algebra.module.opposites
⟷
Mathlib.Algebra.Module.Opposites
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
-import Mathbin.Algebra.Module.Equiv
-import Mathbin.GroupTheory.GroupAction.Opposite
+import Algebra.Module.Equiv
+import GroupTheory.GroupAction.Opposite
#align_import algebra.module.opposites from "leanprover-community/mathlib"@"fac369018417f980cec5fcdafc766a69f88d8cfe"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.module.opposites
-! leanprover-community/mathlib commit fac369018417f980cec5fcdafc766a69f88d8cfe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Algebra.Module.Equiv
import Mathbin.GroupTheory.GroupAction.Opposite
+#align_import algebra.module.opposites from "leanprover-community/mathlib"@"fac369018417f980cec5fcdafc766a69f88d8cfe"
+
/-!
# Module operations on `Mᵐᵒᵖ`
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -43,37 +43,49 @@ def opLinearEquiv : M ≃ₗ[R] Mᵐᵒᵖ :=
#align mul_opposite.op_linear_equiv MulOpposite.opLinearEquiv
-/
+#print MulOpposite.coe_opLinearEquiv /-
@[simp]
theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
rfl
#align mul_opposite.coe_op_linear_equiv MulOpposite.coe_opLinearEquiv
+-/
+#print MulOpposite.coe_opLinearEquiv_symm /-
@[simp]
theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = unop :=
rfl
#align mul_opposite.coe_op_linear_equiv_symm MulOpposite.coe_opLinearEquiv_symm
+-/
+#print MulOpposite.coe_opLinearEquiv_toLinearMap /-
@[simp]
theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → Mᵐᵒᵖ) = op :=
rfl
#align mul_opposite.coe_op_linear_equiv_to_linear_map MulOpposite.coe_opLinearEquiv_toLinearMap
+-/
+#print MulOpposite.coe_opLinearEquiv_symm_toLinearMap /-
@[simp]
theorem coe_opLinearEquiv_symm_toLinearMap :
((opLinearEquiv R).symm.toLinearMap : Mᵐᵒᵖ → M) = unop :=
rfl
#align mul_opposite.coe_op_linear_equiv_symm_to_linear_map MulOpposite.coe_opLinearEquiv_symm_toLinearMap
+-/
+#print MulOpposite.opLinearEquiv_toAddEquiv /-
@[simp]
theorem opLinearEquiv_toAddEquiv : (opLinearEquiv R : M ≃ₗ[R] Mᵐᵒᵖ).toAddEquiv = opAddEquiv :=
rfl
#align mul_opposite.op_linear_equiv_to_add_equiv MulOpposite.opLinearEquiv_toAddEquiv
+-/
+#print MulOpposite.opLinearEquiv_symm_toAddEquiv /-
@[simp]
theorem opLinearEquiv_symm_toAddEquiv :
(opLinearEquiv R : M ≃ₗ[R] Mᵐᵒᵖ).symm.toAddEquiv = opAddEquiv.symm :=
rfl
#align mul_opposite.op_linear_equiv_symm_to_add_equiv MulOpposite.opLinearEquiv_symm_toAddEquiv
+-/
end MulOpposite
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -43,62 +43,32 @@ def opLinearEquiv : M ≃ₗ[R] Mᵐᵒᵖ :=
#align mul_opposite.op_linear_equiv MulOpposite.opLinearEquiv
-/
-/- warning: mul_opposite.coe_op_linear_equiv -> MulOpposite.coe_opLinearEquiv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv MulOpposite.coe_opLinearEquivₓ'. -/
@[simp]
theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
rfl
#align mul_opposite.coe_op_linear_equiv MulOpposite.coe_opLinearEquiv
-/- warning: mul_opposite.coe_op_linear_equiv_symm -> MulOpposite.coe_opLinearEquiv_symm is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm MulOpposite.coe_opLinearEquiv_symmₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = unop :=
rfl
#align mul_opposite.coe_op_linear_equiv_symm MulOpposite.coe_opLinearEquiv_symm
-/- warning: mul_opposite.coe_op_linear_equiv_to_linear_map -> MulOpposite.coe_opLinearEquiv_toLinearMap is a dubious translation:
-lean 3 declaration is
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@[simp]
theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → Mᵐᵒᵖ) = op :=
rfl
#align mul_opposite.coe_op_linear_equiv_to_linear_map MulOpposite.coe_opLinearEquiv_toLinearMap
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@[simp]
theorem coe_opLinearEquiv_symm_toLinearMap :
((opLinearEquiv R).symm.toLinearMap : Mᵐᵒᵖ → M) = unop :=
rfl
#align mul_opposite.coe_op_linear_equiv_symm_to_linear_map MulOpposite.coe_opLinearEquiv_symm_toLinearMap
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@[simp]
theorem opLinearEquiv_toAddEquiv : (opLinearEquiv R : M ≃ₗ[R] Mᵐᵒᵖ).toAddEquiv = opAddEquiv :=
rfl
#align mul_opposite.op_linear_equiv_to_add_equiv MulOpposite.opLinearEquiv_toAddEquiv
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@[simp]
theorem opLinearEquiv_symm_toAddEquiv :
(opLinearEquiv R : M ≃ₗ[R] Mᵐᵒᵖ).symm.toAddEquiv = opAddEquiv.symm :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -44,10 +44,7 @@ def opLinearEquiv : M ≃ₗ[R] Mᵐᵒᵖ :=
-/
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+<too large>
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv MulOpposite.coe_opLinearEquivₓ'. -/
@[simp]
theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
@@ -55,10 +52,7 @@ theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
#align mul_opposite.coe_op_linear_equiv MulOpposite.coe_opLinearEquiv
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u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.unop.{u2} M)
+<too large>
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm MulOpposite.coe_opLinearEquiv_symmₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = unop :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -47,7 +47,7 @@ def opLinearEquiv : M ≃ₗ[R] Mᵐᵒᵖ :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.op.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => MulOpposite.{u2} M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.op.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : M) => MulOpposite.{u2} M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.op.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv MulOpposite.coe_opLinearEquivₓ'. -/
@[simp]
theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
@@ -58,7 +58,7 @@ theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.unop.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MulOpposite.{u2} M) => M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.unop.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2187 : MulOpposite.{u2} M) => M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.unop.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm MulOpposite.coe_opLinearEquiv_symmₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = unop :=
@@ -69,7 +69,7 @@ theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = u
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_to_linear_map MulOpposite.coe_opLinearEquiv_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → Mᵐᵒᵖ) = op :=
@@ -80,7 +80,7 @@ theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → M
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6193 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm_to_linear_map MulOpposite.coe_opLinearEquiv_symm_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm_toLinearMap :
mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e
@@ -69,7 +69,7 @@ theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = u
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_to_linear_map MulOpposite.coe_opLinearEquiv_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → Mᵐᵒᵖ) = op :=
@@ -80,7 +80,7 @@ theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → M
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6191 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm_to_linear_map MulOpposite.coe_opLinearEquiv_symm_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm_toLinearMap :
mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479
@@ -36,22 +36,18 @@ instance : Module R (MulOpposite M) :=
add_smul := fun r₁ r₂ x => unop_injective <| add_smul r₁ r₂ (unop x)
zero_smul := fun x => unop_injective <| zero_smul _ (unop x) }
-/- warning: mul_opposite.op_linear_equiv -> MulOpposite.opLinearEquiv is a dubious translation:
-lean 3 declaration is
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)
-but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)
-Case conversion may be inaccurate. Consider using '#align mul_opposite.op_linear_equiv MulOpposite.opLinearEquivₓ'. -/
+#print MulOpposite.opLinearEquiv /-
/-- The function `op` is a linear equivalence. -/
def opLinearEquiv : M ≃ₗ[R] Mᵐᵒᵖ :=
{ opAddEquiv with map_smul' := MulOpposite.op_smul }
#align mul_opposite.op_linear_equiv MulOpposite.opLinearEquiv
+-/
/- warning: mul_opposite.coe_op_linear_equiv -> MulOpposite.coe_opLinearEquiv is a dubious translation:
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.op.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => MulOpposite.{u2} M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.op.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : M) => MulOpposite.{u2} M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) R M (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R M (MulOpposite.{u2} M) (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.op.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv MulOpposite.coe_opLinearEquivₓ'. -/
@[simp]
theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
@@ -62,7 +58,7 @@ theorem coe_opLinearEquiv : (opLinearEquiv R : M → Mᵐᵒᵖ) = op :=
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeFn.{succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (fun (_x : LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.hasCoeToFun.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.unop.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MulOpposite.{u2} M) => M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.unop.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Hom.GroupAction._hyg.2186 : MulOpposite.{u2} M) => M) _x) (SMulHomClass.toFunLike.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (SMulZeroClass.toSMul.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toZero.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribSMul.toSMulZeroClass.{u1, u2} R (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))) (DistribMulAction.toDistribSMul.{u1, u2} R (MulOpposite.{u2} M) (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3))))) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribSMul.toSMulZeroClass.{u1, u2} R M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (DistribMulAction.toDistribSMul.{u1, u2} R M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (DistribMulActionHomClass.toSMulHomClass.{u2, u1, u2, u2} (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) R (MulOpposite.{u2} M) M (MonoidWithZero.toMonoid.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)) (AddCommMonoid.toAddMonoid.{u2} M _inst_2) (Module.toDistribMulAction.{u1, u2} R (MulOpposite.{u2} M) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (Module.toDistribMulAction.{u1, u2} R M _inst_1 _inst_2 _inst_3) (SemilinearMapClass.distribMulActionHomClass.{u1, u2, u2, u2} R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (SemilinearEquivClass.instSemilinearMapClass.{u1, u1, u2, u2, u2} R R (MulOpposite.{u2} M) M (LinearEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (LinearEquiv.instSemilinearEquivClassLinearEquiv.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1)))))) (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.unop.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm MulOpposite.coe_opLinearEquiv_symmₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = unop :=
@@ -73,7 +69,7 @@ theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = u
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_to_linear_map MulOpposite.coe_opLinearEquiv_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → Mᵐᵒᵖ) = op :=
@@ -84,7 +80,7 @@ theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → M
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm_to_linear_map MulOpposite.coe_opLinearEquiv_symm_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm_toLinearMap :
@@ -96,7 +92,7 @@ theorem coe_opLinearEquiv_symm_toLinearMap :
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (AddEquiv.{u2, u2} M (MulOpposite.{u2} M) (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddZeroClass.toHasAdd.{u2} (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))))) (LinearEquiv.toAddEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.opAddEquiv.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (AddEquiv.{u2, u2} M (MulOpposite.{u2} M) (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddZeroClass.toAdd.{u2} (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2))))) (LinearEquiv.toAddEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.opAddEquiv.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (AddEquiv.{u2, u2} M (MulOpposite.{u2} M) (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (AddZeroClass.toAdd.{u2} (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2))))) (LinearEquiv.toAddEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (MulOpposite.opAddEquiv.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))))
Case conversion may be inaccurate. Consider using '#align mul_opposite.op_linear_equiv_to_add_equiv MulOpposite.opLinearEquiv_toAddEquivₓ'. -/
@[simp]
theorem opLinearEquiv_toAddEquiv : (opLinearEquiv R : M ≃ₗ[R] Mᵐᵒᵖ).toAddEquiv = opAddEquiv :=
@@ -107,7 +103,7 @@ theorem opLinearEquiv_toAddEquiv : (opLinearEquiv R : M ≃ₗ[R] Mᵐᵒᵖ).to
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (AddEquiv.{u2, u2} (MulOpposite.{u2} M) M (AddZeroClass.toHasAdd.{u2} (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)))) (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (LinearEquiv.toAddEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (AddEquiv.symm.{u2, u2} M (MulOpposite.{u2} M) (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulOpposite.hasAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (MulOpposite.opAddEquiv.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (AddEquiv.{u2, u2} (MulOpposite.{u2} M) M (AddZeroClass.toAdd.{u2} (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2)))) (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (LinearEquiv.toAddEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (AddEquiv.symm.{u2, u2} M (MulOpposite.{u2} M) (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulOpposite.instAddMulOpposite.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (MulOpposite.opAddEquiv.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (AddEquiv.{u2, u2} (MulOpposite.{u2} M) M (AddZeroClass.toAdd.{u2} (MulOpposite.{u2} M) (AddMonoid.toAddZeroClass.{u2} (MulOpposite.{u2} M) (AddCommMonoid.toAddMonoid.{u2} (MulOpposite.{u2} M) (MulOpposite.addCommMonoid.{u2} M _inst_2)))) (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (LinearEquiv.toAddEquiv.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (AddEquiv.symm.{u2, u2} M (MulOpposite.{u2} M) (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulOpposite.add.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) (MulOpposite.opAddEquiv.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))))
Case conversion may be inaccurate. Consider using '#align mul_opposite.op_linear_equiv_symm_to_add_equiv MulOpposite.opLinearEquiv_symm_toAddEquivₓ'. -/
@[simp]
theorem opLinearEquiv_symm_toAddEquiv :
mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212
@@ -73,7 +73,7 @@ theorem coe_opLinearEquiv_symm : ((opLinearEquiv R).symm : Mᵐᵒᵖ → M) = u
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) => M -> (MulOpposite.{u2} M)) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3)) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : M) => MulOpposite.{u2} M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (MulOpposite.{u2} M) _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3))) (MulOpposite.op.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_to_linear_map MulOpposite.coe_opLinearEquiv_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → Mᵐᵒᵖ) = op :=
@@ -84,7 +84,7 @@ theorem coe_opLinearEquiv_toLinearMap : ((opLinearEquiv R).toLinearMap : M → M
lean 3 declaration is
forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} ((fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (coeFn.{succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (fun (_x : LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) => (MulOpposite.{u2} M) -> M) (LinearMap.hasCoeToFun.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.addCommMonoid.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
but is expected to have type
- forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6178 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
+ forall (R : Type.{u1}) {M : Type.{u2}} [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2], Eq.{succ u2} (forall (a : MulOpposite.{u2} M), (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) a) (FunLike.coe.{succ u2, succ u2, succ u2} (LinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3) (MulOpposite.{u2} M) (fun (_x : MulOpposite.{u2} M) => (fun (x._@.Mathlib.Algebra.Module.LinearMap._hyg.6190 : MulOpposite.{u2} M) => M) _x) (LinearMap.instFunLikeLinearMap.{u1, u1, u2, u2} R R (MulOpposite.{u2} M) M _inst_1 _inst_1 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (LinearEquiv.toLinearMap.{u1, u1, u2, u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.{u2} M) M (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_2 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) _inst_3 (LinearEquiv.symm.{u1, u1, u2, u2} R R M (MulOpposite.{u2} M) _inst_1 _inst_1 _inst_2 (MulOpposite.instAddCommMonoidMulOpposite.{u2} M _inst_2) _inst_3 (MulOpposite.module.{u1, u2} R M _inst_1 _inst_2 _inst_3) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) (MulOpposite.opLinearEquiv.{u1, u2} R M _inst_1 _inst_2 _inst_3)))) (MulOpposite.unop.{u2} M)
Case conversion may be inaccurate. Consider using '#align mul_opposite.coe_op_linear_equiv_symm_to_linear_map MulOpposite.coe_opLinearEquiv_symm_toLinearMapₓ'. -/
@[simp]
theorem coe_opLinearEquiv_symm_toLinearMap :
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -23,10 +23,9 @@ universe u v
variable (R : Type u) {M : Type v} [Semiring R] [AddCommMonoid M] [Module R M]
/-- `MulOpposite.distribMulAction` extends to a `Module` -/
-instance module : Module R (MulOpposite M) :=
- { MulOpposite.distribMulAction M R with
- add_smul := fun r₁ r₂ x => unop_injective <| add_smul r₁ r₂ (unop x)
- zero_smul := fun x => unop_injective <| zero_smul _ (unop x) }
+instance instModule : Module R Mᵐᵒᵖ where
+ add_smul _ _ _ := unop_injective <| add_smul _ _ _
+ zero_smul _ := unop_injective <| zero_smul _ _
/-- The function `op` is a linear equivalence. -/
def opLinearEquiv : M ≃ₗ[R] Mᵐᵒᵖ :=
@@ -2,15 +2,12 @@
Copyright (c) 2020 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.module.opposites
-! leanprover-community/mathlib commit f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Algebra.Module.Equiv
import Mathlib.GroupTheory.GroupAction.Opposite
+#align_import algebra.module.opposites from "leanprover-community/mathlib"@"f7fc89d5d5ff1db2d1242c7bb0e9062ce47ef47c"
+
/-!
# Module operations on `Mᵐᵒᵖ`
@@ -15,7 +15,7 @@ import Mathlib.GroupTheory.GroupAction.Opposite
# Module operations on `Mᵐᵒᵖ`
This file contains definitions that build on top of the group action definitions in
-`GroupRheory.GroupAction.Opposite`.
+`GroupTheory.GroupAction.Opposite`.
-/
The unported dependencies are