linear_algebra.multilinear.basis ⟷ Mathlib.LinearAlgebra.Multilinear.Basis

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 -/
-import Mathbin.LinearAlgebra.Basis
-import Mathbin.LinearAlgebra.Multilinear.Basic
+import LinearAlgebra.Basis
+import LinearAlgebra.Multilinear.Basic
 
 #align_import linear_algebra.multilinear.basis from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.multilinear.basis
-! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Basis
 import Mathbin.LinearAlgebra.Multilinear.Basic
 
+#align_import linear_algebra.multilinear.basis from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
 /-!
 # Multilinear maps in relation to bases.
 

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

@@ -35,6 +35,7 @@ variable [CommSemiring R] [AddCommMonoid M₂] [AddCommMonoid M₃] [∀ i, AddC
 
 variable [∀ i, Module R (M i)] [Module R M₂] [Module R M₃]
 
+#print Basis.ext_multilinear_fin /-
 /-- Two multilinear maps indexed by `fin n` are equal if they are equal when all arguments are
 basis vectors. -/
 theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n → Type _}
@@ -57,7 +58,9 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
       dsimp [Fin.tail]
       rw [Fin.cons_succ, Fin.cons_succ]
 #align basis.ext_multilinear_fin Basis.ext_multilinear_fin
+-/
 
+#print Basis.ext_multilinear /-
 /-- Two multilinear maps indexed by a `fintype` are equal if they are equal when all arguments
 are basis vectors. Unlike `basis.ext_multilinear_fin`, this only uses a single basis; a
 dependently-typed version would still be true, but the proof would need a dependently-typed
@@ -69,4 +72,5 @@ theorem Basis.ext_multilinear [Finite ι] {f g : MultilinearMap R (fun i : ι =>
     (dom_dom_congr_eq_iff (Fintype.equivFin ι) f g).mp
       (Basis.ext_multilinear_fin (fun i => e) fun i => h (i ∘ _))
 #align basis.ext_multilinear Basis.ext_multilinear
+-/
 

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

@@ -35,9 +35,6 @@ variable [CommSemiring R] [AddCommMonoid M₂] [AddCommMonoid M₃] [∀ i, AddC
 
 variable [∀ i, Module R (M i)] [Module R M₂] [Module R M₃]
 
-/- warning: basis.ext_multilinear_fin -> Basis.ext_multilinear_fin is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear_fin Basis.ext_multilinear_finₓ'. -/
 /-- Two multilinear maps indexed by `fin n` are equal if they are equal when all arguments are
 basis vectors. -/
 theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n → Type _}
@@ -61,9 +58,6 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
       rw [Fin.cons_succ, Fin.cons_succ]
 #align basis.ext_multilinear_fin Basis.ext_multilinear_fin
 
-/- warning: basis.ext_multilinear -> Basis.ext_multilinear is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear Basis.ext_multilinearₓ'. -/
 /-- Two multilinear maps indexed by a `fintype` are equal if they are equal when all arguments
 are basis vectors. Unlike `basis.ext_multilinear_fin`, this only uses a single basis; a
 dependently-typed version would still be true, but the proof would need a dependently-typed

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

@@ -69,9 +69,8 @@ are basis vectors. Unlike `basis.ext_multilinear_fin`, this only uses a single b
 dependently-typed version would still be true, but the proof would need a dependently-typed
 version of `dom_dom_congr`. -/
 theorem Basis.ext_multilinear [Finite ι] {f g : MultilinearMap R (fun i : ι => M₂) M₃} {ι₁ : Type _}
-    (e : Basis ι₁ R M₂) (h : ∀ v : ι → ι₁, (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
-  by
-  cases nonempty_fintype ι
+    (e : Basis ι₁ R M₂) (h : ∀ v : ι → ι₁, (f fun i => e (v i)) = g fun i => e (v i)) : f = g := by
+  cases nonempty_fintype ι;
   exact
     (dom_dom_congr_eq_iff (Fintype.equivFin ι) f g).mp
       (Basis.ext_multilinear_fin (fun i => e) fun i => h (i ∘ _))

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

@@ -36,10 +36,7 @@ variable [CommSemiring R] [AddCommMonoid M₂] [AddCommMonoid M₃] [∀ i, AddC
 variable [∀ i, Module R (M i)] [Module R M₂] [Module R M₃]
 
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 Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear_fin Basis.ext_multilinear_finₓ'. -/
 /-- Two multilinear maps indexed by `fin n` are equal if they are equal when all arguments are
 basis vectors. -/
@@ -65,10 +62,7 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
 #align basis.ext_multilinear_fin Basis.ext_multilinear_fin
 
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 Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear Basis.ext_multilinearₓ'. -/
 /-- Two multilinear maps indexed by a `fintype` are equal if they are equal when all arguments
 are basis vectors. Unlike `basis.ext_multilinear_fin`, this only uses a single basis; a

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -39,7 +39,7 @@ variable [∀ i, Module R (M i)] [Module R M₂] [Module R M₃]
 lean 3 declaration is
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 but is expected to have type
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+  forall {R : Type.{u4}} {n : Nat} {M : (Fin n) -> Type.{u3}} {M₂ : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u2} M₂] [_inst_4 : forall (i : Fin n), AddCommMonoid.{u3} (M i)] [_inst_5 : forall (i : Fin n), Module.{u4, u3} R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i)] [_inst_6 : Module.{u4, u2} R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] {f : MultilinearMap.{u4, u3, u2, 0} R (Fin n) M M₂ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : Fin n) => _inst_4 i) _inst_2 (fun (i : Fin n) => _inst_5 i) _inst_6} {g : MultilinearMap.{u4, u3, u2, 0} R (Fin n) M M₂ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : Fin n) => _inst_4 i) _inst_2 (fun (i : Fin n) => _inst_5 i) _inst_6} {ι₁ : (Fin n) -> Type.{u1}} (e : forall (i : Fin n), Basis.{u1, u4, u3} (ι₁ i) R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i) (_inst_5 i)), (forall (v : forall (i : Fin n), ι₁ i), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : forall (i : Fin n), M i) => M₂) (fun (i : Fin n) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, succ u3} (Basis.{u1, u4, u3} (ι₁ i) R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i) (_inst_5 i)) (ι₁ i) (fun (a : ι₁ i) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁ i) => M i) a) (Basis.funLike.{u1, u4, u3} (ι₁ i) R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i) (_inst_5 i)) (e i) (v i))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MultilinearMap.{u4, u3, u2, 0} R (Fin n) M M₂ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : Fin n) => _inst_4 i) _inst_2 (fun (i : Fin n) => _inst_5 i) _inst_6) (forall (i : Fin n), M i) (fun (f : forall (i : Fin n), M i) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : forall (i : Fin n), M i) => M₂) f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u4, u3, u2, 0} R (Fin n) M M₂ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : Fin n) => _inst_4 i) _inst_2 (fun (i : Fin n) => _inst_5 i) _inst_6) f (fun (i : Fin n) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, succ u3} (Basis.{u1, u4, u3} (ι₁ i) R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i) (_inst_5 i)) (ι₁ i) (fun (_x : ι₁ i) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁ i) => M i) _x) (Basis.funLike.{u1, u4, u3} (ι₁ i) R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i) (_inst_5 i)) (e i) (v i))) (FunLike.coe.{max (succ u3) (succ u2), succ u3, succ u2} (MultilinearMap.{u4, u3, u2, 0} R (Fin n) M M₂ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : Fin n) => _inst_4 i) _inst_2 (fun (i : Fin n) => _inst_5 i) _inst_6) (forall (i : Fin n), M i) (fun (f : forall (i : Fin n), M i) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.418 : forall (i : Fin n), M i) => M₂) f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u4, u3, u2, 0} R (Fin n) M M₂ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : Fin n) => _inst_4 i) _inst_2 (fun (i : Fin n) => _inst_5 i) _inst_6) g (fun (i : Fin n) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, succ u3} (Basis.{u1, u4, u3} (ι₁ i) R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i) (_inst_5 i)) (ι₁ i) (fun (_x : ι₁ i) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁ i) => M i) _x) (Basis.funLike.{u1, u4, u3} (ι₁ i) R (M i) (CommSemiring.toSemiring.{u4} R _inst_1) (_inst_4 i) (_inst_5 i)) (e i) (v i)))) -> (Eq.{max (succ u3) (succ u2)} (MultilinearMap.{u4, u3, u2, 0} R (Fin n) M M₂ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : Fin n) => _inst_4 i) _inst_2 (fun (i : Fin n) => _inst_5 i) _inst_6) f g)
 Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear_fin Basis.ext_multilinear_finₓ'. -/
 /-- Two multilinear maps indexed by `fin n` are equal if they are equal when all arguments are
 basis vectors. -/
@@ -68,7 +68,7 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
 lean 3 declaration is
   forall {R : Type.{u1}} {ι : Type.{u2}} {M₂ : Type.{u3}} {M₃ : Type.{u4}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u3} M₂] [_inst_3 : AddCommMonoid.{u4} M₃] [_inst_6 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_7 : Module.{u1, u4} R M₃ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] [_inst_8 : Finite.{succ u2} ι] {f : MultilinearMap.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7} {g : MultilinearMap.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7} {ι₁ : Type.{u5}} (e : Basis.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6), (forall (v : ι -> ι₁), Eq.{succ u4} M₃ (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (MultilinearMap.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) (fun (f : MultilinearMap.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) => (ι -> M₂) -> M₃) (MultilinearMap.hasCoeToFun.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) f (fun (i : ι) => coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6) (fun (_x : Basis.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6) => ι₁ -> M₂) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6) ι₁ (fun (_x : ι₁) => M₂) (Basis.funLike.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6)) e (v i))) (coeFn.{max (succ u2) (succ u3) (succ u4), max (max (succ u2) (succ u3)) (succ u4)} (MultilinearMap.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) (fun (f : MultilinearMap.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) => (ι -> M₂) -> M₃) (MultilinearMap.hasCoeToFun.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) g (fun (i : ι) => coeFn.{max (succ u5) (succ u1) (succ u3), max (succ u5) (succ u3)} (Basis.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6) (fun (_x : Basis.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6) => ι₁ -> M₂) (FunLike.hasCoeToFun.{max (succ u5) (succ u1) (succ u3), succ u5, succ u3} (Basis.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6) ι₁ (fun (_x : ι₁) => M₂) (Basis.funLike.{u5, u1, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_6)) e (v i)))) -> (Eq.{max (succ u2) (succ u3) (succ u4)} (MultilinearMap.{u1, u3, u4, u2} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) f g)
 but is expected to have type
-  forall {R : Type.{u4}} {ι : Type.{u5}} {M₂ : Type.{u3}} {M₃ : Type.{u2}} [_inst_1 : CommSemiring.{u4} R] [_inst_2 : AddCommMonoid.{u3} M₂] [_inst_3 : AddCommMonoid.{u2} M₃] [_inst_6 : Module.{u4, u3} R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2] [_inst_7 : Module.{u4, u2} R M₃ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_3] [_inst_8 : Finite.{succ u5} ι] {f : MultilinearMap.{u4, u3, u2, u5} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7} {g : MultilinearMap.{u4, u3, u2, u5} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7} {ι₁ : Type.{u1}} (e : Basis.{u1, u4, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_6), (forall (v : ι -> ι₁), Eq.{succ u2} ((fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.419 : ι -> M₂) => M₃) (fun (i : ι) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, succ u3} (Basis.{u1, u4, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_6) ι₁ (fun (a : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁) => M₂) a) (Basis.funLike.{u1, u4, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_6) e (v i))) (FunLike.coe.{max (max (succ u5) (succ u3)) (succ u2), max (succ u5) (succ u3), succ u2} (MultilinearMap.{u4, u3, u2, u5} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basis._hyg.901 : ι) => M₂) M₃ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) (ι -> M₂) (fun (f : ι -> M₂) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.419 : ι -> M₂) => M₃) f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u4, u3, u2, u5} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) f (fun (i : ι) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, succ u3} (Basis.{u1, u4, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_6) ι₁ (fun (_x : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁) => M₂) _x) (Basis.funLike.{u1, u4, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_6) e (v i))) (FunLike.coe.{max (max (succ u5) (succ u3)) (succ u2), max (succ u5) (succ u3), succ u2} (MultilinearMap.{u4, u3, u2, u5} R ι (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basis._hyg.913 : ι) => M₂) M₃ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) (ι -> M₂) (fun (f : ι -> M₂) => (fun (x._@.Mathlib.LinearAlgebra.Multilinear.Basic._hyg.419 : ι -> M₂) => M₃) f) (MultilinearMap.instFunLikeMultilinearMapForAll.{u4, u3, u2, u5} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) g (fun (i : ι) => FunLike.coe.{max (max (succ u4) (succ u3)) (succ u1), succ u1, succ u3} (Basis.{u1, u4, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_6) ι₁ (fun (_x : ι₁) => (fun (x._@.Mathlib.LinearAlgebra.Basis._hyg.548 : ι₁) => M₂) _x) (Basis.funLike.{u1, u4, u3} ι₁ R M₂ (CommSemiring.toSemiring.{u4} R _inst_1) _inst_2 _inst_6) e (v i)))) -> (Eq.{max (max (succ u5) (succ u3)) (succ u2)} (MultilinearMap.{u4, u3, u2, u5} R ι (fun (i : ι) => M₂) M₃ (CommSemiring.toSemiring.{u4} R _inst_1) (fun (i : ι) => _inst_2) _inst_3 (fun (i : ι) => _inst_6) _inst_7) f g)
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 Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear Basis.ext_multilinearₓ'. -/
 /-- Two multilinear maps indexed by a `fintype` are equal if they are equal when all arguments
 are basis vectors. Unlike `basis.ext_multilinear_fin`, this only uses a single basis; a

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.multilinear.basis
-! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.LinearAlgebra.Multilinear.Basic
 /-!
 # Multilinear maps in relation to bases.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves lemmas about the action of multilinear maps on basis vectors.
 
 ## TODO

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

@@ -32,6 +32,12 @@ variable [CommSemiring R] [AddCommMonoid M₂] [AddCommMonoid M₃] [∀ i, AddC
 
 variable [∀ i, Module R (M i)] [Module R M₂] [Module R M₃]
 
+/- warning: basis.ext_multilinear_fin -> Basis.ext_multilinear_fin is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear_fin Basis.ext_multilinear_finₓ'. -/
 /-- Two multilinear maps indexed by `fin n` are equal if they are equal when all arguments are
 basis vectors. -/
 theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n → Type _}
@@ -55,6 +61,12 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
       rw [Fin.cons_succ, Fin.cons_succ]
 #align basis.ext_multilinear_fin Basis.ext_multilinear_fin
 
+/- warning: basis.ext_multilinear -> Basis.ext_multilinear is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align basis.ext_multilinear Basis.ext_multilinearₓ'. -/
 /-- Two multilinear maps indexed by a `fintype` are equal if they are equal when all arguments
 are basis vectors. Unlike `basis.ext_multilinear_fin`, this only uses a single basis; a
 dependently-typed version would still be true, but the proof would need a dependently-typed

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: Joseph Myers
 
 ! This file was ported from Lean 3 source module linear_algebra.multilinear.basis
-! leanprover-community/mathlib commit 1cfdf5f34e1044ecb65d10be753008baaf118edf
+! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -59,9 +59,8 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
 are basis vectors. Unlike `basis.ext_multilinear_fin`, this only uses a single basis; a
 dependently-typed version would still be true, but the proof would need a dependently-typed
 version of `dom_dom_congr`. -/
-theorem Basis.ext_multilinear [DecidableEq ι] [Finite ι]
-    {f g : MultilinearMap R (fun i : ι => M₂) M₃} {ι₁ : Type _} (e : Basis ι₁ R M₂)
-    (h : ∀ v : ι → ι₁, (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
+theorem Basis.ext_multilinear [Finite ι] {f g : MultilinearMap R (fun i : ι => M₂) M₃} {ι₁ : Type _}
+    (e : Basis ι₁ R M₂) (h : ∀ v : ι → ι₁, (f fun i => e (v i)) = g fun i => e (v i)) : f = g :=
   by
   cases nonempty_fintype ι
   exact

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)

@@ -24,9 +24,7 @@ This file proves lemmas about the action of multilinear maps on basis vectors.
 open MultilinearMap
 
 variable {R : Type*} {ι : Type*} {n : ℕ} {M : Fin n → Type*} {M₂ : Type*} {M₃ : Type*}
-
 variable [CommSemiring R] [AddCommMonoid M₂] [AddCommMonoid M₃] [∀ i, AddCommMonoid (M i)]
-
 variable [∀ i, Module R (M i)] [Module R M₂] [Module R M₃]
 
 /-- Two multilinear maps indexed by `Fin n` are equal if they are equal when all arguments are

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

This has nice performance benefits.

@@ -23,7 +23,7 @@ This file proves lemmas about the action of multilinear maps on basis vectors.
 
 open MultilinearMap
 
-variable {R : Type _} {ι : Type _} {n : ℕ} {M : Fin n → Type _} {M₂ : Type _} {M₃ : Type _}
+variable {R : Type*} {ι : Type*} {n : ℕ} {M : Fin n → Type*} {M₂ : Type*} {M₃ : Type*}
 
 variable [CommSemiring R] [AddCommMonoid M₂] [AddCommMonoid M₃] [∀ i, AddCommMonoid (M i)]
 
@@ -31,7 +31,7 @@ variable [∀ i, Module R (M i)] [Module R M₂] [Module R M₃]
 
 /-- Two multilinear maps indexed by `Fin n` are equal if they are equal when all arguments are
 basis vectors. -/
-theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n → Type _}
+theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n → Type*}
     (e : ∀ i, Basis (ι₁ i) R (M i))
     (h : ∀ v : ∀ i, ι₁ i, (f fun i => e i (v i)) = g fun i => e i (v i)) : f = g := by
   induction' n with m hm
@@ -55,7 +55,7 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
 are basis vectors. Unlike `Basis.ext_multilinear_fin`, this only uses a single basis; a
 dependently-typed version would still be true, but the proof would need a dependently-typed
 version of `dom_dom_congr`. -/
-theorem Basis.ext_multilinear [Finite ι] {f g : MultilinearMap R (fun _ : ι => M₂) M₃} {ι₁ : Type _}
+theorem Basis.ext_multilinear [Finite ι] {f g : MultilinearMap R (fun _ : ι => M₂) M₃} {ι₁ : Type*}
     (e : Basis ι₁ R M₂) (h : ∀ v : ι → ι₁, (f fun i => e (v i)) = g fun i => e (v i)) : f = g := by
   cases nonempty_fintype ι
   exact

• 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) 2021 Joseph Myers. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joseph Myers
-
-! This file was ported from Lean 3 source module linear_algebra.multilinear.basis
-! 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.Basis
 import Mathlib.LinearAlgebra.Multilinear.Basic
 
+#align_import linear_algebra.multilinear.basis from "leanprover-community/mathlib"@"ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a"
+
 /-!
 # Multilinear maps in relation to bases.
 

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -39,10 +39,7 @@ theorem Basis.ext_multilinear_fin {f g : MultilinearMap R M M₂} {ι₁ : Fin n
     (h : ∀ v : ∀ i, ι₁ i, (f fun i => e i (v i)) = g fun i => e i (v i)) : f = g := by
   induction' n with m hm
   · ext x
-    convert h finZeroElim <;>
-    -- Porting note: added below
-    · rename_i x
-      apply finZeroElim x
+    convert h finZeroElim
   · apply Function.LeftInverse.injective uncurry_curryLeft
     refine' Basis.ext (e 0) _
     intro i