linear_algebra.multilinear.tensor_product ⟷ Mathlib.LinearAlgebra.Multilinear.TensorProduct

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
 import LinearAlgebra.Multilinear.Basic
-import LinearAlgebra.TensorProduct
+import LinearAlgebra.TensorProduct.Basic
 
 #align_import linear_algebra.multilinear.tensor_product from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 

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.LinearAlgebra.Multilinear.Basic
-import Mathbin.LinearAlgebra.TensorProduct
+import LinearAlgebra.Multilinear.Basic
+import LinearAlgebra.TensorProduct
 
 #align_import linear_algebra.multilinear.tensor_product from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 

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 linear_algebra.multilinear.tensor_product
-! 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.Multilinear.Basic
 import Mathbin.LinearAlgebra.TensorProduct
 
+#align_import linear_algebra.multilinear.tensor_product from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
 /-!
 # Constructions relating multilinear maps and tensor products.
 

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

@@ -35,6 +35,7 @@ variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
 
 variable {N : Type _} [AddCommMonoid N] [Module R N]
 
+#print MultilinearMap.domCoprod /-
 /-- Given two multilinear maps `(ι₁ → N) → N₁` and `(ι₂ → N) → N₂`, this produces the map
 `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂` by taking the coproduct of the domain and the tensor product
 of the codomain.
@@ -65,6 +66,7 @@ def domCoprod (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
     letI := (@Sum.inr_injective ι₁ ι₂).DecidableEq
     cases i <;> simp [TensorProduct.smul_tmul', TensorProduct.tmul_smul]
 #align multilinear_map.dom_coprod MultilinearMap.domCoprod
+-/
 
 #print MultilinearMap.domCoprod' /-
 /-- A more bundled version of `multilinear_map.dom_coprod` that maps
@@ -81,12 +83,15 @@ def domCoprod' :
 #align multilinear_map.dom_coprod' MultilinearMap.domCoprod'
 -/
 
+#print MultilinearMap.domCoprod'_apply /-
 @[simp]
 theorem domCoprod'_apply (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
     (b : MultilinearMap R (fun _ : ι₂ => N) N₂) : domCoprod' (a ⊗ₜ[R] b) = domCoprod a b :=
   rfl
 #align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_apply
+-/
 
+#print MultilinearMap.domCoprod_domDomCongr_sumCongr /-
 /-- When passed an `equiv.sum_congr`, `multilinear_map.dom_dom_congr` distributes over
 `multilinear_map.dom_coprod`. -/
 theorem domCoprod_domDomCongr_sumCongr (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
@@ -95,6 +100,7 @@ theorem domCoprod_domDomCongr_sumCongr (a : MultilinearMap R (fun _ : ι₁ => N
       (a.domDomCongr σa).domCoprod (b.domDomCongr σb) :=
   rfl
 #align multilinear_map.dom_coprod_dom_dom_congr_sum_congr MultilinearMap.domCoprod_domDomCongr_sumCongr
+-/
 
 end DomCoprod
 

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

@@ -23,7 +23,7 @@ namespace MultilinearMap
 
 section DomCoprod
 
-open TensorProduct
+open scoped TensorProduct
 
 variable {R ι₁ ι₂ ι₃ ι₄ : Type _}
 

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

@@ -35,12 +35,6 @@ variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
 
 variable {N : Type _} [AddCommMonoid N] [Module R N]
 
-/- warning: multilinear_map.dom_coprod -> MultilinearMap.domCoprod is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {ι₁ : Type.{u2}} {ι₂ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] {N₁ : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} N₁] [_inst_3 : Module.{u1, u4} R N₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {N₂ : Type.{u5}} [_inst_4 : AddCommMonoid.{u5} N₂] [_inst_5 : Module.{u1, u5} R N₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {N : Type.{u6}} [_inst_6 : AddCommMonoid.{u6} N] [_inst_7 : Module.{u1, u6} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (MultilinearMap.{u1, u6, u4, u2} R ι₁ (fun (_x : ι₁) => N) N₁ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₁) => _inst_6) _inst_2 (fun (i : ι₁) => _inst_7) _inst_3) -> (MultilinearMap.{u1, u6, u5, u3} R ι₂ (fun (_x : ι₂) => N) N₂ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₂) => _inst_6) _inst_4 (fun (i : ι₂) => _inst_7) _inst_5) -> (MultilinearMap.{u1, u6, max u4 u5, max u2 u3} R (Sum.{u2, u3} ι₁ ι₂) (fun (_x : Sum.{u2, u3} ι₁ ι₂) => N) (TensorProduct.{u1, u4, u5} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : Sum.{u2, u3} ι₁ ι₂) => _inst_6) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (i : Sum.{u2, u3} ι₁ ι₂) => _inst_7) (TensorProduct.module.{u1, u4, u5} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod MultilinearMap.domCoprodₓ'. -/
 /-- Given two multilinear maps `(ι₁ → N) → N₁` and `(ι₂ → N) → N₂`, this produces the map
 `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂` by taking the coproduct of the domain and the tensor product
 of the codomain.
@@ -87,18 +81,12 @@ def domCoprod' :
 #align multilinear_map.dom_coprod' MultilinearMap.domCoprod'
 -/
 
-/- warning: multilinear_map.dom_coprod'_apply -> MultilinearMap.domCoprod'_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
     (b : MultilinearMap R (fun _ : ι₂ => N) N₂) : domCoprod' (a ⊗ₜ[R] b) = domCoprod a b :=
   rfl
 #align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_apply
 
-/- warning: multilinear_map.dom_coprod_dom_dom_congr_sum_congr -> MultilinearMap.domCoprod_domDomCongr_sumCongr is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_dom_dom_congr_sum_congr MultilinearMap.domCoprod_domDomCongr_sumCongrₓ'. -/
 /-- When passed an `equiv.sum_congr`, `multilinear_map.dom_dom_congr` distributes over
 `multilinear_map.dom_coprod`. -/
 theorem domCoprod_domDomCongr_sumCongr (a : MultilinearMap R (fun _ : ι₁ => N) N₁)

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

@@ -80,18 +80,10 @@ def domCoprod' :
       MultilinearMap R (fun _ : Sum ι₁ ι₂ => N) (N₁ ⊗[R] N₂) :=
   TensorProduct.lift <|
     LinearMap.mk₂ R domCoprod
-      (fun m₁ m₂ n => by
-        ext
-        simp only [dom_coprod_apply, TensorProduct.add_tmul, add_apply])
-      (fun c m n => by
-        ext
-        simp only [dom_coprod_apply, TensorProduct.smul_tmul', smul_apply])
-      (fun m n₁ n₂ => by
-        ext
-        simp only [dom_coprod_apply, TensorProduct.tmul_add, add_apply])
-      fun c m n => by
-      ext
-      simp only [dom_coprod_apply, TensorProduct.tmul_smul, smul_apply]
+      (fun m₁ m₂ n => by ext; simp only [dom_coprod_apply, TensorProduct.add_tmul, add_apply])
+      (fun c m n => by ext; simp only [dom_coprod_apply, TensorProduct.smul_tmul', smul_apply])
+      (fun m n₁ n₂ => by ext; simp only [dom_coprod_apply, TensorProduct.tmul_add, add_apply])
+      fun c m n => by ext; simp only [dom_coprod_apply, TensorProduct.tmul_smul, smul_apply]
 #align multilinear_map.dom_coprod' MultilinearMap.domCoprod'
 -/
 

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

@@ -96,10 +96,7 @@ def domCoprod' :
 -/
 
 /- warning: multilinear_map.dom_coprod'_apply -> MultilinearMap.domCoprod'_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
@@ -108,10 +105,7 @@ theorem domCoprod'_apply (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
 #align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_apply
 
 /- warning: multilinear_map.dom_coprod_dom_dom_congr_sum_congr -> MultilinearMap.domCoprod_domDomCongr_sumCongr is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_dom_dom_congr_sum_congr MultilinearMap.domCoprod_domDomCongr_sumCongrₓ'. -/
 /-- When passed an `equiv.sum_congr`, `multilinear_map.dom_dom_congr` distributes over
 `multilinear_map.dom_coprod`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -99,7 +99,7 @@ def domCoprod' :
 lean 3 declaration is
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 but is expected to have type
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u1} ι₁ ι₂) => _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (smulCommClass_self.{u6, max u4 u2} R (TensorProduct.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, max u4 u2} R (TensorProduct.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{max u4 u2} (TensorProduct.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (AddCommMonoid.toAddMonoid.{max u4 u2} (TensorProduct.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (TensorProduct.addCommMonoid.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5))) (Module.toMulActionWithZero.{u6, max u4 u2} R 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_inst_3)))) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u5, u2, u1, u6, u6} ι₂ (fun (_x : ι₂) => N) N₂ (fun (i : ι₂) => _inst_6) _inst_4 R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₂) => _inst_7) _inst_5 _inst_5 (smulCommClass_self.{u6, u2} R N₂ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u2} R N₂ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u2} N₂ (AddCommMonoid.toAddMonoid.{u2} N₂ _inst_4)) (Module.toMulActionWithZero.{u6, u2} R N₂ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4 _inst_5)))) a b)) (MultilinearMap.domCoprod.{u6, u3, u1, u4, u2, u5} R ι₁ ι₂ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7 a b)
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : MultilinearMap R (fun _ : ι₁ => N) N₁)

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

@@ -99,7 +99,7 @@ def domCoprod' :
 lean 3 declaration is
   forall {R : Type.{u1}} {ι₁ : Type.{u2}} {ι₂ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] {N₁ : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} N₁] [_inst_3 : Module.{u1, u4} R N₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {N₂ : Type.{u5}} [_inst_4 : AddCommMonoid.{u5} N₂] [_inst_5 : Module.{u1, u5} R N₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {N : Type.{u6}} [_inst_6 : AddCommMonoid.{u6} N] [_inst_7 : Module.{u1, u6} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (a : MultilinearMap.{u1, u6, u4, u2} R ι₁ (fun (_x : ι₁) => N) N₁ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₁) => _inst_6) _inst_2 (fun (i : ι₁) => _inst_7) _inst_3) (b : MultilinearMap.{u1, u6, u5, u3} R ι₂ (fun (_x : ι₂) => N) N₂ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₂) => _inst_6) _inst_4 (fun (i : ι₂) => _inst_7) _inst_5), Eq.{max (succ (max u2 u3)) (succ u6) (succ (max u4 u5))} (MultilinearMap.{u1, u6, max u4 u5, max u2 u3} R (Sum.{u2, u3} ι₁ ι₂) (fun (_x : Sum.{u2, u3} ι₁ ι₂) 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 but is expected to have type
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_inst_3)))) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u5, u2, u1, u6, u6} ι₂ (fun (_x : ι₂) => N) N₂ (fun (i : ι₂) => _inst_6) _inst_4 R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₂) => _inst_7) _inst_5 _inst_5 (smulCommClass_self.{u6, u2} R N₂ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u2} R N₂ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u2} N₂ (AddCommMonoid.toAddMonoid.{u2} N₂ _inst_4)) (Module.toMulActionWithZero.{u6, u2} R N₂ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4 _inst_5)))) a b)) (MultilinearMap.domCoprod.{u6, u3, u1, u4, u2, u5} R ι₁ ι₂ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7 a b)
 Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : MultilinearMap R (fun _ : ι₁ => N) N₁)

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: Eric Wieser
 
 ! This file was ported from Lean 3 source module linear_algebra.multilinear.tensor_product
-! 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.
 -/
@@ -13,6 +13,9 @@ import Mathbin.LinearAlgebra.TensorProduct
 
 /-!
 # Constructions relating multilinear maps and tensor products.
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/
 
 

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

@@ -32,6 +32,12 @@ variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
 
 variable {N : Type _} [AddCommMonoid N] [Module R N]
 
+/- warning: multilinear_map.dom_coprod -> MultilinearMap.domCoprod is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {ι₁ : Type.{u2}} {ι₂ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] {N₁ : Type.{u4}} [_inst_2 : AddCommMonoid.{u4} N₁] [_inst_3 : Module.{u1, u4} R N₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {N₂ : Type.{u5}} [_inst_4 : AddCommMonoid.{u5} N₂] [_inst_5 : Module.{u1, u5} R N₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {N : Type.{u6}} [_inst_6 : AddCommMonoid.{u6} N] [_inst_7 : Module.{u1, u6} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6], (MultilinearMap.{u1, u6, u4, u2} R ι₁ (fun (_x : ι₁) => N) N₁ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₁) => _inst_6) _inst_2 (fun (i : ι₁) => _inst_7) _inst_3) -> (MultilinearMap.{u1, u6, u5, u3} R ι₂ (fun (_x : ι₂) => N) N₂ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₂) => _inst_6) _inst_4 (fun (i : ι₂) => _inst_7) _inst_5) -> (MultilinearMap.{u1, u6, max u4 u5, max u2 u3} R (Sum.{u2, u3} ι₁ ι₂) (fun (_x : Sum.{u2, u3} ι₁ ι₂) => N) (TensorProduct.{u1, u4, u5} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : Sum.{u2, u3} ι₁ ι₂) => _inst_6) (TensorProduct.addCommMonoid.{u1, u4, u5} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (i : Sum.{u2, u3} ι₁ ι₂) => _inst_7) (TensorProduct.module.{u1, u4, u5} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod MultilinearMap.domCoprodₓ'. -/
 /-- Given two multilinear maps `(ι₁ → N) → N₁` and `(ι₂ → N) → N₂`, this produces the map
 `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂` by taking the coproduct of the domain and the tensor product
 of the codomain.
@@ -63,6 +69,7 @@ def domCoprod (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
     cases i <;> simp [TensorProduct.smul_tmul', TensorProduct.tmul_smul]
 #align multilinear_map.dom_coprod MultilinearMap.domCoprod
 
+#print MultilinearMap.domCoprod' /-
 /-- A more bundled version of `multilinear_map.dom_coprod` that maps
 `((ι₁ → N) → N₁) ⊗ ((ι₂ → N) → N₂)` to `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂`. -/
 def domCoprod' :
@@ -83,13 +90,26 @@ def domCoprod' :
       ext
       simp only [dom_coprod_apply, TensorProduct.tmul_smul, smul_apply]
 #align multilinear_map.dom_coprod' MultilinearMap.domCoprod'
+-/
 
+/- warning: multilinear_map.dom_coprod'_apply -> MultilinearMap.domCoprod'_apply is a dubious translation:
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(TensorProduct.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u6} R _inst_1) (TensorProduct.addCommMonoid.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u6, u4, u2} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5))))) (RingHom.id.{u6} R (Semiring.toNonAssocSemiring.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)))) (MultilinearMap.domCoprod'.{u6, u3, u1, u4, u2, u5} R ι₁ ι₂ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7) (TensorProduct.tmul.{u6, max (max u5 u4) u3, max (max u5 u2) u1} R _inst_1 (MultilinearMap.{u6, u5, u4, u3} R ι₁ (fun (_x : ι₁) => N) N₁ (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₁) => _inst_6) _inst_2 (fun (i : ι₁) => _inst_7) _inst_3) (MultilinearMap.{u6, u5, u2, u1} R ι₂ (fun (_x : ι₂) => N) N₂ (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₂) => _inst_6) _inst_4 (fun (i : ι₂) => _inst_7) _inst_5) (MultilinearMap.addCommMonoid.{u6, u5, u4, u3} R ι₁ (fun (_x : ι₁) => N) N₁ (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₁) => _inst_6) _inst_2 (fun (i : ι₁) => _inst_7) _inst_3) (MultilinearMap.addCommMonoid.{u6, u5, u2, u1} R ι₂ (fun (_x : ι₂) => N) N₂ (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₂) => _inst_6) _inst_4 (fun (i : ι₂) => _inst_7) _inst_5) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u5, u4, u3, u6, u6} ι₁ (fun (_x : ι₁) => N) N₁ (fun (i : ι₁) => _inst_6) _inst_2 R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₁) => _inst_7) _inst_3 _inst_3 (smulCommClass_self.{u6, u4} R N₁ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u4} R N₁ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u4} N₁ (AddCommMonoid.toAddMonoid.{u4} N₁ _inst_2)) (Module.toMulActionWithZero.{u6, u4} R N₁ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_2 _inst_3)))) (MultilinearMap.instModuleMultilinearMapAddCommMonoid.{u5, u2, u1, u6, u6} ι₂ (fun (_x : ι₂) => N) N₂ (fun (i : ι₂) => _inst_6) _inst_4 R R (CommSemiring.toSemiring.{u6} R _inst_1) (CommSemiring.toSemiring.{u6} R _inst_1) (fun (i : ι₂) => _inst_7) _inst_5 _inst_5 (smulCommClass_self.{u6, u2} R N₂ (CommSemiring.toCommMonoid.{u6} R _inst_1) (MulActionWithZero.toMulAction.{u6, u2} R N₂ (Semiring.toMonoidWithZero.{u6} R (CommSemiring.toSemiring.{u6} R _inst_1)) (AddMonoid.toZero.{u2} N₂ (AddCommMonoid.toAddMonoid.{u2} N₂ _inst_4)) (Module.toMulActionWithZero.{u6, u2} R N₂ (CommSemiring.toSemiring.{u6} R _inst_1) _inst_4 _inst_5)))) a b)) (MultilinearMap.domCoprod.{u6, u3, u1, u4, u2, u5} R ι₁ ι₂ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7 a b)
+Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_applyₓ'. -/
 @[simp]
 theorem domCoprod'_apply (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
     (b : MultilinearMap R (fun _ : ι₂ => N) N₂) : domCoprod' (a ⊗ₜ[R] b) = domCoprod a b :=
   rfl
 #align multilinear_map.dom_coprod'_apply MultilinearMap.domCoprod'_apply
 
+/- warning: multilinear_map.dom_coprod_dom_dom_congr_sum_congr -> MultilinearMap.domCoprod_domDomCongr_sumCongr is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {ι₁ : Type.{u2}} {ι₂ : Type.{u3}} {ι₃ : Type.{u4}} {ι₄ : Type.{u5}} [_inst_1 : CommSemiring.{u1} R] {N₁ : Type.{u6}} [_inst_2 : AddCommMonoid.{u6} N₁] [_inst_3 : Module.{u1, u6} R N₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] {N₂ : Type.{u7}} [_inst_4 : AddCommMonoid.{u7} N₂] [_inst_5 : Module.{u1, u7} R N₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_4] {N : Type.{u8}} [_inst_6 : AddCommMonoid.{u8} N] [_inst_7 : Module.{u1, u8} R N (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6] (a : MultilinearMap.{u1, u8, u6, u2} R ι₁ (fun (_x : ι₁) => N) N₁ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₁) => _inst_6) _inst_2 (fun (i : ι₁) => _inst_7) _inst_3) (b : MultilinearMap.{u1, u8, u7, u3} R ι₂ (fun (_x : ι₂) => N) N₂ (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : ι₂) => _inst_6) _inst_4 (fun (i : ι₂) => _inst_7) _inst_5) (σa : Equiv.{succ u2, succ u4} ι₁ ι₃) (σb : Equiv.{succ u3, succ u5} ι₂ ι₄), Eq.{max (succ (max u4 u5)) (succ u8) (succ (max u6 u7))} (MultilinearMap.{u1, u8, max u6 u7, max u4 u5} R (Sum.{u4, u5} ι₃ ι₄) (fun (i : Sum.{u4, u5} ι₃ ι₄) => N) (TensorProduct.{u1, u6, u7} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (fun (i : Sum.{u4, u5} ι₃ ι₄) => _inst_6) (TensorProduct.addCommMonoid.{u1, u6, u7} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (i : Sum.{u4, u5} ι₃ ι₄) => _inst_7) (TensorProduct.module.{u1, u6, u7} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5)) (MultilinearMap.domDomCongr.{u1, u8, max u6 u7, max u2 u3, max u4 u5} R N (TensorProduct.{u1, u6, u7} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 (TensorProduct.addCommMonoid.{u1, u6, u7} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) _inst_7 (TensorProduct.module.{u1, u6, u7} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (Sum.{u2, u3} ι₁ ι₂) (Sum.{u4, u5} ι₃ ι₄) (Equiv.sumCongr.{u2, u3, u4, u5} ι₁ ι₂ ι₃ ι₄ σa σb) (MultilinearMap.domCoprod.{u1, u2, u3, u6, u7, u8} R ι₁ ι₂ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7 a b)) (MultilinearMap.domCoprod.{u1, u4, u5, u6, u7, u8} R ι₃ ι₄ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7 (MultilinearMap.domDomCongr.{u1, u8, u6, u2, u4} R N N₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_2 _inst_7 _inst_3 ι₁ ι₃ σa a) (MultilinearMap.domDomCongr.{u1, u8, u7, u3, u5} R N N₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_6 _inst_4 _inst_7 _inst_5 ι₂ ι₄ σb b))
+but is expected to have type
+  forall {R : Type.{u8}} {ι₁ : Type.{u5}} {ι₂ : Type.{u3}} {ι₃ : Type.{u2}} {ι₄ : Type.{u1}} [_inst_1 : CommSemiring.{u8} R] {N₁ : Type.{u6}} [_inst_2 : AddCommMonoid.{u6} N₁] [_inst_3 : Module.{u8, u6} R N₁ (CommSemiring.toSemiring.{u8} R _inst_1) _inst_2] {N₂ : Type.{u4}} [_inst_4 : AddCommMonoid.{u4} N₂] [_inst_5 : Module.{u8, u4} R N₂ (CommSemiring.toSemiring.{u8} R _inst_1) _inst_4] {N : Type.{u7}} [_inst_6 : AddCommMonoid.{u7} N] [_inst_7 : Module.{u8, u7} R N (CommSemiring.toSemiring.{u8} R _inst_1) _inst_6] (a : MultilinearMap.{u8, u7, u6, u5} R ι₁ (fun (_x : ι₁) => N) N₁ (CommSemiring.toSemiring.{u8} R _inst_1) (fun (i : ι₁) => _inst_6) _inst_2 (fun (i : ι₁) => _inst_7) _inst_3) (b : MultilinearMap.{u8, u7, u4, u3} R ι₂ (fun (_x : ι₂) => N) N₂ (CommSemiring.toSemiring.{u8} R _inst_1) (fun (i : ι₂) => _inst_6) _inst_4 (fun (i : ι₂) => _inst_7) _inst_5) (σa : Equiv.{succ u5, succ u2} ι₁ ι₃) (σb : Equiv.{succ u3, succ u1} ι₂ ι₄), Eq.{max (max (max (max (succ u2) (succ u1)) (succ u6)) (succ u4)) (succ u7)} (MultilinearMap.{u8, u7, max u6 u4, max u2 u1} R (Sum.{u2, u1} ι₃ ι₄) (fun (i : Sum.{u2, u1} ι₃ ι₄) => N) (TensorProduct.{u8, u6, u4} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u8} R _inst_1) (fun (i : Sum.{u2, u1} ι₃ ι₄) => _inst_6) (TensorProduct.addCommMonoid.{u8, u6, u4} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (fun (i : Sum.{u2, u1} ι₃ ι₄) => _inst_7) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u8, u6, u4} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5)) (MultilinearMap.domDomCongr.{u8, u7, max u6 u4, max u5 u3, max u2 u1} R N (TensorProduct.{u8, u6, u4} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (CommSemiring.toSemiring.{u8} R _inst_1) _inst_6 (TensorProduct.addCommMonoid.{u8, u6, u4} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) _inst_7 (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u8, u6, u4} R _inst_1 N₁ N₂ _inst_2 _inst_4 _inst_3 _inst_5) (Sum.{u5, u3} ι₁ ι₂) (Sum.{u2, u1} ι₃ ι₄) (Equiv.sumCongr.{u5, u2, u3, u1} ι₁ ι₃ ι₂ ι₄ σa σb) (MultilinearMap.domCoprod.{u8, u5, u3, u6, u4, u7} R ι₁ ι₂ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7 a b)) (MultilinearMap.domCoprod.{u8, u2, u1, u6, u4, u7} R ι₃ ι₄ _inst_1 N₁ _inst_2 _inst_3 N₂ _inst_4 _inst_5 N _inst_6 _inst_7 (MultilinearMap.domDomCongr.{u8, u7, u6, u5, u2} R N N₁ (CommSemiring.toSemiring.{u8} R _inst_1) _inst_6 _inst_2 _inst_7 _inst_3 ι₁ ι₃ σa a) (MultilinearMap.domDomCongr.{u8, u7, u4, u3, u1} R N N₂ (CommSemiring.toSemiring.{u8} R _inst_1) _inst_6 _inst_4 _inst_7 _inst_5 ι₂ ι₄ σb b))
+Case conversion may be inaccurate. Consider using '#align multilinear_map.dom_coprod_dom_dom_congr_sum_congr MultilinearMap.domCoprod_domDomCongr_sumCongrₓ'. -/
 /-- When passed an `equiv.sum_congr`, `multilinear_map.dom_dom_congr` distributes over
 `multilinear_map.dom_coprod`. -/
 theorem domCoprod_domDomCongr_sumCongr (a : MultilinearMap R (fun _ : ι₁ => N) N₁)

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: Eric Wieser
 
 ! This file was ported from Lean 3 source module linear_algebra.multilinear.tensor_product
-! leanprover-community/mathlib commit 48883dcd064d0e1800aec4b21633c3a361d516c0
+! leanprover-community/mathlib commit ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -26,8 +26,6 @@ variable {R ι₁ ι₂ ι₃ ι₄ : Type _}
 
 variable [CommSemiring R]
 
-variable [DecidableEq ι₁] [DecidableEq ι₂] [DecidableEq ι₃] [DecidableEq ι₄]
-
 variable {N₁ : Type _} [AddCommMonoid N₁] [Module R N₁]
 
 variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
@@ -53,8 +51,16 @@ def domCoprod (a : MultilinearMap R (fun _ : ι₁ => N) N₁)
     MultilinearMap R (fun _ : Sum ι₁ ι₂ => N) (N₁ ⊗[R] N₂)
     where
   toFun v := (a fun i => v (Sum.inl i)) ⊗ₜ b fun i => v (Sum.inr i)
-  map_add' v i p q := by cases i <;> simp [TensorProduct.add_tmul, TensorProduct.tmul_add]
-  map_smul' v i c p := by cases i <;> simp [TensorProduct.smul_tmul', TensorProduct.tmul_smul]
+  map_add' _ v i p q := by
+    skip
+    letI := (@Sum.inl_injective ι₁ ι₂).DecidableEq
+    letI := (@Sum.inr_injective ι₁ ι₂).DecidableEq
+    cases i <;> simp [TensorProduct.add_tmul, TensorProduct.tmul_add]
+  map_smul' _ v i c p := by
+    skip
+    letI := (@Sum.inl_injective ι₁ ι₂).DecidableEq
+    letI := (@Sum.inr_injective ι₁ ι₂).DecidableEq
+    cases i <;> simp [TensorProduct.smul_tmul', TensorProduct.tmul_smul]
 #align multilinear_map.dom_coprod MultilinearMap.domCoprod
 
 /-- A more bundled version of `multilinear_map.dom_coprod` that maps

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)

@@ -21,13 +21,9 @@ section DomCoprod
 open TensorProduct
 
 variable {R ι₁ ι₂ ι₃ ι₄ : Type*}
-
 variable [CommSemiring R]
-
 variable {N₁ : Type*} [AddCommMonoid N₁] [Module R N₁]
-
 variable {N₂ : Type*} [AddCommMonoid N₂] [Module R N₂]
-
 variable {N : Type*} [AddCommMonoid N] [Module R N]
 
 /-- Given two multilinear maps `(ι₁ → N) → N₁` and `(ι₂ → N) → N₂`, this produces the map

Move:

• Mathlib/Algebra/Module/DirectLimitAndTensorProduct.lean to LinearAlgebra/TensorProduct/DirectLimit.lean
• Mathlib/LinearAlgebra/TensorProduct to Mathlib/LinearAlgebra.TensorProduct.Basic.lean
• Mathlib/RingTheory/TensorProduct to Mathlib/RingTheory/TensorProduct/Basic.lean.

This follows suggestions 1, 2, 3 of

https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Tensor.20Products.20of.20modules.20and.20rings/near/424605543

Co-authored-by: Antoine Chambert-Loir <antoine.chambert-loir@math.univ-paris-diderot.fr>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
 import Mathlib.LinearAlgebra.Multilinear.Basic
-import Mathlib.LinearAlgebra.TensorProduct
+import Mathlib.LinearAlgebra.TensorProduct.Basic
 
 #align_import linear_algebra.multilinear.tensor_product from "leanprover-community/mathlib"@"ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a"
 

More principled version of #7281.

@@ -12,6 +12,7 @@ import Mathlib.LinearAlgebra.TensorProduct
 # Constructions relating multilinear maps and tensor products.
 -/
 
+suppress_compilation
 
 namespace MultilinearMap
 

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

This has nice performance benefits.

@@ -19,15 +19,15 @@ section DomCoprod
 
 open TensorProduct
 
-variable {R ι₁ ι₂ ι₃ ι₄ : Type _}
+variable {R ι₁ ι₂ ι₃ ι₄ : Type*}
 
 variable [CommSemiring R]
 
-variable {N₁ : Type _} [AddCommMonoid N₁] [Module R N₁]
+variable {N₁ : Type*} [AddCommMonoid N₁] [Module R N₁]
 
-variable {N₂ : Type _} [AddCommMonoid N₂] [Module R N₂]
+variable {N₂ : Type*} [AddCommMonoid N₂] [Module R N₂]
 
-variable {N : Type _} [AddCommMonoid N] [Module R N]
+variable {N : Type*} [AddCommMonoid N] [Module R N]
 
 /-- Given two multilinear maps `(ι₁ → N) → N₁` and `(ι₂ → N) → N₂`, this produces the map
 `(ι₁ ⊕ ι₂ → N) → N₁ ⊗ N₂` by taking the coproduct of the domain and the tensor product

• 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) 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 linear_algebra.multilinear.tensor_product
-! 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.TensorProduct
 
+#align_import linear_algebra.multilinear.tensor_product from "leanprover-community/mathlib"@"ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a"
+
 /-!
 # Constructions relating multilinear maps and tensor products.
 -/

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>