linear_algebra.multilinear.finite_dimensional ⟷ Mathlib.LinearAlgebra.Multilinear.FiniteDimensional

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,8 +3,8 @@ Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathbin.LinearAlgebra.Multilinear.Basic
-import Mathbin.LinearAlgebra.FreeModule.Finite.Matrix
+import LinearAlgebra.Multilinear.Basic
+import LinearAlgebra.FreeModule.Finite.Matrix
 
 #align_import linear_algebra.multilinear.finite_dimensional from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module linear_algebra.multilinear.finite_dimensional
-! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Multilinear.Basic
 import Mathbin.LinearAlgebra.FreeModule.Finite.Matrix
 
+#align_import linear_algebra.multilinear.finite_dimensional from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
+
 /-! # Multilinear maps over finite dimensional spaces
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -73,13 +73,17 @@ private theorem free_and_finite :
     cases ih fun i => N i.succ
     exact ⟨Module.Free.linearMap _ _ _, Module.Finite.linearMap _ _⟩
 
+#print Module.Finite.multilinearMap /-
 instance Module.Finite.multilinearMap : Module.Finite R (MultilinearMap R M₁ M₂) :=
   free_and_finite.2
 #align module.finite.multilinear_map Module.Finite.multilinearMap
+-/
 
+#print Module.Free.multilinearMap /-
 instance Module.Free.multilinearMap : Module.Free R (MultilinearMap R M₁ M₂) :=
   free_and_finite.1
 #align module.free.multilinear_map Module.Free.multilinearMap
+-/
 
 end MultilinearMap
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -73,22 +73,10 @@ private theorem free_and_finite :
     cases ih fun i => N i.succ
     exact ⟨Module.Free.linearMap _ _ _, Module.Finite.linearMap _ _⟩
 
-/- warning: module.finite.multilinear_map -> Module.Finite.multilinearMap is a dubious translation:
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-  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_6 : forall (i : ι), Module.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i))] [_inst_7 : Module.Finite.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_8 : Module.Free.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)], Module.Finite.{u2, max u1 u4 u3} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (MultilinearMap.module.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => _inst_6 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : Module.Finite.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_6 : Module.Free.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_7 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_8 : forall (i : ι), Module.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i))] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)], Module.Finite.{u2, max (max u1 u3) u4} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => _inst_8 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
-Case conversion may be inaccurate. Consider using '#align module.finite.multilinear_map Module.Finite.multilinearMapₓ'. -/
 instance Module.Finite.multilinearMap : Module.Finite R (MultilinearMap R M₁ M₂) :=
   free_and_finite.2
 #align module.finite.multilinear_map Module.Finite.multilinearMap
 
-/- warning: module.free.multilinear_map -> Module.Free.multilinearMap is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_6 : forall (i : ι), Module.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i))] [_inst_7 : Module.Finite.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_8 : Module.Free.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)], Module.Free.{u2, max u1 u4 u3} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (MultilinearMap.module.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => _inst_6 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
-but is expected to have type
-  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : Module.Finite.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_6 : Module.Free.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_7 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_8 : forall (i : ι), Module.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i))] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)], Module.Free.{u2, max (max u1 u3) u4} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => _inst_8 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
-Case conversion may be inaccurate. Consider using '#align module.free.multilinear_map Module.Free.multilinearMapₓ'. -/
 instance Module.Free.multilinearMap : Module.Free R (MultilinearMap R M₁ M₂) :=
   free_and_finite.1
 #align module.free.multilinear_map Module.Free.multilinearMap

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -72,7 +72,6 @@ private theorem free_and_finite :
           Module.Finite.equiv (multilinearCurryLeftEquiv R N M₂)⟩
     cases ih fun i => N i.succ
     exact ⟨Module.Free.linearMap _ _ _, Module.Finite.linearMap _ _⟩
-#align multilinear_map.free_and_finite multilinear_map.free_and_finite
 
 /- warning: module.finite.multilinear_map -> Module.Finite.multilinearMap is a dubious translation:
 lean 3 declaration is

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module linear_algebra.multilinear.finite_dimensional
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
+! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.FreeModule.Finite.Matrix
 
 /-! # Multilinear maps over finite dimensional spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The main results are that multilinear maps over finitely-generated, free modules are
 finitely-generated and free.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

@@ -71,10 +71,22 @@ private theorem free_and_finite :
     exact ⟨Module.Free.linearMap _ _ _, Module.Finite.linearMap _ _⟩
 #align multilinear_map.free_and_finite multilinear_map.free_and_finite
 
+/- warning: module.finite.multilinear_map -> Module.Finite.multilinearMap is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_6 : forall (i : ι), Module.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i))] [_inst_7 : Module.Finite.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_8 : Module.Free.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)], Module.Finite.{u2, max u1 u4 u3} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (MultilinearMap.module.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => _inst_6 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : Module.Finite.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_6 : Module.Free.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_7 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_8 : forall (i : ι), Module.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i))] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)], Module.Finite.{u2, max (max u1 u3) u4} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => _inst_8 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
+Case conversion may be inaccurate. Consider using '#align module.finite.multilinear_map Module.Finite.multilinearMapₓ'. -/
 instance Module.Finite.multilinearMap : Module.Finite R (MultilinearMap R M₁ M₂) :=
   free_and_finite.2
 #align module.finite.multilinear_map Module.Finite.multilinearMap
 
+/- warning: module.free.multilinear_map -> Module.Free.multilinearMap is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_6 : forall (i : ι), Module.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i))] [_inst_7 : Module.Finite.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_8 : Module.Free.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (_inst_6 i)], Module.Free.{u2, max u1 u4 u3} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_6 i) _inst_4) (MultilinearMap.module.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_5 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (fun (i : ι) => _inst_6 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2))) (AddZeroClass.toHasZero.{u3} M₂ (AddMonoid.toAddZeroClass.{u3} M₂ (AddCommMonoid.toAddMonoid.{u3} M₂ (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)))) (Module.toMulActionWithZero.{u2, u3} R M₂ (Ring.toSemiring.{u2} R (CommRing.toRing.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
+but is expected to have type
+  forall {ι : Type.{u1}} {R : Type.{u2}} {M₂ : Type.{u3}} {M₁ : ι -> Type.{u4}} [_inst_1 : Finite.{succ u1} ι] [_inst_2 : CommRing.{u2} R] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_5 : Module.Finite.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_6 : Module.Free.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4] [_inst_7 : forall (i : ι), AddCommGroup.{u4} (M₁ i)] [_inst_8 : forall (i : ι), Module.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i))] [_inst_9 : forall (i : ι), Module.Finite.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)] [_inst_10 : forall (i : ι), Module.Free.{u2, u4} R (M₁ i) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (_inst_8 i)], Module.Free.{u2, max (max u1 u3) u4} R (MultilinearMap.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (MultilinearMap.addCommMonoid.{u2, u4, u3, u1} R ι M₁ M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) (fun (i : ι) => _inst_8 i) _inst_4) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u4, u3, u1, u2, u2} ι M₁ M₂ (fun (i : ι) => AddCommGroup.toAddCommMonoid.{u4} (M₁ i) (_inst_7 i)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) R R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (fun (i : ι) => _inst_8 i) _inst_4 _inst_4 (smulCommClass_self.{u2, u3} R M₂ (CommRing.toCommMonoid.{u2} R _inst_2) (MulActionWithZero.toMulAction.{u2, u3} R M₂ (Semiring.toMonoidWithZero.{u2} R (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2))) (NegZeroClass.toZero.{u3} M₂ (SubNegZeroMonoid.toNegZeroClass.{u3} M₂ (SubtractionMonoid.toSubNegZeroMonoid.{u3} M₂ (SubtractionCommMonoid.toSubtractionMonoid.{u3} M₂ (AddCommGroup.toDivisionAddCommMonoid.{u3} M₂ _inst_3))))) (Module.toMulActionWithZero.{u2, u3} R M₂ (CommSemiring.toSemiring.{u2} R (CommRing.toCommSemiring.{u2} R _inst_2)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_4))))
+Case conversion may be inaccurate. Consider using '#align module.free.multilinear_map Module.Free.multilinearMapₓ'. -/
 instance Module.Free.multilinearMap : Module.Free R (MultilinearMap R M₁ M₂) :=
   free_and_finite.1
 #align module.free.multilinear_map Module.Free.multilinearMap

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module linear_algebra.multilinear.finite_dimensional
-! leanprover-community/mathlib commit bf2a9e0156cc11bf44893ea1b4b2da8ae655c901
+! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -28,7 +28,7 @@ namespace MultilinearMap
 
 variable {ι R M₂ : Type _} {M₁ : ι → Type _}
 
-variable [DecidableEq ι] [Finite ι]
+variable [Finite ι]
 
 variable [CommRing R] [AddCommGroup M₂] [Module R M₂]
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -52,12 +52,12 @@ private theorem free_and_finite :
     cases nonempty_fintype ι
     cases this _ (M₁ ∘ (Fintype.equivFin ι).symm)
     have e := dom_dom_congr_linear_equiv' R M₁ M₂ (Fintype.equivFin ι)
-    exact ⟨Module.Free.ofEquiv e.symm, Module.Finite.equiv e.symm⟩
+    exact ⟨Module.Free.of_equiv e.symm, Module.Finite.equiv e.symm⟩
   intro n N _ _ _ _
   induction' n with n ih
   ·
     exact
-      ⟨Module.Free.ofEquiv (const_linear_equiv_of_is_empty R N M₂),
+      ⟨Module.Free.of_equiv (const_linear_equiv_of_is_empty R N M₂),
         Module.Finite.equiv (const_linear_equiv_of_is_empty R N M₂)⟩
   · suffices
       Module.Free R (N 0 →ₗ[R] MultilinearMap R (fun i : Fin n => N i.succ) M₂) ∧
@@ -65,7 +65,7 @@ private theorem free_and_finite :
       by
       cases this
       exact
-        ⟨Module.Free.ofEquiv (multilinearCurryLeftEquiv R N M₂),
+        ⟨Module.Free.of_equiv (multilinearCurryLeftEquiv R N M₂),
           Module.Finite.equiv (multilinearCurryLeftEquiv R N M₂)⟩
     cases ih fun i => N i.succ
     exact ⟨Module.Free.linearMap _ _ _, Module.Finite.linearMap _ _⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -24,11 +24,8 @@ there.
 namespace MultilinearMap
 
 variable {ι R M₂ : Type*} {M₁ : ι → Type*}
-
 variable [Finite ι]
-
 variable [CommRing R] [AddCommGroup M₂] [Module R M₂]
-
 variable [Module.Finite R M₂] [Module.Free R M₂]
 
 -- Porting note: split out from `free_and_finite` because of inscrutable typeclass errors
@@ -51,7 +48,6 @@ private theorem free_and_finite_fin (n : ℕ) (N : Fin n → Type*) [∀ i, AddC
     exact ⟨Module.Free.linearMap _ _ _ _, Module.Finite.linearMap _ _ _ _⟩
 
 variable [∀ i, AddCommGroup (M₁ i)] [∀ i, Module R (M₁ i)]
-
 variable [∀ i, Module.Finite R (M₁ i)] [∀ i, Module.Free R (M₁ i)]
 
 -- the induction requires us to show both at once

LinearAlgebra/LinearIndependent: generalize linearIndependent_algHom_toLinearMap(') to allow different domain and codomain of the AlgHom.

LinearAlgebra/Basic: add LinearEquiv.congrLeft that works for two rings with commuting actions on the codomain.

LinearAlgebra/FreeModule/Finite/Matrix: generalize Module.Free.linearMap, Module.Finite.linearMap, and FiniteDimensional.finrank_linearMap to work with two different rings that may be noncommutative. Add FiniteDimensional.rank_linearMap, FiniteDimensional.(fin)rank_linearMap_self, and card/cardinal_mk_algHom_le_rank.

FieldTheory/Tower: remove the instance LinearMap.finite_dimensional'' which becomes redundant; mark finrank_linear_map' as deprecated (superseded by finrank_linearMap_self.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -48,7 +48,7 @@ private theorem free_and_finite_fin (n : ℕ) (N : Fin n → Type*) [∀ i, AddC
         ⟨Module.Free.of_equiv (multilinearCurryLeftEquiv R N M₂),
           Module.Finite.equiv (multilinearCurryLeftEquiv R N M₂)⟩
     cases ih fun i => N i.succ
-    exact ⟨Module.Free.linearMap _ _ _, Module.Finite.linearMap _ _⟩
+    exact ⟨Module.Free.linearMap _ _ _ _, Module.Finite.linearMap _ _ _ _⟩
 
 variable [∀ i, AddCommGroup (M₁ i)] [∀ i, Module R (M₁ i)]
 

Also cleanup FunLike-related code and move code about Semirings to a new section.

For linear equivalences, generalization to a Semiring required introducing a new Semiring argument, so that R-linear objects are related by an S-linear equivalence.

@@ -38,8 +38,8 @@ private theorem free_and_finite_fin (n : ℕ) (N : Fin n → Type*) [∀ i, AddC
   induction' n with n ih
   · haveI : IsEmpty (Fin Nat.zero) := inferInstanceAs (IsEmpty (Fin 0))
     exact
-      ⟨Module.Free.of_equiv (constLinearEquivOfIsEmpty R N M₂),
-        Module.Finite.equiv (constLinearEquivOfIsEmpty R N M₂)⟩
+      ⟨Module.Free.of_equiv (constLinearEquivOfIsEmpty R R N M₂),
+        Module.Finite.equiv (constLinearEquivOfIsEmpty R R N M₂)⟩
   · suffices
       Module.Free R (N 0 →ₗ[R] MultilinearMap R (fun i : Fin n => N i.succ) M₂) ∧
         Module.Finite R (N 0 →ₗ[R] MultilinearMap R (fun i : Fin n => N i.succ) M₂) by
@@ -61,7 +61,7 @@ private theorem free_and_finite :
   have := @free_and_finite_fin R M₂ _ _ _ _ _ (Fintype.card ι)
     (fun x => M₁ ((Fintype.equivFin ι).symm x))
   cases' this with l r
-  have e := domDomCongrLinearEquiv' R M₁ M₂ (Fintype.equivFin ι)
+  have e := domDomCongrLinearEquiv' R R M₁ M₂ (Fintype.equivFin ι)
   exact ⟨Module.Free.of_equiv e.symm, Module.Finite.equiv e.symm⟩
 
 instance _root_.Module.Finite.multilinearMap : Module.Finite R (MultilinearMap R M₁ M₂) :=

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -23,7 +23,7 @@ there.
 
 namespace MultilinearMap
 
-variable {ι R M₂ : Type _} {M₁ : ι → Type _}
+variable {ι R M₂ : Type*} {M₁ : ι → Type*}
 
 variable [Finite ι]
 
@@ -32,7 +32,7 @@ variable [CommRing R] [AddCommGroup M₂] [Module R M₂]
 variable [Module.Finite R M₂] [Module.Free R M₂]
 
 -- Porting note: split out from `free_and_finite` because of inscrutable typeclass errors
-private theorem free_and_finite_fin (n : ℕ) (N : Fin n → Type _) [∀ i, AddCommGroup (N i)]
+private theorem free_and_finite_fin (n : ℕ) (N : Fin n → Type*) [∀ i, AddCommGroup (N i)]
     [∀ i, Module R (N i)] [∀ i, Module.Finite R (N i)] [∀ i, Module.Free R (N i)] :
     Module.Free R (MultilinearMap R N M₂) ∧ Module.Finite R (MultilinearMap R N M₂) := by
   induction' n with n ih

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module linear_algebra.multilinear.finite_dimensional
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Multilinear.Basic
 import Mathlib.LinearAlgebra.FreeModule.Finite.Matrix
 
+#align_import linear_algebra.multilinear.finite_dimensional from "leanprover-community/mathlib"@"ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a"
+
 /-! # Multilinear maps over finite dimensional spaces
 
 The main results are that multilinear maps over finitely-generated, free modules are