["Set","Iio"],["Finset","coe_Iic"],["congrArg"],["Set","Iic_add_Iio_subset"],["Set","add"],["congr"],["Finset","add"],["Eq"],["instHAdd"],["Set"],["Finset","instHasSubset"],["Finset","coe_subset"],["Set","Iic"],["Finset","Iio"],["Finset","Iic"],["HAdd","hAdd"],["Set","instHasSubset"],["Finset","coe_add"],["SetLike","coe"],["HasSubset","Subset"],["id"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["Finset","Ico_add_Ioc_subset"],"typeFallback":"forall {α : Type.{u_1}} 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[inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.2994251275._hygCtx._hyg.18 : LocallyFiniteOrder.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.2994251275._hygCtx._hyg.6)] (a : α) (b : α) (c : α) (d : α), HasSubset.Subset.{u_1} (Finset.{u_1} α) (Finset.instHasSubset.{u_1} α) (HAdd.hAdd.{u_1, u_1, u_1} (Finset.{u_1} α) (Finset.{u_1} α) (Finset.{u_1} α) (instHAdd.{u_1} (Finset.{u_1} α) (Finset.add.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.2994251275._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.2994251275._hygCtx._hyg.3)) (Finset.Ico.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.2994251275._hygCtx._hyg.6) inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.2994251275._hygCtx._hyg.18 a b) (Finset.Ioc.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.2994251275._hygCtx._hyg.6) 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LocallyFiniteOrder α] (a b c d : α),\n  Finset.Ico a b + Finset.Ioc c d ⊆ Finset.Ioo (a + c) (b + 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LocallyFiniteOrder α] (a b c d : α),\n  Finset.Ico a b + Finset.Icc c d ⊆ Finset.Ico (a + c) (b + 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LocallyFiniteOrder α] (a b c d : α),\n  Finset.Ioc a b + Finset.Ico c d ⊆ Finset.Ioo (a + c) (b + 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LocallyFiniteOrder.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.6] (a : α) (b : α) (c : α) (d : α), HasSubset.Subset.{u_1} (Finset.{u_1} α) (Finset.instHasSubset.{u_1} α) (HMul.hMul.{u_1, u_1, u_1} (Finset.{u_1} α) (Finset.{u_1} α) (Finset.{u_1} α) (instHMul.{u_1} (Finset.{u_1} α) (Finset.mul.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.3)) (Finset.Icc.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.18 a b) (Finset.Icc.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.18 c d)) (Finset.Icc.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.18 (HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.3) a c) (HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.798766832._hygCtx._hyg.3) b d))","typeFull":"∀ {α : Type u_1} [inst : Mul α] [inst_1 : Preorder α] [inst_2 : DecidableEq α] [MulLeftMono α] [MulRightMono α]\n  [inst_5 : LocallyFiniteOrder α] (a b c d : α), Finset.Icc a b * Finset.Icc c d ⊆ Finset.Icc (a * c) (b * d)","typeReadable":"∀ {α : Type u_1} [inst : Mul α] [inst_1 : Preorder α] [inst_2 : DecidableEq α] [MulLeftMono α] [MulRightMono α]\n  [inst_5 : LocallyFiniteOrder α] (a b c d : α), Finset.Icc a b * Finset.Icc c d ⊆ Finset.Icc (a * c) (b * 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inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.6) inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.18 (HAdd.hAdd.{u_1, u_1, u_1} α α α (instHAdd.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.3) a c) (HAdd.hAdd.{u_1, u_1, u_1} α α α (instHAdd.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.3) b d))","typeFull":"∀ {α : Type u_1} [inst : Add α] [inst_1 : PartialOrder α] [inst_2 : DecidableEq α] [AddLeftStrictMono α]\n  [AddRightStrictMono α] [inst_5 : LocallyFiniteOrder α] (a b c d : α),\n  Finset.Icc a b + Finset.Ico c d ⊆ Finset.Ico (a + c) (b + d)","typeReadable":"∀ {α : Type u_1} [inst : Add α] [inst_1 : PartialOrder α] [inst_2 : DecidableEq α] [AddLeftStrictMono α]\n  [AddRightStrictMono α] [inst_5 : LocallyFiniteOrder α] (a b c d : α),\n  Finset.Icc a b + Finset.Ico c d ⊆ Finset.Ico (a + c) (b + d)","typeReferences":[["PartialOrder","toPreorder"],["Finset"],["AddRightStrictMono"],["Add"],["instHAdd"],["DecidableEq"],["AddLeftStrictMono"],["Preorder","toLT"],["Finset","Icc"],["Finset","instHasSubset"],["HAdd","hAdd"],["LocallyFiniteOrder"],["HasSubset","Subset"],["PartialOrder"],["Finset","add"],["Finset","Ico"]],"valueReferences":[["Finset","instSetLike"],["PartialOrder","toPreorder"],["Finset"],["Eq","trans"],["Set","Icc"],["Finset","coe_Ico"],["Iff","mp"],["Finset","coe_Icc"],["congrArg"],["Set","add"],["congr"],["Finset","add"],["Set","Icc_add_Ico_subset"],["Set","Ico"],["Eq"],["instHAdd"],["Set"],["Finset","Icc"],["Finset","instHasSubset"],["Finset","coe_subset"],["HAdd","hAdd"],["Set","instHasSubset"],["Finset","coe_add"],["SetLike","coe"],["HasSubset","Subset"],["id"],["Finset","Ico"],["Eq","mpr"]]},{"isProp":true,"kind":"theorem","name":["Finset","Icc_mul_Ico_subset'"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.3 : Mul.{u_1} α] [inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.6 : PartialOrder.{u_1} α] [inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.9 : DecidableEq.{succ u_1} α] [inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.12 : MulLeftStrictMono.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.3 (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.6))] [inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.15 : MulRightStrictMono.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.3 (Preorder.toLT.{u_1} α (PartialOrder.toPreorder.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3185206329._hygCtx._hyg.6))] 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LocallyFiniteOrder α] (a b c d : α),\n  Finset.Icc a b * Finset.Ico c d ⊆ Finset.Ico (a * c) (b * 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LocallyFiniteOrderBot.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.6] (a : α) (b : α), HasSubset.Subset.{u_1} (Finset.{u_1} α) (Finset.instHasSubset.{u_1} α) (HAdd.hAdd.{u_1, u_1, u_1} (Finset.{u_1} α) (Finset.{u_1} α) (Finset.{u_1} α) (instHAdd.{u_1} (Finset.{u_1} α) (Finset.add.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.3)) (Finset.Iic.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.18 a) (Finset.Iic.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.6 inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.18 b)) (Finset.Iic.{u_1} α inst._@.Mathlib.Algebra.Group.Pointwise.Finset.Interval.3995380686._hygCtx._hyg.6 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.WithOne.Map.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Conj.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.GroupWithZero.Pointwise.Set.Card.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.sym.json

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inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.1890278916._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.1890278916._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.1890278916._hygCtx._hyg.10))))))","typeFull":"∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L],\n  IsScalarTower R (CommutatorRing L) (CommutatorRing L)","typeReadable":"∀ (R : Type u) (L : Type v) [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L],\n  IsScalarTower R (CommutatorRing L) (CommutatorRing L)","typeReferences":[["IsScalarTower"],["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["instDistribSMul"],["LieAlgebra"],["LieAlgebra","instCommutatorRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["MonoidWithZero","toMonoid"],["LieAlgebra","toModule"],["AddGroup","toSubNegMonoid"],["LieAlgebra","instLieRingCommutatorRing"],["LieRing","toAddCommGroup"],["DistribSMul","toSMulZeroClass"],["CommRing","toCommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["CommRing"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["instNonUnitalNonAssocRingCommutatorRing"],["CommutatorRing"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["LieRing"]],"valueReferences":[["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["smul_lie"],["lieAlgebraSelfModule"],["instDistribSMul"],["IsScalarTower","mk"],["LieAlgebra","instCommutatorRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["MonoidWithZero","toMonoid"],["LieAlgebra","toModule"],["LieAlgebra","instLieRingCommutatorRing"],["AddGroup","toSubNegMonoid"],["LieRing","toAddCommGroup"],["DistribSMul","toSMulZeroClass"],["CommRing","toCommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["lieRingSelfModule"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["instNonUnitalNonAssocRingCommutatorRing"],["CommutatorRing"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LieHom","toNonUnitalAlgHom","_proof_1"],"typeFallback":"forall {R : Type.{u_3}} {L : Type.{u_2}} [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.4 : CommRing.{u_3} R] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.7 : LieRing.{u_2} L] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.10 : LieAlgebra.{u_3, u_2} R L inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.7] {L₂ : Type.{u_1}} [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.15 : LieRing.{u_1} L₂] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.18 : LieAlgebra.{u_3, u_1} R L₂ inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.15] (f : LieHom.{u_3, u_2, u_1} R L L₂ 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inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.15 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.18 f)) x))","typeFull":"∀ {R : Type u_3} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {L₂ : Type u_1}\n  [inst_3 : LieRing L₂] [inst_4 : LieAlgebra R L₂] (f : L →ₗ⁅R⁆ L₂) (m : R) (x : L),\n  (↑f).toFun (m • x) = (RingHom.id R) m • (↑f).toFun x","typeReadable":"∀ {R : Type u_3} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {L₂ : Type u_1}\n  [inst_3 : LieRing L₂] [inst_4 : LieAlgebra R L₂] (f : L →ₗ⁅R⁆ L₂) (m : R) (x : L),\n  (↑f).toFun (m • x) = (RingHom.id R) m • (↑f).toFun x","typeReferences":[["RingHom"],["RingHom","instFunLike"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LieAlgebra"],["DFunLike","coe"],["LieHom"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddHom","toFun"],["LieAlgebra","toModule"],["LieRing","toAddCommGroup"],["Eq"],["DistribSMul","toSMulZeroClass"],["CommRing","toCommSemiring"],["CommSemiring","toSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["CommRing"],["AddZeroClass","toAddZero"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["LieHom","toLinearMap"],["AddZero","toZero"],["LieRing"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["CommRing","toCommSemiring"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["CommSemiring","toSemiring"],["AddCommGroup","toAddCommMonoid"],["LieAlgebra","toModule"],["LieHom","toLinearMap"],["LieRing","toAddCommGroup"],["LinearMap","map_smul'"]]},{"isProp":true,"kind":"theorem","name":["LieHom","toNonUnitalAlgHom_apply"],"typeFallback":"forall {R : Type.{u}} {L : Type.{v}} [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.7 : LieRing.{v} L] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.10 : LieAlgebra.{u, v} R L inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.7] {L₂ : Type.{w}} [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.15 : LieRing.{w} L₂] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.18 : LieAlgebra.{u, w} R L₂ inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.15] (f : LieHom.{u, v, w} R L L₂ inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4153817917._hygCtx._hyg.4 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u_3} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {L₂ : Type u_1}\n  [inst_3 : LieRing L₂] [inst_4 : LieAlgebra R L₂] (f : L →ₗ⁅R⁆ L₂) (x y : L),\n  (↑f).toFun (x + y) = (↑f).toFun x + (↑f).toFun y","typeReadable":"∀ {R : Type u_3} {L : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L] {L₂ : Type u_1}\n  [inst_3 : LieRing L₂] [inst_4 : LieAlgebra R L₂] (f : L →ₗ⁅R⁆ L₂) (x y : L),\n  (↑f).toFun (x + y) = (↑f).toFun x + (↑f).toFun 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L)","typeReferences":[["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["instDistribSMul"],["LieAlgebra"],["LieAlgebra","instCommutatorRing"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["MonoidWithZero","toMonoid"],["LieAlgebra","toModule"],["AddGroup","toSubNegMonoid"],["LieAlgebra","instLieRingCommutatorRing"],["LieRing","toAddCommGroup"],["DistribSMul","toSMulZeroClass"],["CommRing","toCommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["CommRing"],["SMulCommClass"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["instNonUnitalNonAssocRingCommutatorRing"],["CommutatorRing"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["LieRing"]],"valueReferences":[["SMulCommClass","mk"],["AddCommGroup","toAddGroup"],["SMulZeroClass","toSMul"],["lieAlgebraSelfModule"],["instDistribSMul"],["LieAlgebra","instCommutatorRing"],["Bracket","bracket"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["MonoidWithZero","toMonoid"],["Eq","symm"],["instHSMul"],["LieAlgebra","toModule"],["LieAlgebra","instLieRingCommutatorRing"],["AddGroup","toSubNegMonoid"],["LieRingModule","toBracket"],["LieRing","toAddCommGroup"],["DistribSMul","toSMulZeroClass"],["CommRing","toCommSemiring"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["lieRingSelfModule"],["Module","toDistribMulAction"],["SubNegMonoid","toAddMonoid"],["HSMul","hSMul"],["AddCommGroup","toAddCommMonoid"],["instNonUnitalNonAssocRingCommutatorRing"],["lie_smul"],["CommutatorRing"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LieHom","toNonUnitalAlgHom_injective"],"typeFallback":"forall {R : Type.{u}} {L : Type.{v}} [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.4 : CommRing.{u} R] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.7 : LieRing.{v} L] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.10 : LieAlgebra.{u, v} R L inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.7] {L₂ : Type.{w}} [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.15 : LieRing.{w} L₂] [inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.18 : LieAlgebra.{u, w} R L₂ inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Lie.NonUnitalNonAssocAlgebra.4005011115._hygCtx._hyg.15], Function.Injective.{max (succ v) (succ w), max (succ v) (succ w)} (LieHom.{u, v, w} R L L₂ 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CommRing R] →\n      [inst_1 : LieRing L] →\n        [inst_2 : LieAlgebra R L] →\n          {L₂ : Type w} →\n            [inst_3 : LieRing L₂] →\n              [inst_4 : LieAlgebra R L₂] → (L →ₗ⁅R⁆ L₂) → CommutatorRing L →ₙₐ[R] CommutatorRing L₂","typeReferences":[["MulOneClass","toMulOne"],["CommRing","toCommSemiring"],["MonoidHom","id"],["NonUnitalAlgHom"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["CommSemiring","toSemiring"],["Semiring","toMonoidWithZero"],["MulZeroOneClass","toMulOneClass"],["CommRing"],["LieAlgebra"],["LieAlgebra","instCommutatorRing"],["LieHom"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["Module","toDistribMulAction"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["instNonUnitalNonAssocRingCommutatorRing"],["LieAlgebra","toModule"],["LieAlgebra","instLieRingCommutatorRing"],["CommutatorRing"],["NonAssocSemiring","toMulZeroOneClass"],["LieRing"]],"valueReferences":[["MulOneClass","toMulOne"],["MonoidHom","id"],["MonoidHom"],["MonoidHom","instFunLike"],["SMulZeroClass","toSMul"],["MulZeroOneClass","toMulOneClass"],["AddCommMonoid","toAddMonoid"],["LieAlgebra","instCommutatorRing"],["DFunLike","coe"],["LieHom"],["NonUnitalNonAssocRing","toNonUnitalNonAssocSemiring"],["LieHom","toNonUnitalAlgHom","_proof_1"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["LieAlgebra","toModule"],["LieAlgebra","instLieRingCommutatorRing"],["NonAssocSemiring","toMulZeroOneClass"],["DistribSMul","toSMulZeroClass"],["LieHom","toNonUnitalAlgHom","_proof_2"],["CommRing","toCommSemiring"],["LieHom","toNonUnitalAlgHom","_proof_3"],["CommSemiring","toSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["NonUnitalAlgHom","mk"],["LieHom","map_lie"],["Module","toDistribMulAction"],["LieHom","instFunLike"],["instNonUnitalNonAssocRingCommutatorRing"],["MulActionHom","mk"],["CommutatorRing"],["AddZero","toZero"],["DistribMulActionHom","mk"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["LieHom","toNonUnitalAlgHom","_proof_2"],"typeFallback":"forall 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.ModEq.sym.json

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

data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.GroupWithZero.WithZero.sym.json

@@ -0,0 +1 @@
+[{"isProp":false,"kind":"definition","name":["OrderIso","withZeroUnits"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3 : LinearOrderedCommGroupWithZero.{u_1} α], OrderIso.{u_1, u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) α (Preorder.toLE.{u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (WithZero.instPreorder.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α 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(x2._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.21 : WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) => LE.le.{u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (Preorder.toLE.{u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (WithZero.instPreorder.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3))))) (Units.instPreorder.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))) (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α (LinearOrderedCommMonoidWithZero.toLinearOrder.{u_1} α (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))))))) x1._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.21 x2._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.21) (fun (x1._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.33 : α) (x2._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.33 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α (LinearOrderedCommMonoidWithZero.toLinearOrder.{u_1} α (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))))) x1._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.33 x2._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.33)) (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) => α) (RelIso.instFunLike.{u_1, u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) α (fun (x1._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.21 : WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α 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inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3) n) (WithZero.recZeroCoe.{u_1, succ u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3))))) (fun (x._@.Mathlib.Algebra.GroupWithZero.WithZero.173458267._hygCtx._hyg.43 : WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) => α) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (MulZeroClass.toZero.{u_1} α (MulZeroOneClass.toMulZeroClass.{u_1} α (MonoidWithZero.toMulZeroOneClass.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α 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n","typeReferences":[["PartialOrder","toPreorder"],["Units","instPreorder"],["WithZero"],["LinearOrderedCommMonoidWithZero","toLinearOrder"],["MonoidWithZero","toMulZeroOneClass"],["DFunLike","coe"],["instDistribLatticeOfLinearOrder"],["GroupWithZero","toMonoidWithZero"],["MonoidWithZero","toMonoid"],["WithZero","recZeroCoe"],["Zero","toOfNat0"],["LinearOrderedCommGroupWithZero","toCommGroupWithZero"],["WithZero","instPreorder"],["Preorder","toLE"],["RelIso"],["Eq"],["LinearOrderedCommGroupWithZero"],["RelIso","instFunLike"],["Units"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["LinearOrderedCommGroupWithZero","toLinearOrderedCommMonoidWithZero"],["OfNat","ofNat"],["DistribLattice","toLattice"],["OrderIso","withZeroUnits"],["MulZeroOneClass","toMulZeroClass"],["Units","val"],["MulZeroClass","toZero"],["LE","le"],["CommGroupWithZero","toGroupWithZero"]],"valueReferences":[["Lattice","toSemilatticeInf"],["PartialOrder","toPreorder"],["Units","instPreorder"],["LinearOrderedCommGroupWithZero","toLinearOrderedCommMonoidWithZero"],["LinearOrderedCommMonoidWithZero","toLinearOrder"],["WithZero"],["DFunLike","coe"],["instDistribLatticeOfLinearOrder"],["OrderIso","withZeroUnits"],["DistribLattice","toLattice"],["Eq","refl"],["MonoidWithZero","toMonoid"],["GroupWithZero","toMonoidWithZero"],["LE","le"],["LinearOrderedCommGroupWithZero","toCommGroupWithZero"],["RelIso"],["Preorder","toLE"],["WithZero","instPreorder"],["RelIso","instFunLike"],["Units"],["CommGroupWithZero","toGroupWithZero"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["OrderIso","withZeroUnits","_proof_1"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3 : LinearOrderedCommGroupWithZero.{u_1} α] {a._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.25 : WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))} {b._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.26 : WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))}, Iff (LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α (instDistribLatticeOfLinearOrder.{u_1} α (LinearOrderedCommMonoidWithZero.toLinearOrder.{u_1} α (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))))) (DFunLike.coe.{succ u_1, succ u_1, succ u_1} (Equiv.{succ u_1, succ u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) α) (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (fun 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=> LinearOrder.toDecidableEq.{u_1} α (LinearOrderedCommMonoidWithZero.toLinearOrder.{u_1} α (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)) a (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (MulZeroClass.toZero.{u_1} α (MulZeroOneClass.toMulZeroClass.{u_1} α (MonoidWithZero.toMulZeroOneClass.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3))))))))))) b._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.26)) (LE.le.{u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α 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inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (WithZero.instLinearOrder.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3))))) (Units.instLinearOrder.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))) (LinearOrderedCommMonoidWithZero.toLinearOrder.{u_1} α (LinearOrderedCommGroupWithZero.toLinearOrderedCommMonoidWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3))))))) a._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.25 b._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.26)","typeFull":"∀ {α : Type u_1} [inst : LinearOrderedCommGroupWithZero α] {a b : WithZero αˣ},\n  WithZero.withZeroUnitsEquiv.toEquiv a ≤ WithZero.withZeroUnitsEquiv.toEquiv b ↔ a ≤ b","typeReadable":"∀ {α : Type u_1} [inst : LinearOrderedCommGroupWithZero α] {a b : WithZero αˣ},\n  WithZero.withZeroUnitsEquiv.toEquiv a ≤ WithZero.withZeroUnitsEquiv.toEquiv b ↔ a ≤ b","typeReferences":[["Units","instMul"],["PartialOrder","toPreorder"],["Equiv","instEquivLike"],["WithZero"],["LinearOrderedCommMonoidWithZero","toLinearOrder"],["MulZeroClass","toMul"],["MonoidWithZero","toMulZeroOneClass"],["DFunLike","coe"],["Equiv"],["instDistribLatticeOfLinearOrder"],["WithZero","instMulZeroClass"],["GroupWithZero","toMonoidWithZero"],["MonoidWithZero","toMonoid"],["EquivLike","toFunLike"],["WithZero","instLinearOrder"],["Zero","toOfNat0"],["LinearOrderedCommGroupWithZero","toCommGroupWithZero"],["Preorder","toLE"],["LinearOrderedCommGroupWithZero"],["Units"],["SemilatticeInf","toPartialOrder"],["Lattice","toSemilatticeInf"],["MulEquiv","toEquiv"],["LinearOrderedCommGroupWithZero","toLinearOrderedCommMonoidWithZero"],["OfNat","ofNat"],["LinearOrder","toPartialOrder"],["LinearOrder","toDecidableEq"],["DistribLattice","toLattice"],["MulZeroOneClass","toMulZeroClass"],["Units","instLinearOrder"],["MulZeroClass","toZero"],["WithZero","withZeroUnitsEquiv"],["Iff"],["LE","le"],["CommGroupWithZero","toGroupWithZero"]],"valueReferences":[["Units","instMul"],["PartialOrder","toPreorder"],["Equiv","instEquivLike"],["LinearOrderedCommMonoidWithZero","toLinearOrder"],["WithZero"],["MulZeroClass","toMul"],["MonoidWithZero","toMulZeroOneClass"],["DFunLike","coe"],["Equiv"],["instDistribLatticeOfLinearOrder"],["WithZero","instMulZeroClass"],["GroupWithZero","toMonoidWithZero"],["MonoidWithZero","toMonoid"],["EquivLike","toFunLike"],["Zero","toOfNat0"],["WithZero","instLinearOrder"],["LinearOrderedCommGroupWithZero","toCommGroupWithZero"],["Units"],["SemilatticeInf","toPartialOrder"],["StrictMono","le_iff_le"],["Lattice","toSemilatticeInf"],["MulEquiv","toEquiv"],["LinearOrderedCommGroupWithZero","toLinearOrderedCommMonoidWithZero"],["OfNat","ofNat"],["LinearOrder","toDecidableEq"],["DistribLattice","toLattice"],["MulZeroOneClass","toMulZeroClass"],["MulZeroClass","toZero"],["Units","instLinearOrder"],["WithZero","withZeroUnitsEquiv_strictMono"],["WithZero","withZeroUnitsEquiv"],["CommGroupWithZero","toGroupWithZero"]]},{"isProp":true,"kind":"theorem","name":["WithZero","withZeroUnitsEquiv_symm_strictMono"],"typeFallback":"forall 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(MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1563569877._hygCtx._hyg.3)))))) (MulZeroClass.toMul.{u_1} α (MulZeroOneClass.toMulZeroClass.{u_1} α (MonoidWithZero.toMulZeroOneClass.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1563569877._hygCtx._hyg.3)))))) (MulZeroClass.toMul.{u_1} (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1563569877._hygCtx._hyg.3)))))) (WithZero.instMulZeroClass.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α 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LinearOrderedCommGroupWithZero α], StrictMono ⇑WithZero.withZeroUnitsEquiv.symm","typeReadable":"∀ {α : Type u_1} [inst : LinearOrderedCommGroupWithZero α], StrictMono 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(x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : α) => WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (RelIso.instFunLike.{u_1, u_1} α (WithZero.{u_1} (Units.{u_1} α (MonoidWithZero.toMonoid.{u_1} α (GroupWithZero.toMonoidWithZero.{u_1} α (CommGroupWithZero.toGroupWithZero.{u_1} α (LinearOrderedCommGroupWithZero.toCommGroupWithZero.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.1819683416._hygCtx._hyg.3)))))) (fun (x1._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.33 : α) (x2._@.Mathlib.Order.Hom.Basic.294108515._hygCtx._hyg.33 : α) => LE.le.{u_1} α (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α (DistribLattice.toLattice.{u_1} α 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(x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.23.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.67 : WithZero.{u_1} α), (LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.22.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.64 x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.23.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.67) -> Prop)) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.20.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.58 : WithZero.{u_1} α) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.21.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.61 : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α))) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.20.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.58) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.22.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.64 : WithZero.{u_1} α) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.23.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.67 : WithZero.{u_1} α) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.24.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.70 : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.22.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.64 x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.23.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.67), (forall (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.90 : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α))) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α)))) (a : WithZero.{u_1} α) (b : WithZero.{u_1} α) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.89 : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) a b), motive (Option.none.{u_1} α) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.90 a b x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.89) -> (forall (x : α) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.116 : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α))) (WithZero.coe.{u_1} α x)) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.115 : WithZero.{u_1} α) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.114 : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α))) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.115), motive (Option.some.{u_1} α x) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.116 (Option.none.{u_1} α) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.115 x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.114) -> (forall (x : α) (x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.142 : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α))) (WithZero.coe.{u_1} α x)) (a : α) (h : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (WithZero.coe.{u_1} α a) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α)))), motive (Option.some.{u_1} α x) x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.142 (Option.some.{u_1} α a) (Option.none.{u_1} α) h) -> (forall (x : α) (hx : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (OfNat.ofNat.{u_1} (WithZero.{u_1} α) 0 (Zero.toOfNat0.{u_1} (WithZero.{u_1} α) (WithZero.instZero.{u_1} α))) (WithZero.coe.{u_1} α x)) (a : α) (b : α) (h : LE.le.{u_1} (WithZero.{u_1} α) (Preorder.toLE.{u_1} (WithZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.6)) (WithZero.coe.{u_1} α a) (WithZero.coe.{u_1} α b)), motive (Option.some.{u_1} α x) hx (Option.some.{u_1} α a) (Option.some.{u_1} α b) h) -> (motive x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.20.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.58 x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.21.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.61 x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.22.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.64 x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.23.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.67 x._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx.24.Mathlib.Algebra.Order.GroupWithZero.WithZero.2492407808._hygCtx._hyg.70)","typeFull":"∀ {α : Type u_1} [inst : Preorder α] (motive : (x : WithZero α) → 0 ≤ x → (x x_1 : WithZero α) → x ≤ x_1 → Prop)\n  (x : WithZero α) (x_1 : 0 ≤ x) (x_2 x_3 : WithZero α) (x_4 : x_2 ≤ x_3),\n  (∀ (x : 0 ≤ 0) (a b : WithZero α) (x_5 : a ≤ b), motive none x a b x_5) →\n    (∀ (x : α) (x_5 : 0 ≤ ↑x) (x_6 : WithZero α) (x_7 : 0 ≤ x_6), motive (some x) x_5 none x_6 x_7) →\n      (∀ (x : α) (x_5 : 0 ≤ ↑x) (a : α) (h : ↑a ≤ 0), motive (some x) x_5 (some a) none h) →\n        (∀ (x : α) (hx : 0 ≤ ↑x) (a b : α) (h : ↑a ≤ ↑b), motive (some x) hx (some a) (some b) h) →\n          motive x x_1 x_2 x_3 x_4","typeReadable":"∀ {α : Type u_1} [inst : Preorder α] (motive : (x : WithZero α) → 0 ≤ x → (x x_1 : WithZero α) → x ≤ x_1 → Prop)\n  (x : WithZero α) (x_1 : 0 ≤ x) (x_2 x_3 : WithZero α) (x_4 : x_2 ≤ x_3),\n  (∀ (x : 0 ≤ 0) (a b : WithZero α) (x_5 : a ≤ b), motive none x a b x_5) →\n    (∀ (x : α) (x_5 : 0 ≤ ↑x) (x_6 : WithZero α) (x_7 : 0 ≤ x_6), motive (some x) x_5 none x_6 x_7) →\n      (∀ (x : α) (x_5 : 0 ≤ ↑x) (a : α) (h : ↑a ≤ 0), motive (some x) x_5 (some a) none h) →\n        (∀ (x : α) (hx : 0 ≤ ↑x) (a b : α) (h : ↑a ≤ ↑b), motive (some x) hx (some a) (some b) h) →\n          motive x x_1 x_2 x_3 x_4","typeReferences":[["Preorder"],["WithZero","coe"],["Option","none"],["LE","le"],["WithZero"],["WithZero","instZero"],["Zero","toOfNat0"],["Option","some"],["WithZero","instPreorder"],["Preorder","toLE"],["OfNat","ofNat"]],"valueReferences":[["Option","casesOn"],["WithZero"],["LE","le"],["WithZero","instZero"],["Zero","toOfNat0"],["Option","some"],["WithZero","instPreorder"],["Preorder","toLE"],["OfNat","ofNat"]]},{"isProp":true,"kind":"theorem","name":["instMulPosMonoWithZeroOfMulRightMono"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2448235384._hygCtx._hyg.3 : Mul.{u_1} α] [inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2448235384._hygCtx._hyg.6 : Preorder.{u_1} α] [inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2448235384._hygCtx._hyg.9 : MulRightMono.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2448235384._hygCtx._hyg.3 (Preorder.toLE.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2448235384._hygCtx._hyg.6)], MulPosMono.{u_1} (WithZero.{u_1} α) (MulZeroClass.toMul.{u_1} (WithZero.{u_1} α) (WithZero.instMulZeroClass.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2448235384._hygCtx._hyg.3)) (WithZero.instZero.{u_1} α) (WithZero.instPreorder.{u_1} α inst._@.Mathlib.Algebra.Order.GroupWithZero.WithZero.2448235384._hygCtx._hyg.6)","typeFull":"∀ {α : Type u_1} [inst : Mul α] [inst_1 : Preorder α] [MulRightMono α], MulPosMono (WithZero α)","typeReadable":"∀ {α : Type u_1} [inst : Mul α] [inst_1 : Preorder α] [MulRightMono α], MulPosMono (WithZero α)","typeReferences":[["WithZero","instMulZeroClass"],["MulRightMono"],["Preorder"],["MulZeroClass","toMul"],["WithZero"],["Mul"],["WithZero","instZero"],["MulPosMono"],["WithZero","instPreorder"],["Preorder","toLE"]],"valueReferences":[["WithZero","coe_ne_zero","_simp_1"],["Eq","trans"],["Eq","mp"],["MulZeroClass","toMul"],["WithZero"],["mul_le_mul_left"],["HMul","hMul"],["congrArg"],["WithZero","instMulZeroClass"],["False","elim"],["WithZero","coe"],["congr"],["WithZero","nonpos_iff_eq_zero","_simp_1"],["MulPosMono","mk"],["Zero","toOfNat0"],["Std","le_refl","_simp_1"],["congrFun'"],["Eq"],["Preorder","toLE"],["WithZero","instPreorder"],["WithZero","le"],["True"],["WithZero","zero_le","_simp_1"],["MulZeroClass","mul_zero"],["MulZeroClass","zero_mul"],["instReflLe"],["OfNat","ofNat"],["of_eq_true"],["MulZeroClass","toZero"],["LE","le"],["id"],["_private","Mathlib","Algebra","Order","GroupWithZero","WithZero",0,"instPosMulMonoWithZeroOfMulLeftMono","match_1"],["WithZero","instZero"],["False"],["instHMul"],["Eq","mpr"],["WithZero","coe_le_coe","_simp_1"]]}]