diff --git "a/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.TransferInstance.sym.json" "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.TransferInstance.sym.json"
new file mode 100644--- /dev/null
+++ "b/data_5e932f97dd25535344f80f9dd8da3aab83df0fe6/Mathlib.Algebra.Module.TransferInstance.sym.json"
@@ -0,0 +1 @@
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α), (r + s) • x = r • x + s • x","typeReadable":"∀ (R : Type u_2) {α : Type u_1} {β : Type u_3} [inst : Semiring R] (e : α ≃ β) [inst_1 : AddCommMonoid β]\n  [inst_2 : Module R β] (r s : R) (x : α), (r + s) • x = r • x + s • 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{β : Type u_1} [inst : Semiring R] (e : α ≃ β) [inst_1 : AddCommMonoid β]\n  [inst_2 : Module R β] (r : R) (x : α), e.addEquiv.toFun (r • x) = (RingHom.id R) r • e.addEquiv.toFun x","typeReadable":"∀ (R : Type u_3) {α : Type u_2} {β : Type u_1} [inst : Semiring R] (e : α ≃ β) [inst_1 : AddCommMonoid β]\n  [inst_2 : Module R β] (r : R) (x : α), e.addEquiv.toFun (r • x) = (RingHom.id R) r • e.addEquiv.toFun 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(R : Type.{u_1}) {α : Type.{u_2}} {β : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.5 : Semiring.{u_1} R] (e : Equiv.{succ u_2, succ u_3} α β) [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18 : AddCommMonoid.{u_3} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.21 : Module.{u_1, u_3} R β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18], LinearEquiv.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.5 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.5)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.5)) 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R] → (e : α ≃ β) → [inst_1 : AddCommMonoid β] → [inst_2 : Module R β] → α ≃ₗ[R] β","typeReferences":[["Equiv","module"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["Equiv","addCommMonoid"],["RingHom","id"],["Module"],["RingHomInvPair","ids"],["LinearEquiv"],["Equiv"],["Semiring"]],"valueReferences":[["Equiv","module"],["Equiv","linearEquiv","_proof_3"],["Equiv","addCommMonoid"],["Equiv","linearEquiv","_proof_4"],["LinearMap","mk"],["AddHom","mk"],["Equiv","add"],["AddEquiv","toEquiv"],["Equiv","linearEquiv","_proof_2"],["Equiv","addEquiv"],["Semiring","toNonAssocSemiring"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["RingHom","id"],["Equiv","linearEquiv","_proof_1"],["RingHomInvPair","ids"],["LinearEquiv","mk"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["Equiv","toFun"]]},{"isProp":true,"kind":"theorem","name":["LinearEquiv","isScalarTower"],"typeFallback":"forall {R : Type.{u_1}} {α : Type.{u_2}} {β : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 : Semiring.{u_1} R] (A : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9 : Semiring.{u_4} A] [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.12 : Module.{u_1, u_4} R A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} A (Semiring.toNonAssocSemiring.{u_4} A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9)))] [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19 : AddCommMonoid.{u_3} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.22 : Module.{u_4, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.26 : Module.{u_1, u_2} R α inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16] [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.30 : Module.{u_1, u_3} R β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19] [inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.34 : IsScalarTower.{u_1, u_4, u_3} R A β (SMulZeroClass.toSMul.{u_1, u_4} R A (AddZero.toZero.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddMonoidWithOne.toAddMonoid.{u_4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} A (Semiring.toNonAssocSemiring.{u_4} A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R A (AddMonoid.toAddZeroClass.{u_4} A (AddMonoidWithOne.toAddMonoid.{u_4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} A (Semiring.toNonAssocSemiring.{u_4} A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9))))) (DistribMulAction.toDistribSMul.{u_1, u_4} R A (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5)) (AddMonoidWithOne.toAddMonoid.{u_4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} A (Semiring.toNonAssocSemiring.{u_4} A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9)))) (Module.toDistribMulAction.{u_1, u_4} R A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u_4} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_4} A (Semiring.toNonAssocSemiring.{u_4} A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9))) inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.12)))) (SMulZeroClass.toSMul.{u_4, u_3} A β (AddZero.toZero.{u_3} β (AddZeroClass.toAddZero.{u_3} β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_4, u_3} A β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_4, u_3} A β (MonoidWithZero.toMonoid.{u_4} A (Semiring.toMonoidWithZero.{u_4} A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9)) (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19) (Module.toDistribMulAction.{u_4, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.22)))) (SMulZeroClass.toSMul.{u_1, u_3} R β (AddZero.toZero.{u_3} β (AddZeroClass.toAddZero.{u_3} β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_1, u_3} R β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_1, u_3} R β (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5)) (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19) (Module.toDistribMulAction.{u_1, u_3} R β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.30))))] (e : LinearEquiv.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5) α β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.30), IsScalarTower.{u_1, u_4, u_2} R A α (SMulZeroClass.toSMul.{u_1, u_4} R A (AddZero.toZero.{u_4} A (AddZeroClass.toAddZero.{u_4} A (AddMonoid.toAddZeroClass.{u_4} A (AddMonoidWithOne.toAddMonoid.{u_4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} A (NonAssocSemiring.toAddCommMonoidWithOne.{u_4} A (Semiring.toNonAssocSemiring.{u_4} A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9))))))) (DistribSMul.toSMulZeroClass.{u_1, u_4} R A (AddMonoid.toAddZeroClass.{u_4} A (AddMonoidWithOne.toAddMonoid.{u_4} A (AddCommMonoidWithOne.toAddMonoidWithOne.{u_4} A 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inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16 (AddEquiv.module.{u_2, u_3, u_4} α β A inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.22 (LinearEquiv.toAddEquiv.{u_1, u_1, u_2, u_3} R R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5)) (RingHom.id.{u_1} R (Semiring.toNonAssocSemiring.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5)) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5) (RingHomInvPair.ids.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5) α β inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.26 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.30 e)))))) (SMulZeroClass.toSMul.{u_1, u_2} R α (AddZero.toZero.{u_2} α (AddZeroClass.toAddZero.{u_2} α (AddMonoid.toAddZeroClass.{u_2} α (AddCommMonoid.toAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16)))) (DistribSMul.toSMulZeroClass.{u_1, u_2} R α (AddMonoid.toAddZeroClass.{u_2} α (AddCommMonoid.toAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16)) (DistribMulAction.toDistribSMul.{u_1, u_2} R α (MonoidWithZero.toMonoid.{u_1} R (Semiring.toMonoidWithZero.{u_1} R inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5)) (AddCommMonoid.toAddMonoid.{u_2} α inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16) (Module.toDistribMulAction.{u_1, u_2} R α inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.16 inst._@.Mathlib.Algebra.Module.TransferInstance.1890278916._hygCtx._hyg.26))))","typeFull":"∀ {R : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Semiring R] (A : Type u_4) [inst_1 : Semiring A]\n  [inst_2 : Module R A] [inst_3 : AddCommMonoid α] [inst_4 : AddCommMonoid β] [inst_5 : Module A β]\n  [inst_6 : Module R α] [inst_7 : Module R β] [IsScalarTower R A β] (e : α ≃ₗ[R] β), IsScalarTower R A α","typeReadable":"∀ {R : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Semiring R] (A : Type u_4) [inst_1 : Semiring A]\n  [inst_2 : Module R A] [inst_3 : AddCommMonoid α] [inst_4 : AddCommMonoid β] [inst_5 : Module A β]\n  [inst_6 : Module R α] [inst_7 : Module R β] [IsScalarTower R A β] (e : α ≃ₗ[R] β), IsScalarTower R A α","typeReferences":[["IsScalarTower"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["LinearEquiv"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["AddEquiv","module"],["MonoidWithZero","toMonoid"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["NonAssocSemiring","toAddCommMonoidWithOne"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["LinearEquiv","toAddEquiv"],["Module","toDistribMulAction"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["Semiring"]],"valueReferences":[["Equiv","instEquivLike"],["Equiv","mk"],["LinearEquiv","map_smul"],["LinearMap","toAddHom"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddMonoidWithOne","toAddMonoid"],["DFunLike","coe"],["IsScalarTower","mk"],["Equiv"],["congrArg"],["LinearEquiv","invFun"],["Semiring","toNonAssocSemiring"],["AddEquiv","module"],["RingHom","id"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["Equiv","symm"],["instHSMul"],["congrFun'"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddHom","toFun"],["AddCommMonoidWithOne","toAddMonoidWithOne"],["Eq"],["NonAssocSemiring","toAddCommMonoidWithOne"],["LinearEquiv","left_inv"],["DistribSMul","toSMulZeroClass"],["NonUnitalNonAssocSemiring","toAddCommMonoid"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["LinearEquiv","toLinearMap"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["LinearEquiv","symm"],["LinearEquiv","toAddEquiv"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["id"],["RingHomInvPair","ids"],["smul_assoc"],["Eq","mpr"],["LinearEquiv","right_inv"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Equiv","linearEquiv","_proof_1"],"typeFallback":"forall {α : Type.{u_2}} {β : Type.{u_1}} (e : Equiv.{succ u_2, succ u_1} α β) [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18 : AddCommMonoid.{u_1} β] (x : α) (y : α), Eq.{succ u_1} β (Equiv.toFun.{succ u_2, succ u_1} α β (AddEquiv.toEquiv.{u_2, u_1} α β (Equiv.add.{u_2, u_1} α β e (AddCommMagma.toAdd.{u_1} β (AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18)))) (AddCommMagma.toAdd.{u_1} β (AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18))) (Equiv.addEquiv.{u_2, u_1} α β e (AddCommMagma.toAdd.{u_1} β (AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18))))) (HAdd.hAdd.{u_2, u_2, u_2} α α α (instHAdd.{u_2} α (Equiv.add.{u_2, u_1} α β e 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e.addEquiv.toFun x + e.addEquiv.toFun y","typeReadable":"∀ {α : Type u_2} {β : Type u_1} (e : α ≃ β) [inst : AddCommMonoid β] (x y : α),\n  e.addEquiv.toFun (x + y) = e.addEquiv.toFun x + e.addEquiv.toFun y","typeReferences":[["HAdd","hAdd"],["AddCommMonoid"],["Equiv","addEquiv"],["AddCommMonoid","toAddCommSemigroup"],["instHAdd"],["Equiv","add"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Equiv","toFun"],["AddEquiv","toEquiv"],["Eq"],["Equiv"]],"valueReferences":[["Equiv","addEquiv"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","add"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","map_add'"]]},{"isProp":true,"kind":"theorem","name":["Equiv","linearEquiv","_proof_4"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_2}} (e : Equiv.{succ u_1, succ u_2} α β) [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18 : AddCommMonoid.{u_2} β], Function.RightInverse.{succ u_1, succ u_2} α β (Equiv.invFun.{succ u_1, 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(AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18))) (Equiv.addEquiv.{u_1, u_2} α β e (AddCommMagma.toAdd.{u_2} β (AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524416._hygCtx._hyg.18))))))","typeFull":"∀ {α : Type u_1} {β : Type u_2} (e : α ≃ β) [inst : AddCommMonoid β],\n  Function.RightInverse e.addEquiv.invFun e.addEquiv.toFun","typeReadable":"∀ {α : Type u_1} {β : Type u_2} (e : α ≃ β) [inst : AddCommMonoid β],\n  Function.RightInverse e.addEquiv.invFun e.addEquiv.toFun","typeReferences":[["Function","RightInverse"],["AddCommMonoid"],["Equiv","addEquiv"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["Equiv","add"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"],["Equiv"]],"valueReferences":[["Equiv","addEquiv"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","right_inv"],["Equiv","add"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","module","_proof_1"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_3}} (A : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 : Semiring.{u_2} A] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16 : AddCommMonoid.{u_1} α] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19 : AddCommMonoid.{u_3} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.22 : Module.{u_2, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19] (e : AddEquiv.{u_1, u_3} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_3} β (AddCommSemigroup.toAddCommMagma.{u_3} β (AddCommMonoid.toAddCommSemigroup.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)))) (x : A) (y : A) (b : α), Eq.{succ u_1} α (HSMul.hSMul.{u_2, u_1, u_1} A α α (instHSMul.{u_2, u_1} A α (Equiv.smul.{u_2, u_1, u_3} A α β (AddEquiv.toEquiv.{u_1, u_3} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α 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(AddCommMonoid.toAddCommSemigroup.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19))) e) (SMulZeroClass.toSMul.{u_2, u_3} A β (AddZero.toZero.{u_3} β (AddZeroClass.toAddZero.{u_3} β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_2, u_3} A β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_2, u_3} A β (MonoidWithZero.toMonoid.{u_2} A (Semiring.toMonoidWithZero.{u_2} A inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9)) (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19) (Module.toDistribMulAction.{u_2, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.22)))))) x (HSMul.hSMul.{u_2, u_1, u_1} A α α (instHSMul.{u_2, u_1} A α (Equiv.smul.{u_2, u_1, u_3} A α β (AddEquiv.toEquiv.{u_1, u_3} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_3} β (AddCommSemigroup.toAddCommMagma.{u_3} β (AddCommMonoid.toAddCommSemigroup.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19))) e) (SMulZeroClass.toSMul.{u_2, u_3} A β (AddZero.toZero.{u_3} β (AddZeroClass.toAddZero.{u_3} β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_2, u_3} A β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_2, u_3} A β (MonoidWithZero.toMonoid.{u_2} A (Semiring.toMonoidWithZero.{u_2} A inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9)) (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19) (Module.toDistribMulAction.{u_2, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.22)))))) y b))","typeFull":"∀ {α : Type u_1} {β : Type u_3} (A : Type u_2) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (x y : A) (b : α), (x * y) • b = x • y • b","typeReadable":"∀ {α : Type u_1} {β : Type u_3} (A : Type u_2) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (x y : A) (b : α), (x * y) • b = x • y • b","typeReferences":[["Module"],["Equiv","smul"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["Semigroup","toMul"],["AddCommMonoid"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Monoid","toSemigroup"],["Eq"],["DistribSMul","toSMulZeroClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["AddEquiv"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["instHMul"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Equiv","instEquivLike"],["Eq","trans"],["Equiv","smul"],["NonUnitalSemiring","toSemigroupWithZero"],["SemigroupAction","toSMul"],["HMul","hMul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["Equiv"],["AddEquiv","instEquivLike"],["congrArg"],["Semigroup","toMul"],["congr"],["EquivLike","toFunLike"],["forall_congr"],["MonoidWithZero","toMonoid"],["DistribMulAction","toMulAction"],["Equiv","symm"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Monoid","toSemigroup"],["Eq"],["Semiring","toNonUnitalSemiring"],["SemigroupAction","mul_smul"],["DistribSMul","toSMulZeroClass"],["AddEquiv","apply_symm_apply"],["AddEquiv","symm"],["True"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["AddEquiv","toEquiv"],["AddEquiv"],["implies_true"],["eq_self"],["Module","toDistribMulAction"],["EquivLike","toEquiv"],["AddCommMonoid","toAddCommSemigroup"],["of_eq_true"],["HSMul","hSMul"],["instHMul"],["SemigroupWithZero","toSemigroup"],["MulAction","toSemigroupAction"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Equiv","noZeroSMulDivisors"],"typeFallback":"forall {α : Type.{u_2}} {β : Type.{u_3}} (e : Equiv.{succ u_2, succ u_3} α β) (R : Type.{u_4}) [inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.14 : Zero.{u_4} R] [inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.17 : Zero.{u_3} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.20 : SMul.{u_4, u_3} R β] [inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.24 : NoZeroSMulDivisors.{u_4, u_3} R β inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.14 inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.17 inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.20], have this : Zero.{u_2} α := Equiv.zero.{u_2, u_3} α β e inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.17; have this_1 : SMul.{u_4, u_2} R α := Equiv.smul.{u_4, u_2, u_3} R α β e inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.20; NoZeroSMulDivisors.{u_4, u_2} R α inst._@.Mathlib.Algebra.Module.TransferInstance.1924264250._hygCtx._hyg.14 this this_1","typeFull":"∀ {α : Type u_2} {β : Type u_3} (e : α ≃ β) (R : Type u_4) [inst : Zero R] [inst_1 : Zero β] [inst_2 : SMul R β]\n  [NoZeroSMulDivisors R β],\n  have this := e.zero;\n  have this_1 := Equiv.smul R e;\n  NoZeroSMulDivisors R α","typeReadable":"∀ {α : Type u_2} {β : Type u_3} (e : α ≃ β) (R : Type u_4) [inst : Zero R] [inst_1 : Zero β] [inst_2 : SMul R β]\n  [NoZeroSMulDivisors R β],\n  have this := e.zero;\n  have this_1 := Equiv.smul R e;\n  NoZeroSMulDivisors R α","typeReferences":[["SMul"],["Equiv","smul"],["Zero"],["NoZeroSMulDivisors"],["Equiv"],["Equiv","zero"]],"valueReferences":[["implies_congr"],["Equiv","instEquivLike"],["Eq","trans"],["Equiv","smul"],["NoZeroSMulDivisors","mk"],["DFunLike","coe"],["OfNat","ofNat"],["Equiv"],["Equiv","apply_symm_apply"],["congrArg"],["Equiv","zero"],["Or"],["HSMul","hSMul"],["EquivLike","toFunLike"],["id"],["Equiv","symm"],["instHSMul"],["congrFun'"],["Eq","mpr"],["Zero","toOfNat0"],["_private","Mathlib","Algebra","Module","TransferInstance",0,"Equiv","noZeroSMulDivisors","_simp_1_1"],["Eq"],["NoZeroSMulDivisors","eq_zero_or_eq_zero_of_smul_eq_zero"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","linearEquiv","_proof_2"],"typeFallback":"forall {α : Type.{u_2}} {β : Type.{u_1}} (A : Type.{u_3}) [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.9 : Semiring.{u_3} A] [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16 : AddCommMonoid.{u_2} α] [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19 : AddCommMonoid.{u_1} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.22 : Module.{u_3, u_1} A β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19] (e : AddEquiv.{u_2, u_1} α β (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_1} β (AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19)))) (x._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.62 : A) (x._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.64 : α), Eq.{succ u_1} β (DFunLike.coe.{max (succ u_2) (succ u_1), succ u_2, succ u_1} 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(AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_1} β (AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))))) e (DFunLike.coe.{max (succ u_1) (succ u_2), succ u_1, succ u_2} (AddEquiv.{u_1, u_2} β α (AddCommMagma.toAdd.{u_1} β (AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))) (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16)))) β (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : β) => α) (EquivLike.toFunLike.{max (succ u_1) (succ u_2), succ u_1, succ u_2} 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(AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))) e) x._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.64)))) (HSMul.hSMul.{u_3, u_1, u_1} A β β (instHSMul.{u_3, u_1} A β (SMulZeroClass.toSMul.{u_3, u_1} A β (AddZero.toZero.{u_1} β (AddZeroClass.toAddZero.{u_1} β (AddMonoid.toAddZeroClass.{u_1} β (AddCommMonoid.toAddMonoid.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_3, u_1} A β (AddMonoid.toAddZeroClass.{u_1} β (AddCommMonoid.toAddMonoid.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_3, u_1} A β (MonoidWithZero.toMonoid.{u_3} A (Semiring.toMonoidWithZero.{u_3} A inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.9)) (AddCommMonoid.toAddMonoid.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19) (Module.toDistribMulAction.{u_3, u_1} A β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.22))))) x._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.62 (DFunLike.coe.{max (succ u_2) (succ u_1), succ u_2, succ u_1} (Equiv.{succ u_2, succ u_1} α β) α (fun (x._@.Mathlib.Data.FunLike.Basic.2582841819._hygCtx._hyg.11 : α) => β) (EquivLike.toFunLike.{max (succ u_2) (succ u_1), succ u_2, succ u_1} (Equiv.{succ u_2, succ u_1} α β) α β (Equiv.instEquivLike.{succ u_2, succ u_1} α β)) (AddEquiv.toEquiv.{u_2, u_1} α β (AddCommMagma.toAdd.{u_2} α (AddCommSemigroup.toAddCommMagma.{u_2} α (AddCommMonoid.toAddCommSemigroup.{u_2} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_1} β (AddCommSemigroup.toAddCommMagma.{u_1} β (AddCommMonoid.toAddCommSemigroup.{u_1} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))) e) x._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.64))","typeFull":"∀ {α : Type u_2} {β : Type u_1} (A : Type u_3) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (x : A) (x_1 : α), e (e.symm (x • e.toEquiv x_1)) = x • e.toEquiv x_1","typeReadable":"∀ {α : Type u_2} {β : Type u_1} (A : Type u_3) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (x : A) (x_1 : α), e (e.symm (x • e.toEquiv x_1)) = x • e.toEquiv x_1","typeReferences":[["Equiv","instEquivLike"],["Module"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddEquiv","instEquivLike"],["Equiv"],["AddCommMonoid"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["DistribSMul","toSMulZeroClass"],["AddEquiv","symm"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["AddEquiv"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["HSMul","hSMul"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["AddEquiv","apply_symm_apply"],["Equiv","instEquivLike"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["DFunLike","coe"],["Equiv"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["HSMul","hSMul"],["instHSMul"],["AddCommMagma","toAdd"],["AddCommSemigroup","toAddCommMagma"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"],["DistribSMul","toSMulZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","module","_proof_6"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_3}} (A : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 : Semiring.{u_2} A] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16 : AddCommMonoid.{u_1} α] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19 : AddCommMonoid.{u_3} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.22 : Module.{u_2, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19] (e : AddEquiv.{u_1, u_3} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_3} β (AddCommSemigroup.toAddCommMagma.{u_3} β (AddCommMonoid.toAddCommSemigroup.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)))) (x : α), Eq.{succ u_1} α (HSMul.hSMul.{u_2, u_1, u_1} A α α (instHSMul.{u_2, u_1} A α (Equiv.smul.{u_2, u_1, u_3} A α β (AddEquiv.toEquiv.{u_1, u_3} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_3} β (AddCommSemigroup.toAddCommMagma.{u_3} β (AddCommMonoid.toAddCommSemigroup.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19))) e) (SMulZeroClass.toSMul.{u_2, u_3} A β (AddZero.toZero.{u_3} β (AddZeroClass.toAddZero.{u_3} β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_2, u_3} A β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_2, u_3} A β (MonoidWithZero.toMonoid.{u_2} A (Semiring.toMonoidWithZero.{u_2} A inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9)) (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19) (Module.toDistribMulAction.{u_2, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.22)))))) (OfNat.ofNat.{u_2} A 0 (Zero.toOfNat0.{u_2} A (MulZeroClass.toZero.{u_2} A (NonUnitalNonAssocSemiring.toMulZeroClass.{u_2} A (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u_2} A (Semiring.toNonAssocSemiring.{u_2} A inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9)))))) x) (OfNat.ofNat.{u_1} α 0 (Zero.toOfNat0.{u_1} α (AddZero.toZero.{u_1} α (AddZeroClass.toAddZero.{u_1} α (AddMonoid.toAddZeroClass.{u_1} α (AddCommMonoid.toAddMonoid.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16))))))","typeFull":"∀ {α : Type u_1} {β : Type u_3} (A : Type u_2) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (x : α), 0 • x = 0","typeReadable":"∀ {α : Type u_1} {β : Type u_3} (A : Type u_2) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (x : α), 0 • x = 0","typeReferences":[["Module"],["Equiv","smul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddCommMonoid"],["Semiring","toNonAssocSemiring"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Zero","toOfNat0"],["Eq"],["DistribSMul","toSMulZeroClass"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["AddEquiv"],["OfNat","ofNat"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["MulZeroClass","toZero"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["HSMul","hSMul"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["Equiv","instEquivLike"],["Eq","trans"],["Equiv","smul"],["AddEquivClass","instAddMonoidHomClass"],["AddEquiv","instAddEquivClass"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddEquiv","instEquivLike"],["Equiv"],["congrArg"],["Semiring","toNonAssocSemiring"],["EquivLike","toFunLike"],["forall_congr"],["MonoidWithZero","toMonoid"],["Equiv","symm"],["instHSMul"],["congrFun'"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Zero","toOfNat0"],["map_zero"],["Eq"],["MulActionWithZero","toSMulWithZero"],["DistribSMul","toSMulZeroClass"],["AddEquiv","symm"],["True"],["NonAssocSemiring","toNonUnitalNonAssocSemiring"],["AddMonoidHomClass","toZeroHomClass"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Module","toMulActionWithZero"],["AddZeroClass","toAddZero"],["AddEquiv","toEquiv"],["AddEquiv"],["OfNat","ofNat"],["implies_true"],["eq_self"],["Module","toDistribMulAction"],["EquivLike","toEquiv"],["AddCommMonoid","toAddCommSemigroup"],["of_eq_true"],["MulZeroClass","toZero"],["HSMul","hSMul"],["NonUnitalNonAssocSemiring","toMulZeroClass"],["zero_smul"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","linearEquiv","_proof_3"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16 : AddCommMonoid.{u_1} α] [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19 : AddCommMonoid.{u_2} β] (e : AddEquiv.{u_1, u_2} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_2} β (AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19)))), Function.LeftInverse.{succ u_1, succ u_2} α β (Equiv.invFun.{succ u_1, succ u_2} α β (AddEquiv.toEquiv.{u_1, u_2} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_2} β (AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))) e)) (Equiv.toFun.{succ u_1, succ u_2} α β (AddEquiv.toEquiv.{u_1, u_2} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_2} β (AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))) e))","typeFull":"∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : AddCommMonoid β] (e : α ≃+ β),\n  Function.LeftInverse e.invFun e.toFun","typeReadable":"∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : AddCommMonoid β] (e : α ≃+ β),\n  Function.LeftInverse e.invFun e.toFun","typeReferences":[["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["Function","LeftInverse"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"],["AddEquiv"]],"valueReferences":[["Equiv","left_inv"],["AddCommMonoid","toAddCommSemigroup"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","module","_proof_2"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_3}} (A : Type.{u_2}) [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 : Semiring.{u_2} A] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16 : AddCommMonoid.{u_1} α] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19 : AddCommMonoid.{u_3} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.22 : Module.{u_2, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19] (e : AddEquiv.{u_1, u_3} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_3} β (AddCommSemigroup.toAddCommMagma.{u_3} β (AddCommMonoid.toAddCommSemigroup.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)))) (b : α), Eq.{succ u_1} α (HSMul.hSMul.{u_2, u_1, u_1} A α α (instHSMul.{u_2, u_1} A α (Equiv.smul.{u_2, u_1, u_3} A α β (AddEquiv.toEquiv.{u_1, u_3} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_3} β (AddCommSemigroup.toAddCommMagma.{u_3} β (AddCommMonoid.toAddCommSemigroup.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19))) e) (SMulZeroClass.toSMul.{u_2, u_3} A β (AddZero.toZero.{u_3} β (AddZeroClass.toAddZero.{u_3} β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)))) (DistribSMul.toSMulZeroClass.{u_2, u_3} A β (AddMonoid.toAddZeroClass.{u_3} β (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19)) (DistribMulAction.toDistribSMul.{u_2, u_3} A β (MonoidWithZero.toMonoid.{u_2} A (Semiring.toMonoidWithZero.{u_2} A inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9)) (AddCommMonoid.toAddMonoid.{u_3} β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19) (Module.toDistribMulAction.{u_2, u_3} A β inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.19 inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.22)))))) (OfNat.ofNat.{u_2} A 1 (One.toOfNat1.{u_2} A (MulOne.toOne.{u_2} A (MulOneClass.toMulOne.{u_2} A (Monoid.toMulOneClass.{u_2} A (MonoidWithZero.toMonoid.{u_2} A (Semiring.toMonoidWithZero.{u_2} A inst._@.Mathlib.Algebra.Module.TransferInstance.1565340097._hygCtx._hyg.9))))))) b) b","typeFull":"∀ {α : Type u_1} {β : Type u_3} (A : Type u_2) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (b : α), 1 • b = b","typeReadable":"∀ {α : Type u_1} {β : Type u_3} (A : Type u_2) [inst : Semiring A] [inst_1 : AddCommMonoid α] [inst_2 : AddCommMonoid β]\n  [inst_3 : Module A β] (e : α ≃+ β) (b : α), 1 • b = b","typeReferences":[["MulOneClass","toMulOne"],["Module"],["Equiv","smul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["AddCommMonoid"],["Monoid","toMulOneClass"],["MonoidWithZero","toMonoid"],["instHSMul"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["DistribSMul","toSMulZeroClass"],["MulOne","toOne"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddEquiv","toEquiv"],["AddZeroClass","toAddZero"],["AddEquiv"],["OfNat","ofNat"],["Module","toDistribMulAction"],["AddCommMonoid","toAddCommSemigroup"],["One","toOfNat1"],["HSMul","hSMul"],["AddZero","toZero"],["Semiring"],["AddMonoid","toAddZeroClass"]],"valueReferences":[["MulOneClass","toMulOne"],["Equiv","instEquivLike"],["Eq","trans"],["Equiv","smul"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["DFunLike","coe"],["AddEquiv","instEquivLike"],["Equiv"],["congrArg"],["EquivLike","toFunLike"],["forall_congr"],["MonoidWithZero","toMonoid"],["Monoid","toMulOneClass"],["DistribMulAction","toMulAction"],["Equiv","symm"],["instHSMul"],["congrFun'"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["Eq"],["DistribSMul","toSMulZeroClass"],["True"],["MulOne","toOne"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["AddZeroClass","toAddZero"],["AddEquiv","toEquiv"],["AddEquiv"],["OfNat","ofNat"],["implies_true"],["eq_self"],["Module","toDistribMulAction"],["EquivLike","toEquiv"],["AddCommMonoid","toAddCommSemigroup"],["of_eq_true"],["One","toOfNat1"],["one_smul"],["HSMul","hSMul"],["EquivLike","coe_symm_apply_apply"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["Equiv","moduleIsTorsionFree"],"typeFallback":"forall (R : Type.{u_1}) {α : Type.{u_2}} {β : Type.{u_3}} [inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.5 : Semiring.{u_1} R] (e : Equiv.{succ u_2, succ u_3} α β) [inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.18 : AddCommMonoid.{u_3} β] [inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.21 : Module.{u_1, u_3} R β inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.18] [inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.25 : Module.IsTorsionFree.{u_1, u_3} R β inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.5 inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.21], let this : AddCommMonoid.{u_2} α := Equiv.addCommMonoid.{u_2, u_3} α β e inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.18; have this_1 : Module.{u_1, u_2} R �� inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.5 (Equiv.addCommMonoid.{u_2, u_3} α β e inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.18) := Equiv.module.{u_1, u_2, u_3} R α β inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.5 e inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.18 inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.21; Module.IsTorsionFree.{u_1, u_2} R α inst._@.Mathlib.Algebra.Module.TransferInstance.498984483._hygCtx._hyg.5 this this_1","typeFull":"∀ (R : Type u_1) {α : Type u_2} {β : Type u_3} [inst : Semiring R] (e : α ≃ β) [inst_1 : AddCommMonoid β]\n  [inst_2 : Module R β] [Module.IsTorsionFree R β],\n  let this := e.addCommMonoid;\n  have this_1 := Equiv.module R e;\n  Module.IsTorsionFree R α","typeReadable":"∀ (R : Type u_1) {α : Type u_2} {β : Type u_3} [inst : Semiring R] (e : α ≃ β) [inst_1 : AddCommMonoid β]\n  [inst_2 : Module R β] [Module.IsTorsionFree R β],\n  let this := e.addCommMonoid;\n  have this_1 := Equiv.module R e;\n  Module.IsTorsionFree R α","typeReferences":[["Equiv","module"],["Module","IsTorsionFree"],["AddCommMonoid"],["Equiv","addCommMonoid"],["Module"],["Equiv"],["Semiring"]],"valueReferences":[["LinearEquiv","injective"],["Eq","trans"],["Equiv","addCommMonoid"],["Function","Injective","moduleIsTorsionFree"],["SMulZeroClass","toSMul"],["AddCommMonoid","toAddMonoid"],["LinearEquiv"],["map_smul"],["DFunLike","coe"],["congrArg"],["SemilinearEquivClass","instSemilinearMapClass"],["Semiring","toNonAssocSemiring"],["RingHom","id"],["forall_congr"],["EquivLike","toFunLike"],["MonoidWithZero","toMonoid"],["instHSMul"],["congrFun'"],["LinearEquiv","instEquivLike"],["Eq"],["DistribSMul","toSMulZeroClass"],["Equiv","module"],["SemilinearMapClass","toMulActionSemiHomClass"],["True"],["DistribMulAction","toDistribSMul"],["Semiring","toMonoidWithZero"],["Equiv","linearEquiv"],["AddZeroClass","toAddZero"],["implies_true"],["eq_self"],["LinearEquiv","instSemilinearEquivClass"],["Module","toDistribMulAction"],["of_eq_true"],["HSMul","hSMul"],["RingHomInvPair","ids"],["AddZero","toZero"],["AddMonoid","toAddZeroClass"]]},{"isProp":true,"kind":"theorem","name":["AddEquiv","linearEquiv","_proof_4"],"typeFallback":"forall {α : Type.{u_1}} {β : Type.{u_2}} [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16 : AddCommMonoid.{u_1} α] [inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19 : AddCommMonoid.{u_2} β] (e : AddEquiv.{u_1, u_2} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_2} β (AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19)))), Function.RightInverse.{succ u_1, succ u_2} α β (Equiv.invFun.{succ u_1, succ u_2} α β (AddEquiv.toEquiv.{u_1, u_2} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_2} β (AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))) e)) (Equiv.toFun.{succ u_1, succ u_2} α β (AddEquiv.toEquiv.{u_1, u_2} α β (AddCommMagma.toAdd.{u_1} α (AddCommSemigroup.toAddCommMagma.{u_1} α (AddCommMonoid.toAddCommSemigroup.{u_1} α inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.16))) (AddCommMagma.toAdd.{u_2} β (AddCommSemigroup.toAddCommMagma.{u_2} β (AddCommMonoid.toAddCommSemigroup.{u_2} β inst._@.Mathlib.Algebra.Module.TransferInstance.2994524417._hygCtx._hyg.19))) e))","typeFull":"∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : AddCommMonoid β] (e : α ≃+ β),\n  Function.RightInverse e.invFun e.toFun","typeReadable":"∀ {α : Type u_1} {β : Type u_2} [inst : AddCommMonoid α] [inst_1 : AddCommMonoid β] (e : α ≃+ β),\n  Function.RightInverse e.invFun e.toFun","typeReferences":[["Function","RightInverse"],["AddCommMonoid"],["AddCommMonoid","toAddCommSemigroup"],["Equiv","invFun"],["Equiv","toFun"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"],["AddEquiv"]],"valueReferences":[["AddCommMonoid","toAddCommSemigroup"],["Equiv","right_inv"],["AddCommSemigroup","toAddCommMagma"],["AddCommMagma","toAdd"],["AddEquiv","toEquiv"]]}]