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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.ContinuedFractions.ContinuantsRecurrence.sym.json

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

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Group.Action.Pretransitive.sym.json

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

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

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Homology.SpectralSequence.ComplexShape.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.MvPolynomial.Funext.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.AbsoluteValue.Euclidean.sym.json

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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset.sym.json

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(MonoidWithZero.toMulZeroOneClass.{u_1} R (CommMonoidWithZero.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset.3278341101._hygCtx._hyg.3)))) (MulZeroClass.toZero.{u_1} R (MulZeroOneClass.toMulZeroClass.{u_1} R (MonoidWithZero.toMulZeroOneClass.{u_1} R (CommMonoidWithZero.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset.3278341101._hygCtx._hyg.3)))) (PartialOrder.toPreorder.{u_1} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset.3278341101._hygCtx._hyg.6)] [inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset.3278341101._hygCtx._hyg.19 : NeZero.{u_1} R (MulZeroClass.toZero.{u_1} R (MulZeroOneClass.toMulZeroClass.{u_1} R (MonoidWithZero.toMulZeroOneClass.{u_1} R (CommMonoidWithZero.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Order.BigOperators.GroupWithZero.Multiset.3278341101._hygCtx._hyg.3)))) (OfNat.ofNat.{u_1} R 1 (One.toOfNat1.{u_1} R (MulOne.toOne.{u_1} R 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Field.Canonical.sym.json

@@ -0,0 +1 @@
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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Group.CompleteLattice.sym.json

@@ -0,0 +1 @@
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(ConditionallyCompleteLattice.toConditionallyCompletePartialOrder.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2253643918._hygCtx._hyg.7))) (fun (i : ι) => f i)) a) (iSup.{u_2, succ u_1} G ι (ConditionallyCompletePartialOrderSup.toSupSet.{u_2} G (ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup.{u_2} G (ConditionallyCompleteLattice.toConditionallyCompletePartialOrder.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2253643918._hygCtx._hyg.7))) (fun (i : ι) => HAdd.hAdd.{u_2, u_2, u_2} G G G (instHAdd.{u_2} G (AddZero.toAdd.{u_2} G (AddZeroClass.toAddZero.{u_2} G (AddMonoid.toAddZeroClass.{u_2} G (SubNegMonoid.toAddMonoid.{u_2} G (AddGroup.toSubNegMonoid.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2253643918._hygCtx._hyg.4)))))) (f i) a)))","typeFull":"∀ {ι : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : ConditionallyCompleteLattice G] [Nonempty ι] {f : ι → G}\n  [AddRightMono G], BddAbove (Set.range f) → ∀ (a : G), (⨆ i, f i) + a = ⨆ i, f i + a","typeReadable":"∀ {ι : Type u_1} {G : Type u_2} [inst : AddGroup G] [inst_1 : ConditionallyCompleteLattice G] [Nonempty ι] {f : ι → G}\n  [AddRightMono G], BddAbove (Set.range f) → ∀ (a : G), (⨆ i, f i) + a = ⨆ i, f i + a","typeReferences":[["PartialOrder","toPreorder"],["instHAdd"],["ConditionallyCompleteLattice","toConditionallyCompletePartialOrder"],["Nonempty"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["Set","range"],["BddAbove"],["HAdd","hAdd"],["ConditionallyCompletePartialOrderSup","toPartialOrder"],["AddRightMono"],["ConditionallyCompletePartialOrder","toConditionallyCompletePartialOrderSup"],["iSup"],["SubNegMonoid","toAddMonoid"],["ConditionallyCompletePartialOrderSup","toSupSet"],["ConditionallyCompleteLattice"],["AddGroup"],["AddGroup","toSubNegMonoid"],["Eq"],["Preorder","toLE"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["ConditionallyCompletePartialOrderSup","toPartialOrder"],["ConditionallyCompletePartialOrder","toConditionallyCompletePartialOrderSup"],["PartialOrder","toPreorder"],["ConditionallyCompleteLattice","toConditionallyCompletePartialOrder"],["OrderIso","addRight"],["OrderIso","map_ciSup"],["Preorder","toLE"]]},{"isProp":true,"kind":"theorem","name":["mul_ciSup"],"typeFallback":"forall {ι : Type.{u_1}} {G : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.4 : Group.{u_2} G] [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.7 : ConditionallyCompleteLattice.{u_2} G] [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.10 : Nonempty.{succ u_1} ι] {f : ι -> G} [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.16 : MulLeftMono.{u_2} G (MulOne.toMul.{u_2} G (MulOneClass.toMulOne.{u_2} G (Monoid.toMulOneClass.{u_2} G (DivInvMonoid.toMonoid.{u_2} G (Group.toDivInvMonoid.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.4))))) (Preorder.toLE.{u_2} G (PartialOrder.toPreorder.{u_2} G (ConditionallyCompletePartialOrderSup.toPartialOrder.{u_2} G (ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup.{u_2} G (ConditionallyCompleteLattice.toConditionallyCompletePartialOrder.{u_2} G 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(ConditionallyCompleteLattice.toConditionallyCompletePartialOrder.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.7))) (fun (i : ι) => f i))) (iSup.{u_2, succ u_1} G ι (ConditionallyCompletePartialOrderSup.toSupSet.{u_2} G (ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup.{u_2} G (ConditionallyCompleteLattice.toConditionallyCompletePartialOrder.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.7))) (fun (i : ι) => HMul.hMul.{u_2, u_2, u_2} G G G (instHMul.{u_2} G (MulOne.toMul.{u_2} G (MulOneClass.toMulOne.{u_2} G (Monoid.toMulOneClass.{u_2} G (DivInvMonoid.toMonoid.{u_2} G (Group.toDivInvMonoid.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.19885722._hygCtx._hyg.4)))))) a (f i))))","typeFull":"∀ {ι : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : ConditionallyCompleteLattice G] [Nonempty ι] {f : ι → G}\n  [MulLeftMono G], BddAbove (Set.range f) → ∀ (a : G), a * ⨆ i, f i = ⨆ i, a * f i","typeReadable":"∀ {ι : Type u_1} {G : Type u_2} [inst : Group G] [inst_1 : ConditionallyCompleteLattice G] [Nonempty ι] {f : ι → G}\n  [MulLeftMono G], BddAbove (Set.range f) → ∀ (a : G), a * ⨆ i, f i = ⨆ i, a * f 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{ι : Type.{u_1}} {G : Type.{u_2}} [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2083629729._hygCtx._hyg.4 : Group.{u_2} G] [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2083629729._hygCtx._hyg.7 : ConditionallyCompleteLattice.{u_2} G] [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2083629729._hygCtx._hyg.10 : Nonempty.{succ u_1} ι] {f : ι -> G} [inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2083629729._hygCtx._hyg.16 : MulRightMono.{u_2} G (MulOne.toMul.{u_2} G (MulOneClass.toMulOne.{u_2} G (Monoid.toMulOneClass.{u_2} G (DivInvMonoid.toMonoid.{u_2} G (Group.toDivInvMonoid.{u_2} G inst._@.Mathlib.Algebra.Order.Group.CompleteLattice.2083629729._hygCtx._hyg.4))))) (Preorder.toLE.{u_2} G (PartialOrder.toPreorder.{u_2} G (ConditionallyCompletePartialOrderSup.toPartialOrder.{u_2} G (ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup.{u_2} G (ConditionallyCompleteLattice.toConditionallyCompletePartialOrder.{u_2} G 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Group.Lattice.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["mul_sup"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.3088842937._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.3088842937._hygCtx._hyg.6 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.3088842937._hygCtx._hyg.9 : MulLeftMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.3088842937._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.3088842937._hygCtx._hyg.3))))] (a : α) (b : α) (c : α), Eq.{succ u_1} α (HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α 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[inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] (a b c : α), c * (a ⊔ b) = c * a ⊔ c * b","typeReadable":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] (a b c : α), c * (a ⊔ b) = c * a ⊔ c * b","typeReferences":[["MulOneClass","toMulOne"],["Lattice","toSemilatticeSup"],["Group"],["MulLeftMono"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["HMul","hMul"],["Max","max"],["MulOne","toMul"],["DivInvMonoid","toMonoid"],["SemilatticeSup","toMax"],["Lattice"],["Monoid","toMulOneClass"],["instHMul"],["Preorder","toLE"],["Eq"],["Group","toDivInvMonoid"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["OrderIso","mulLeft"],["SemilatticeSup","toPartialOrder"],["OrderIso","map_sup"],["Preorder","toLE"]]},{"isProp":true,"kind":"theorem","name":["neg_sup"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.6 : AddGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.9 : AddLeftMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (SubNegMonoid.toAddMonoid.{u_1} α (AddGroup.toSubNegMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.3))))] [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.12 : AddRightMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (SubNegMonoid.toAddMonoid.{u_1} α (AddGroup.toSubNegMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α 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b)","typeReferences":[["AddLeftMono"],["SemilatticeInf","toMin"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["instHAdd"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["SubNegMonoid","toAddMonoid"],["Min","min"],["Lattice"],["AddGroup"],["AddGroup","toSubNegMonoid"],["Preorder","toLE"],["Eq"],["AddMonoid","toAddZeroClass"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["OrderIso","addLeft"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["OrderIso","map_inf"],["Preorder","toLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["sup_add"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.6 : AddGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.9 : AddRightMono.{u_1} α (AddZero.toAdd.{u_1} α 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α","typeReferences":[["MulOneClass","toMulOne"],["MulLeftMono"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["CommGroup"],["MulOne","toMul"],["DivInvMonoid","toMonoid"],["Lattice"],["Monoid","toMulOneClass"],["Preorder","toLE"],["Group","toDivInvMonoid"],["CommGroup","toGroup"],["DistribLattice"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["CommGroup","toDistribLattice","_proof_1"],["DistribLattice","mk"]]},{"isProp":true,"kind":"theorem","name":["inf_sub"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.2801542845._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2801542845._hygCtx._hyg.6 : AddGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2801542845._hygCtx._hyg.9 : AddRightMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (SubNegMonoid.toAddMonoid.{u_1} α (AddGroup.toSubNegMonoid.{u_1} α 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c)","typeReferences":[["SemilatticeInf","toMin"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["AddRightMono"],["SubNegMonoid","toAddMonoid"],["Min","min"],["SubNegMonoid","toSub"],["Lattice"],["HSub","hSub"],["AddGroup"],["AddGroup","toSubNegMonoid"],["instHSub"],["Preorder","toLE"],["Eq"],["AddMonoid","toAddZeroClass"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["OrderIso","map_inf"],["OrderIso","subRight"],["Preorder","toLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["inf_add_sup"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.2117725054._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2117725054._hygCtx._hyg.6 : AddCommGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2117725054._hygCtx._hyg.9 : AddLeftMono.{u_1} α 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(α : Type.{u_2}) [inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.10 : Lattice.{u_2} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.13 : AddCommGroup.{u_2} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.16 : AddLeftMono.{u_2} α (AddZero.toAdd.{u_2} α (AddZeroClass.toAddZero.{u_2} α (AddMonoid.toAddZeroClass.{u_2} α (SubNegMonoid.toAddMonoid.{u_2} α (AddGroup.toSubNegMonoid.{u_2} α (AddCommGroup.toAddGroup.{u_2} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.13)))))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.10))))], Eq.{succ u_2} (DistribLattice.{u_2} α) (AddCommGroup.toDistribLattice.{u_2} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.16) (DistribLattice.mk.{u_2} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.10 (fun (x : α) (y : α) (z : α) => AddCommGroup.toDistribLattice._proof_1.{u_2} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.10 inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.13 inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.16 x y z))","typeFull":"∀ (α : Type u_2) [inst : Lattice α] [inst_1 : AddCommGroup α] [inst_2 : AddLeftMono α],\n  AddCommGroup.toDistribLattice α = { toLattice := inst, le_sup_inf := ⋯ }","typeReadable":"∀ (α : Type u_2) [inst : Lattice α] [inst_1 : AddCommGroup α] [inst_2 : AddLeftMono α],\n  AddCommGroup.toDistribLattice α = { toLattice := inst, le_sup_inf := ⋯ }","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["AddCommGroup","toDistribLattice"],["AddCommGroup","toAddGroup"],["AddCommGroup"],["DistribLattice","mk"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["AddCommGroup","toDistribLattice","_proof_1"],["SubNegMonoid","toAddMonoid"],["Lattice"],["AddGroup","toSubNegMonoid"],["Eq"],["Preorder","toLE"],["DistribLattice"],["AddMonoid","toAddZeroClass"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["AddCommGroup","toDistribLattice"],["Eq","refl"],["DistribLattice"]]},{"isProp":true,"kind":"theorem","name":["mul_inf"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.2383206582._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2383206582._hygCtx._hyg.6 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2383206582._hygCtx._hyg.9 : MulLeftMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α 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(HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2383206582._hygCtx._hyg.6)))))) c a) (HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2383206582._hygCtx._hyg.6)))))) c b))","typeFull":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] (a b c : α), c * (a ⊓ b) = c * a ⊓ c * b","typeReadable":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] (a b c : α), c * (a ⊓ b) = c * a ⊓ c * b","typeReferences":[["MulOneClass","toMulOne"],["Group"],["SemilatticeInf","toMin"],["MulLeftMono"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["HMul","hMul"],["MulOne","toMul"],["DivInvMonoid","toMonoid"],["Min","min"],["Lattice"],["Monoid","toMulOneClass"],["instHMul"],["Preorder","toLE"],["Eq"],["Group","toDivInvMonoid"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["OrderIso","mulLeft"],["OrderIso","map_inf"],["Preorder","toLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["inv_inf"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.6 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.9 : MulLeftMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.3))))] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.12 : MulRightMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2421977650._hygCtx._hyg.3))))] (a : α) (b : α), Eq.{succ u_1} α (Inv.inv.{u_1} α (InvOneClass.toInv.{u_1} α (DivInvOneMonoid.toInvOneClass.{u_1} 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[MulLeftMono α] [MulRightMono α] (a b : α), (a ⊓ b)⁻¹ = a⁻¹ ⊔ b⁻¹","typeReadable":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] [MulRightMono α] (a b : α), (a ⊓ b)⁻¹ = a⁻¹ ⊔ b⁻¹","typeReferences":[["MulOneClass","toMulOne"],["Lattice","toSemilatticeSup"],["Group"],["SemilatticeInf","toMin"],["Group","toDivisionMonoid"],["Inv","inv"],["InvOneClass","toInv"],["MulLeftMono"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["MulRightMono"],["Max","max"],["MulOne","toMul"],["DivInvOneMonoid","toInvOneClass"],["DivInvMonoid","toMonoid"],["Min","min"],["SemilatticeSup","toMax"],["Lattice"],["Monoid","toMulOneClass"],["Eq"],["Preorder","toLE"],["Group","toDivInvMonoid"],["DivisionMonoid","toDivInvOneMonoid"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["OrderIso","inv"],["Lattice","toSemilatticeSup"],["OrderDual"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["OrderIso","map_inf"],["OrderDual","instSemilatticeInf"],["Preorder","toLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":false,"kind":"definition","name":["AddCommGroup","toDistribLattice"],"typeFallback":"forall (α : Type.{u_2}) [inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.10 : Lattice.{u_2} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.13 : AddCommGroup.{u_2} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.16 : AddLeftMono.{u_2} α (AddZero.toAdd.{u_2} α (AddZeroClass.toAddZero.{u_2} α (AddMonoid.toAddZeroClass.{u_2} α (SubNegMonoid.toAddMonoid.{u_2} α (AddGroup.toSubNegMonoid.{u_2} α (AddCommGroup.toAddGroup.{u_2} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.13)))))) (Preorder.toLE.{u_2} α (PartialOrder.toPreorder.{u_2} α (SemilatticeInf.toPartialOrder.{u_2} α (Lattice.toSemilatticeInf.{u_2} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1871075873._hygCtx._hyg.10))))], DistribLattice.{u_2} α","typeFull":"(α : Type u_2) → [inst : Lattice α] → [inst_1 : AddCommGroup α] → [AddLeftMono α] → DistribLattice α","typeReadable":"(α : Type u_2) → [inst : Lattice α] → [inst_1 : AddCommGroup α] → [AddLeftMono α] → DistribLattice α","typeReferences":[["AddLeftMono"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["AddCommGroup","toAddGroup"],["AddCommGroup"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["SubNegMonoid","toAddMonoid"],["Lattice"],["AddGroup","toSubNegMonoid"],["Preorder","toLE"],["DistribLattice"],["AddMonoid","toAddZeroClass"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["DistribLattice","mk"],["AddCommGroup","toDistribLattice","_proof_1"]]},{"isProp":true,"kind":"theorem","name":["div_inf"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.6 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.9 : MulLeftMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α 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inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.6))) c (Min.min.{u_1} α (SemilatticeInf.toMin.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.3)) a b)) (Max.max.{u_1} α (SemilatticeSup.toMax.{u_1} α (Lattice.toSemilatticeSup.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.3)) (HDiv.hDiv.{u_1, u_1, u_1} α α α (instHDiv.{u_1} α (DivInvMonoid.toDiv.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.6))) c a) (HDiv.hDiv.{u_1, u_1, u_1} α α α (instHDiv.{u_1} α (DivInvMonoid.toDiv.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.1653215311._hygCtx._hyg.6))) c b))","typeFull":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] [MulRightMono α] (a b c : α),\n  c / (a ⊓ b) = c / a ⊔ c / b","typeReadable":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulLeftMono α] [MulRightMono α] (a b c : α),\n  c / (a ⊓ b) = c / a ⊔ c / b","typeReferences":[["MulOneClass","toMulOne"],["Lattice","toSemilatticeSup"],["Group"],["SemilatticeInf","toMin"],["MulLeftMono"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["instHDiv"],["DivInvMonoid","toDiv"],["HDiv","hDiv"],["MulRightMono"],["Max","max"],["MulOne","toMul"],["DivInvMonoid","toMonoid"],["Min","min"],["SemilatticeSup","toMax"],["Lattice"],["Monoid","toMulOneClass"],["Eq"],["Preorder","toLE"],["Group","toDivInvMonoid"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["Lattice","toSemilatticeSup"],["OrderDual"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["OrderIso","map_inf"],["OrderDual","instSemilatticeInf"],["Preorder","toLE"],["OrderIso","divLeft"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["sup_mul"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.6 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.9 : MulRightMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.3))))] (a : α) (b : α) (c : α), Eq.{succ u_1} α (HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.6)))))) (Max.max.{u_1} α (SemilatticeSup.toMax.{u_1} α (Lattice.toSemilatticeSup.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.3)) a b) c) (Max.max.{u_1} α (SemilatticeSup.toMax.{u_1} α (Lattice.toSemilatticeSup.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.3)) (HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.6)))))) a c) (HMul.hMul.{u_1, u_1, u_1} α α α (instHMul.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2595461697._hygCtx._hyg.6)))))) b c))","typeFull":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulRightMono α] (a b c : α), (a ⊔ b) * c = a * c ⊔ b * c","typeReadable":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : Group α] [MulRightMono α] (a b c : α), (a ⊔ b) * c = a * c ⊔ b * c","typeReferences":[["MulOneClass","toMulOne"],["Lattice","toSemilatticeSup"],["Group"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["HMul","hMul"],["MulRightMono"],["Max","max"],["MulOne","toMul"],["DivInvMonoid","toMonoid"],["SemilatticeSup","toMax"],["Lattice"],["Monoid","toMulOneClass"],["instHMul"],["Preorder","toLE"],["Eq"],["Group","toDivInvMonoid"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["SemilatticeSup","toPartialOrder"],["OrderIso","map_sup"],["Preorder","toLE"],["OrderIso","mulRight"]]},{"isProp":true,"kind":"theorem","name":["nsmul_two_semiclosed"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.6 : AddGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.9 : AddLeftMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (SubNegMonoid.toAddMonoid.{u_1} α (AddGroup.toSubNegMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.3))))] [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.12 : AddRightMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (SubNegMonoid.toAddMonoid.{u_1} α (AddGroup.toSubNegMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.3))))] {a : α}, 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{α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.6 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.9 : MulLeftMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.3))))] [inst._@.Mathlib.Algebra.Order.Group.Lattice.4235519006._hygCtx._hyg.12 : MulRightMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α 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[inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] (a b c : α), c + a ⊔ b = (c + a) ⊔ (c + b)","typeReadable":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddLeftMono α] (a b c : α), c + a ⊔ b = (c + a) ⊔ (c + b)","typeReferences":[["AddLeftMono"],["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["instHAdd"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["Max","max"],["SubNegMonoid","toAddMonoid"],["SemilatticeSup","toMax"],["Lattice"],["AddGroup"],["AddGroup","toSubNegMonoid"],["Preorder","toLE"],["Eq"],["AddMonoid","toAddZeroClass"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["OrderIso","addLeft"],["Lattice","toSemilatticeSup"],["PartialOrder","toPreorder"],["SemilatticeSup","toPartialOrder"],["OrderIso","map_sup"],["Preorder","toLE"]]},{"isProp":true,"kind":"theorem","name":["inf_add"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.2747377292._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2747377292._hygCtx._hyg.6 : AddGroup.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.2747377292._hygCtx._hyg.9 : AddRightMono.{u_1} α (AddZero.toAdd.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (SubNegMonoid.toAddMonoid.{u_1} α (AddGroup.toSubNegMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2747377292._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.2747377292._hygCtx._hyg.3))))] (a : α) (b : α) (c : α), Eq.{succ u_1} α (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 (AddMonoid.toAddZeroClass.{u_1} α (SubNegMonoid.toAddMonoid.{u_1} α (AddGroup.toSubNegMonoid.{u_1} α 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[inst : Lattice α] [inst_1 : AddGroup α] [AddRightMono α] (a b c : α), a ⊓ b + c = (a + c) ⊓ (b + c)","typeReadable":"∀ {α : Type u_1} [inst : Lattice α] [inst_1 : AddGroup α] [AddRightMono α] (a b c : α), a ⊓ b + c = (a + c) ⊓ (b + c)","typeReferences":[["SemilatticeInf","toMin"],["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["instHAdd"],["AddZero","toAdd"],["AddZeroClass","toAddZero"],["HAdd","hAdd"],["AddRightMono"],["SubNegMonoid","toAddMonoid"],["Min","min"],["Lattice"],["AddGroup"],["AddGroup","toSubNegMonoid"],["Preorder","toLE"],["Eq"],["AddMonoid","toAddZeroClass"],["SemilatticeInf","toPartialOrder"]],"valueReferences":[["PartialOrder","toPreorder"],["Lattice","toSemilatticeInf"],["OrderIso","map_inf"],["OrderIso","addRight"],["Preorder","toLE"],["SemilatticeInf","toPartialOrder"]]},{"isProp":true,"kind":"theorem","name":["inv_sup"],"typeFallback":"forall {α : Type.{u_1}} [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.3 : Lattice.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.6 : Group.{u_1} α] [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.9 : MulLeftMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α (SemilatticeInf.toPartialOrder.{u_1} α (Lattice.toSemilatticeInf.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.3))))] [inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.12 : MulRightMono.{u_1} α (MulOne.toMul.{u_1} α (MulOneClass.toMulOne.{u_1} α (Monoid.toMulOneClass.{u_1} α (DivInvMonoid.toMonoid.{u_1} α (Group.toDivInvMonoid.{u_1} α inst._@.Mathlib.Algebra.Order.Group.Lattice.257213778._hygCtx._hyg.6))))) (Preorder.toLE.{u_1} α (PartialOrder.toPreorder.{u_1} α 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data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Order.Module.Equiv.sym.json

@@ -0,0 +1 @@
+[{"isProp":true,"kind":"theorem","name":["symm_ofLexLinearEquiv"],"typeFallback":"forall (α : Type.{u_1}) (β : Type.{u_2}) [inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.4 : Semiring.{u_1} α] [inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.7 : AddCommMonoid.{u_2} β] [inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.10 : Module.{u_1, u_2} α β inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.7], Eq.{succ u_2} (LinearEquiv.{u_1, u_1, u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.4 (RingHom.id.{u_1} α (Semiring.toNonAssocSemiring.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.4)) (RingHom.id.{u_1} α (Semiring.toNonAssocSemiring.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.2646051169._hygCtx._hyg.4)) 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a))","typeFull":"��� (α : Type u_2) (β : Type u_1) [inst : Semiring α] [inst_1 : AddCommMonoid β] [inst_2 : Module α β] (b : α) (a : β),\n  toLex (b • a) = b • toLex a","typeReadable":"∀ (α : Type u_2) (β : Type u_1) [inst : Semiring α] [inst_1 : AddCommMonoid β] [inst_2 : Module α β] (b : α) (a : β),\n  toLex (b • a) = b • toLex a","typeReferences":[["Equiv","instEquivLike"],["Module"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["toLex"],["Lex","instSMul"],["Equiv"],["Module","toDistribMulAction"],["AddCommMonoid"],["Lex"],["MonoidWithZero","toMonoid"],["EquivLike","toFunLike"],["HSMul","hSMul"],["instHSMul"],["Eq"],["AddZero","toZero"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Module","toDistribMulAction"],["MonoidWithZero","toMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddZeroClass","toAddZero"],["AddZero","toZero"],["toLex_smul"],["DistribSMul","toSMulZeroClass"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["coe_toLexLinearEquiv"],"typeFallback":"forall (α : Type.{u_1}) (β : Type.{u_2}) 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⇑toLex","typeReferences":[["Equiv","instEquivLike"],["instAddCommMonoidLex"],["Module"],["LinearEquiv"],["toLex"],["DFunLike","coe"],["Equiv"],["toLexLinearEquiv"],["AddCommMonoid"],["Lex"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Lex","instModule'"],["LinearEquiv","instEquivLike"],["Eq"],["Semiring"]],"valueReferences":[["toLexLinearEquiv"],["rfl"],["Lex"],["instAddCommMonoidLex"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Lex","instModule'"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["DFunLike","coe"]]},{"isProp":true,"kind":"theorem","name":["coe_ofLexLinearEquiv"],"typeFallback":"forall (α : Type.{u_1}) (β : Type.{u_2}) [inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.4 : Semiring.{u_1} α] [inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.7 : AddCommMonoid.{u_2} β] 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(instAddCommMonoidLex.{u_2} β inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.7) inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.7 (Lex.instModule'.{u_1, u_2} α β inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.10) inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.10 (RingHom.id.{u_1} α (Semiring.toNonAssocSemiring.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.4)) (RingHom.id.{u_1} α (Semiring.toNonAssocSemiring.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.4)) (RingHomInvPair.ids.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.4) (RingHomInvPair.ids.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.4))) (ofLexLinearEquiv.{u_1, u_2} α β inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.7 inst._@.Mathlib.Algebra.Order.Module.Equiv.182052383._hygCtx._hyg.10)) (DFunLike.coe.{succ u_2, succ u_2, succ u_2} (Equiv.{succ u_2, succ u_2} (Lex.{u_2} β) β) (Lex.{u_2} β) (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : Lex.{u_2} β) => β) (EquivLike.toFunLike.{succ u_2, succ u_2, succ u_2} (Equiv.{succ u_2, succ u_2} (Lex.{u_2} β) β) (Lex.{u_2} β) β (Equiv.instEquivLike.{succ u_2, succ u_2} (Lex.{u_2} β) β)) (ofLex.{u_2} β))","typeFull":"∀ (α : Type u_1) (β : Type u_2) [inst : Semiring α] [inst_1 : AddCommMonoid β] [inst_2 : Module α β],\n  ⇑(ofLexLinearEquiv α β) = ⇑ofLex","typeReadable":"∀ (α : Type u_1) (β : Type u_2) [inst : Semiring α] [inst_1 : AddCommMonoid β] [inst_2 : Module α β],\n  ⇑(ofLexLinearEquiv α β) = ⇑ofLex","typeReferences":[["Equiv","instEquivLike"],["instAddCommMonoidLex"],["Module"],["LinearEquiv"],["DFunLike","coe"],["Equiv"],["AddCommMonoid"],["Lex"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Lex","instModule'"],["LinearEquiv","instEquivLike"],["Eq"],["ofLex"],["ofLexLinearEquiv"],["Semiring"]],"valueReferences":[["rfl"],["Lex"],["instAddCommMonoidLex"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["EquivLike","toFunLike"],["RingHomInvPair","ids"],["Lex","instModule'"],["LinearEquiv","instEquivLike"],["LinearEquiv"],["DFunLike","coe"],["ofLexLinearEquiv"]]},{"isProp":true,"kind":"theorem","name":["ofLexLinearEquiv","_proof_1"],"typeFallback":"forall (α : Type.{u_2}) (β : Type.{u_1}) [inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4 : Semiring.{u_2} α] [inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.7 : AddCommMonoid.{u_1} β] 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(α : Type.{u_1}) (β : Type.{u_2}) [inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4 : Semiring.{u_1} α] [inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.7 : AddCommMonoid.{u_2} β] [inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.10 : Module.{u_1, u_2} α β inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.7], LinearEquiv.{u_1, u_1, u_2, u_2} α α inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4 inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4 (RingHom.id.{u_1} α (Semiring.toNonAssocSemiring.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4)) (RingHom.id.{u_1} α (Semiring.toNonAssocSemiring.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4)) (RingHomInvPair.ids.{u_1} α inst._@.Mathlib.Algebra.Order.Module.Equiv.516489428._hygCtx._hyg.4) (RingHomInvPair.ids.{u_1} α 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(toLexLinearEquiv α β).symm = ofLexLinearEquiv α β","typeReadable":"∀ (α : Type u_1) (β : Type u_2) [inst : Semiring α] [inst_1 : AddCommMonoid β] [inst_2 : Module α β],\n  (toLexLinearEquiv α β).symm = ofLexLinearEquiv α β","typeReferences":[["instAddCommMonoidLex"],["Module"],["LinearEquiv"],["LinearEquiv","symm"],["toLexLinearEquiv"],["AddCommMonoid"],["Lex"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["Lex","instModule'"],["Eq"],["ofLexLinearEquiv"],["Semiring"]],"valueReferences":[["toLexLinearEquiv"],["rfl"],["Lex"],["instAddCommMonoidLex"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["RingHomInvPair","ids"],["Lex","instModule'"],["LinearEquiv"],["LinearEquiv","symm"]]}]