linear_algebra.bilinear_form.tensor_product ⟷ Mathlib.LinearAlgebra.BilinearForm.TensorProduct

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

@@ -48,8 +48,8 @@ def LinearMap.BilinForm.tensorDistrib :
           (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ
         LinearMap.toBilin).toLinearMap ∘ₗ
     TensorProduct.dualDistrib R _ _ ∘ₗ
-      (TensorProduct.congr (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
-          (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)).toLinearMap
+      (TensorProduct.congr (LinearMap.BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
+          (LinearMap.BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)).toLinearMap
 #align bilin_form.tensor_distrib LinearMap.BilinForm.tensorDistrib
 -/
 
@@ -92,8 +92,8 @@ noncomputable def LinearMap.BilinForm.tensorDistribEquiv :
   -- the same `linear_equiv`s as from `tensor_distrib`, but with the inner linear map also as an
             -- equiv
             TensorProduct.congr
-            (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
-            (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _) ≪≫ₗ
+            (LinearMap.BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
+            (LinearMap.BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _) ≪≫ₗ
           TensorProduct.dualDistribEquiv R (M₁ ⊗ M₁) (M₂ ⊗ M₂) ≪≫ₗ
         (TensorProduct.tensorTensorTensorComm R _ _ _ _).dualMap ≪≫ₗ
       (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ

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

@@ -3,8 +3,8 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import LinearAlgebra.BilinearForm
-import LinearAlgebra.TensorProduct
+import LinearAlgebra.BilinearForm.Basic
+import LinearAlgebra.TensorProduct.Basic
 
 #align_import linear_algebra.bilinear_form.tensor_product from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 

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

@@ -40,31 +40,33 @@ variable [AddCommMonoid M₁] [AddCommMonoid M₂]
 
 variable [Module R M₁] [Module R M₂]
 
-#print BilinForm.tensorDistrib /-
+#print LinearMap.BilinForm.tensorDistrib /-
 /-- The tensor product of two bilinear forms injects into bilinear forms on tensor products. -/
-def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
+def LinearMap.BilinForm.tensorDistrib :
+    BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
   ((TensorProduct.tensorTensorTensorComm R _ _ _ _).dualMap ≪≫ₗ
           (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ
         LinearMap.toBilin).toLinearMap ∘ₗ
     TensorProduct.dualDistrib R _ _ ∘ₗ
       (TensorProduct.congr (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
           (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)).toLinearMap
-#align bilin_form.tensor_distrib BilinForm.tensorDistrib
+#align bilin_form.tensor_distrib LinearMap.BilinForm.tensorDistrib
 -/
 
 @[simp]
-theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
-    (m₁' : M₁) (m₂' : M₂) :
-    tensorDistrib (B₁ ⊗ₜ B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂' :=
+theorem LinearMap.BilinForm.tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁)
+    (m₂ : M₂) (m₁' : M₁) (m₂' : M₂) :
+    LinearMap.BilinForm.tensorDistrib (B₁ ⊗ₜ B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂' :=
   rfl
-#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ
+#align bilin_form.tensor_distrib_tmul LinearMap.BilinForm.tensorDistrib_tmulₓ
 
-#print BilinForm.tmul /-
+#print LinearMap.BilinForm.tmul /-
 /-- The tensor product of two bilinear forms, a shorthand for dot notation. -/
 @[reducible]
-protected def tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) : BilinForm R (M₁ ⊗[R] M₂) :=
-  tensorDistrib (B₁ ⊗ₜ[R] B₂)
-#align bilin_form.tmul BilinForm.tmul
+protected def LinearMap.BilinForm.tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) :
+    BilinForm R (M₁ ⊗[R] M₂) :=
+  LinearMap.BilinForm.tensorDistrib (B₁ ⊗ₜ[R] B₂)
+#align bilin_form.tmul LinearMap.BilinForm.tmul
 -/
 
 end CommSemiring
@@ -83,9 +85,9 @@ variable [Module.Free R M₂] [Module.Finite R M₂]
 
 variable [Nontrivial R]
 
-#print BilinForm.tensorDistribEquiv /-
+#print LinearMap.BilinForm.tensorDistribEquiv /-
 /-- `tensor_distrib` as an equivalence. -/
-noncomputable def tensorDistribEquiv :
+noncomputable def LinearMap.BilinForm.tensorDistribEquiv :
     BilinForm R M₁ ⊗[R] BilinForm R M₂ ≃ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
   -- the same `linear_equiv`s as from `tensor_distrib`, but with the inner linear map also as an
             -- equiv
@@ -96,15 +98,15 @@ noncomputable def tensorDistribEquiv :
         (TensorProduct.tensorTensorTensorComm R _ _ _ _).dualMap ≪≫ₗ
       (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ
     LinearMap.toBilin
-#align bilin_form.tensor_distrib_equiv BilinForm.tensorDistribEquiv
+#align bilin_form.tensor_distrib_equiv LinearMap.BilinForm.tensorDistribEquiv
 -/
 
-#print BilinForm.tensorDistribEquiv_apply /-
+#print LinearMap.BilinForm.tensorDistribEquiv_apply /-
 @[simp]
-theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
-    tensorDistribEquiv B = tensorDistrib B :=
+theorem LinearMap.BilinForm.tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
+    LinearMap.BilinForm.tensorDistribEquiv B = LinearMap.BilinForm.tensorDistrib B :=
   rfl
-#align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_apply
+#align bilin_form.tensor_distrib_equiv_apply LinearMap.BilinForm.tensorDistribEquiv_apply
 -/
 
 end CommRing

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

@@ -3,8 +3,8 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.LinearAlgebra.BilinearForm
-import Mathbin.LinearAlgebra.TensorProduct
+import LinearAlgebra.BilinearForm
+import LinearAlgebra.TensorProduct
 
 #align_import linear_algebra.bilinear_form.tensor_product from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -52,14 +52,12 @@ def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm
 #align bilin_form.tensor_distrib BilinForm.tensorDistrib
 -/
 
-#print BilinForm.tensorDistrib_tmul /-
 @[simp]
 theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
     (m₁' : M₁) (m₂' : M₂) :
     tensorDistrib (B₁ ⊗ₜ B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂' :=
   rfl
-#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmul
--/
+#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ
 
 #print BilinForm.tmul /-
 /-- The tensor product of two bilinear forms, a shorthand for dot notation. -/

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

@@ -2,15 +2,12 @@
 Copyright (c) 2023 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.bilinear_form.tensor_product
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.BilinearForm
 import Mathbin.LinearAlgebra.TensorProduct
 
+#align_import linear_algebra.bilinear_form.tensor_product from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # The bilinear form on a tensor product
 

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

@@ -55,18 +55,22 @@ def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm
 #align bilin_form.tensor_distrib BilinForm.tensorDistrib
 -/
 
+#print BilinForm.tensorDistrib_tmul /-
 @[simp]
 theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
     (m₁' : M₁) (m₂' : M₂) :
     tensorDistrib (B₁ ⊗ₜ B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂' :=
   rfl
 #align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmul
+-/
 
+#print BilinForm.tmul /-
 /-- The tensor product of two bilinear forms, a shorthand for dot notation. -/
 @[reducible]
 protected def tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) : BilinForm R (M₁ ⊗[R] M₂) :=
   tensorDistrib (B₁ ⊗ₜ[R] B₂)
 #align bilin_form.tmul BilinForm.tmul
+-/
 
 end CommSemiring
 
@@ -100,11 +104,13 @@ noncomputable def tensorDistribEquiv :
 #align bilin_form.tensor_distrib_equiv BilinForm.tensorDistribEquiv
 -/
 
+#print BilinForm.tensorDistribEquiv_apply /-
 @[simp]
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
     tensorDistribEquiv B = tensorDistrib B :=
   rfl
 #align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_apply
+-/
 
 end CommRing
 

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

@@ -31,7 +31,7 @@ universe u v w
 
 variable {ι : Type _} {R : Type _} {M₁ M₂ : Type _}
 
-open TensorProduct
+open scoped TensorProduct
 
 namespace BilinForm
 

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

@@ -55,9 +55,6 @@ def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm
 #align bilin_form.tensor_distrib BilinForm.tensorDistrib
 -/
 
-/- warning: bilin_form.tensor_distrib_tmul -> BilinForm.tensorDistrib_tmul is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ'. -/
 @[simp]
 theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
     (m₁' : M₁) (m₂' : M₂) :
@@ -65,12 +62,6 @@ theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (
   rfl
 #align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmul
 
-/- warning: bilin_form.tmul -> BilinForm.tmul 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 bilin_form.tmul BilinForm.tmulₓ'. -/
 /-- The tensor product of two bilinear forms, a shorthand for dot notation. -/
 @[reducible]
 protected def tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) : BilinForm R (M₁ ⊗[R] M₂) :=
@@ -109,9 +100,6 @@ noncomputable def tensorDistribEquiv :
 #align bilin_form.tensor_distrib_equiv BilinForm.tensorDistribEquiv
 -/
 
-/- warning: bilin_form.tensor_distrib_equiv_apply -> BilinForm.tensorDistribEquiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_applyₓ'. -/
 @[simp]
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
     tensorDistribEquiv B = tensorDistrib B :=

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

@@ -56,10 +56,7 @@ def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm
 -/
 
 /- warning: bilin_form.tensor_distrib_tmul -> BilinForm.tensorDistrib_tmul is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ'. -/
 @[simp]
 theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
@@ -113,10 +110,7 @@ noncomputable def tensorDistribEquiv :
 -/
 
 /- warning: bilin_form.tensor_distrib_equiv_apply -> BilinForm.tensorDistribEquiv_apply is a dubious translation:
-lean 3 declaration is
-  forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M₁] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2)] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : Module.Free.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_7 : Module.Finite.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_8 : Module.Free.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5] [_inst_9 : Module.Finite.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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_inst_3) _inst_4 _inst_5) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (BilinForm.tensorDistrib.{u3, u2, u1} R M₁ M₂ (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) B)
+<too large>
 Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_applyₓ'. -/
 @[simp]
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :

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

@@ -59,7 +59,7 @@ def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm
 lean 3 declaration is
   forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3] (B₁ : BilinForm.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4) (B₂ : BilinForm.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_5) (m₁ : M₁) (m₂ : M₂) (m₁' : M₁) (m₂' : M₂), Eq.{succ u1} R (coeFn.{max (succ u1) (succ (max u2 u3)), max (succ (max u2 u3)) (succ u1)} (BilinForm.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (TensorProduct.module.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5)) (fun (_x : BilinForm.{u1, max u2 u3} R 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R _inst_1)) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R _inst_1)) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1)))))) B₁ B₂)) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 m₁ m₂) (TensorProduct.tmul.{u3, u2, u1} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5 m₁' m₂')) (HMul.hMul.{u3, u3, u3} R R R (instHMul.{u3} R (NonUnitalNonAssocSemiring.toMul.{u3} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R _inst_1))))) (BilinForm.bilin.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_2 _inst_4 B₁ m₁ m₁') (BilinForm.bilin.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R _inst_1) _inst_3 _inst_5 B₂ m₂ m₂'))
 Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ'. -/
 @[simp]
 theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
@@ -116,7 +116,7 @@ noncomputable def tensorDistribEquiv :
 lean 3 declaration is
   forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M₁] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2)] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : Module.Free.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_7 : Module.Finite.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_8 : Module.Free.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5] [_inst_9 : Module.Finite.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5] [_inst_10 : Nontrivial.{u1} R] (B : TensorProduct.{u1, max u1 u2, max u1 u3} R (CommRing.toCommSemiring.{u1} R _inst_1) (BilinForm.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4) (BilinForm.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5) (BilinForm.addCommMonoid.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4) (BilinForm.addCommMonoid.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5) (BilinForm.module.{u1, u2, u1} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4 R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) 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 but is expected to have type
-  forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M₁] [_inst_3 : AddCommGroup.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2)] [_inst_5 : Module.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3)] [_inst_6 : Module.Free.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_7 : Module.Finite.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_8 : Module.Free.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_5] [_inst_9 : Module.Finite.{u3, u1} R 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_inst_3) _inst_4 _inst_5) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (BilinForm.tensorDistrib.{u3, u2, u1} R M₁ M₂ (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) B)
+  forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M₁] [_inst_3 : AddCommGroup.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2)] [_inst_5 : Module.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3)] [_inst_6 : Module.Free.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_7 : Module.Finite.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_8 : Module.Free.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_5] [_inst_9 : Module.Finite.{u3, u1} R 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 Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_applyₓ'. -/
 @[simp]
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :

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

@@ -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.bilinear_form.tensor_product
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! 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.TensorProduct
 /-!
 # The bilinear form on a tensor product
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `bilin_form.tensor_distrib (B₁ ⊗ₜ B₂)`: the bilinear form on `M₁ ⊗ M₂` constructed by applying

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -40,6 +40,7 @@ variable [AddCommMonoid M₁] [AddCommMonoid M₂]
 
 variable [Module R M₁] [Module R M₂]
 
+#print BilinForm.tensorDistrib /-
 /-- The tensor product of two bilinear forms injects into bilinear forms on tensor products. -/
 def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
   ((TensorProduct.tensorTensorTensorComm R _ _ _ _).dualMap ≪≫ₗ
@@ -49,7 +50,14 @@ def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm
       (TensorProduct.congr (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
           (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)).toLinearMap
 #align bilin_form.tensor_distrib BilinForm.tensorDistrib
+-/
 
+/- warning: bilin_form.tensor_distrib_tmul -> BilinForm.tensorDistrib_tmul is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ'. -/
 @[simp]
 theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
     (m₁' : M₁) (m₂' : M₂) :
@@ -57,6 +65,12 @@ theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (
   rfl
 #align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmul
 
+/- warning: bilin_form.tmul -> BilinForm.tmul is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3], (BilinForm.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4) -> (BilinForm.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_5) -> (BilinForm.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (TensorProduct.module.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5))
+but is expected to have type
+  forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommSemiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M₁] [_inst_3 : AddCommMonoid.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2] [_inst_5 : Module.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3], (BilinForm.{u1, u2} R M₁ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_2 _inst_4) -> (BilinForm.{u1, u3} R M₂ (CommSemiring.toSemiring.{u1} R _inst_1) _inst_3 _inst_5) -> (BilinForm.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (CommSemiring.toSemiring.{u1} R _inst_1) (TensorProduct.addCommMonoid.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R _inst_1 M₁ M₂ _inst_2 _inst_3 _inst_4 _inst_5))
+Case conversion may be inaccurate. Consider using '#align bilin_form.tmul BilinForm.tmulₓ'. -/
 /-- The tensor product of two bilinear forms, a shorthand for dot notation. -/
 @[reducible]
 protected def tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) : BilinForm R (M₁ ⊗[R] M₂) :=
@@ -79,6 +93,7 @@ variable [Module.Free R M₂] [Module.Finite R M₂]
 
 variable [Nontrivial R]
 
+#print BilinForm.tensorDistribEquiv /-
 /-- `tensor_distrib` as an equivalence. -/
 noncomputable def tensorDistribEquiv :
     BilinForm R M₁ ⊗[R] BilinForm R M₂ ≃ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
@@ -92,7 +107,14 @@ noncomputable def tensorDistribEquiv :
       (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ
     LinearMap.toBilin
 #align bilin_form.tensor_distrib_equiv BilinForm.tensorDistribEquiv
+-/
 
+/- warning: bilin_form.tensor_distrib_equiv_apply -> BilinForm.tensorDistribEquiv_apply is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} {M₁ : Type.{u2}} {M₂ : Type.{u3}} [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M₁] [_inst_3 : AddCommGroup.{u3} M₂] [_inst_4 : Module.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2)] [_inst_5 : Module.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3)] [_inst_6 : Module.Free.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_7 : Module.Finite.{u1, u2} R M₁ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_8 : Module.Free.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} M₂ _inst_3) _inst_5] [_inst_9 : Module.Finite.{u1, u3} R M₂ (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) 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+but is expected to have type
+  forall {R : Type.{u3}} {M₁ : Type.{u2}} {M₂ : Type.{u1}} [_inst_1 : CommRing.{u3} R] [_inst_2 : AddCommGroup.{u2} M₁] [_inst_3 : AddCommGroup.{u1} M₂] [_inst_4 : Module.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2)] [_inst_5 : Module.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3)] [_inst_6 : Module.Free.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_7 : Module.Finite.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4] [_inst_8 : Module.Free.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_5] [_inst_9 : Module.Finite.{u3, u1} R 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(AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_5 R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (BilinForm.instAddCommMonoidBilinForm.{u3, max u2 u1} R (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M₁ M₂ (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (TensorProduct.addCommMonoid.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M₁ M₂ (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M₁ M₂ (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5)) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, max u3 u2, max u3 u1} R (CommRing.toCommSemiring.{u3} R _inst_1) (BilinForm.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4) (BilinForm.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_5) (BilinForm.instAddCommMonoidBilinForm.{u3, u2} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4) (BilinForm.instAddCommMonoidBilinForm.{u3, u1} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_5) (BilinForm.instModuleBilinFormInstAddCommMonoidBilinForm.{u3, u2, u3} R M₁ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) _inst_4 R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (BilinForm.instModuleBilinFormInstAddCommMonoidBilinForm.{u3, u1, u3} R M₂ (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_5 R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)))))))) (BilinForm.instModuleBilinFormInstAddCommMonoidBilinForm.{u3, max u2 u1, u3} R (TensorProduct.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M₁ M₂ (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (TensorProduct.addCommMonoid.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M₁ M₂ (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u3, u2, u1} R (CommRing.toCommSemiring.{u3} R _inst_1) M₁ M₂ (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (Semiring.toModule.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (smulCommClass_self.{u3, u3} R R (CommSemiring.toCommMonoid.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1)) (MulActionWithZero.toMulAction.{u3, u3} R R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (CommMonoidWithZero.toZero.{u3} R (CommSemiring.toCommMonoidWithZero.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))) (MonoidWithZero.toMulActionWithZero.{u3} R (Semiring.toMonoidWithZero.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))))) (RingHom.id.{u3} R (Semiring.toNonAssocSemiring.{u3} R (CommSemiring.toSemiring.{u3} R (CommRing.toCommSemiring.{u3} R _inst_1))))) (BilinForm.tensorDistrib.{u3, u2, u1} R M₁ M₂ (CommRing.toCommSemiring.{u3} R _inst_1) (AddCommGroup.toAddCommMonoid.{u2} M₁ _inst_2) (AddCommGroup.toAddCommMonoid.{u1} M₂ _inst_3) _inst_4 _inst_5) B)
+Case conversion may be inaccurate. Consider using '#align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_applyₓ'. -/
 @[simp]
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
     tensorDistribEquiv B = tensorDistrib B :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,13 +4,12 @@ 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.bilinear_form.tensor_product
-! leanprover-community/mathlib commit f91d3736cbfcff4614caabcf9ae32d4a880f8813
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.BilinearForm
 import Mathbin.LinearAlgebra.TensorProduct
-import Mathbin.LinearAlgebra.Contraction
 
 /-!
 # The bilinear form on a tensor product

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

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)

@@ -100,15 +100,10 @@ end CommSemiring
 section CommRing
 
 variable [CommRing R]
-
 variable [AddCommGroup M₁] [AddCommGroup M₂]
-
 variable [Module R M₁] [Module R M₂]
-
 variable [Module.Free R M₁] [Module.Finite R M₁]
-
 variable [Module.Free R M₂] [Module.Finite R M₂]
-
 variable [Nontrivial R]
 
 variable (R) in

Following on from #10097, which converted the companion of a quadratic form with a bilinear map, this PR replaces a number of results about quadratic forms and bilinear forms with results about quadratic forms and scalar valued bilinear maps. The long term aim is to be able to consider quadratic maps.

The main change is to LinearAlgebra/QuadraticForm/Basic, but this necessitates changes throughout LinearAlgebra/QuadraticForm/. Minor changes are also required elsewhere:

• LinearAlgebra/CliffordAlgebra/
• LinearAlgebra/Matrix/PosDef
• LinearAlgebra/SesquilinearForm
• A number of additional results about tensor products and linear maps are also required.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>

@@ -3,8 +3,7 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathlib.LinearAlgebra.BilinearForm.Properties
-import Mathlib.LinearAlgebra.TensorProduct
+import Mathlib.LinearAlgebra.Dual
 import Mathlib.LinearAlgebra.TensorProduct.Tower
 
 #align_import linear_algebra.bilinear_form.tensor_product from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
@@ -14,10 +13,10 @@ import Mathlib.LinearAlgebra.TensorProduct.Tower
 
 ## Main definitions
 
-* `BilinForm.tensorDistrib (B₁ ⊗ₜ B₂)`: the bilinear form on `M₁ ⊗ M₂` constructed by applying
-  `B₁` on `M₁` and `B₂` on `M₂`.
-* `BilinForm.tensorDistribEquiv`: `BilinForm.tensorDistrib` as an equivalence on finite free
-  modules.
+* `LinearMap.BilinForm.tensorDistrib (B₁ ⊗ₜ B₂)`: the bilinear form on `M₁ ⊗ M₂` constructed by
+  applying `B₁` on `M₁` and `B₂` on `M₂`.
+* `LinearMap.BilinForm.tensorDistribEquiv`: `BilinForm.tensorDistrib` as an equivalence on finite
+  free modules.
 
 -/
 
@@ -29,8 +28,12 @@ variable {ι : Type uι} {R : Type uR} {A : Type uA} {M₁ : Type uM₁} {M₂ :
 
 open TensorProduct
 
+namespace LinearMap
+
 namespace BilinForm
 
+open LinearMap (BilinForm)
+
 section CommSemiring
 variable [CommSemiring R] [CommSemiring A]
 variable [AddCommMonoid M₁] [AddCommMonoid M₂]
@@ -45,13 +48,12 @@ Note this is heterobasic; the bilinear form on the left can take values in an (c
 over the ring in which the right bilinear form is valued. -/
 def tensorDistrib : BilinForm A M₁ ⊗[R] BilinForm R M₂ →ₗ[A] BilinForm A (M₁ ⊗[R] M₂) :=
   ((TensorProduct.AlgebraTensorModule.tensorTensorTensorComm R A M₁ M₂ M₁ M₂).dualMap
-    ≪≫ₗ (TensorProduct.lift.equiv A (M₁ ⊗[R] M₂) (M₁ ⊗[R] M₂) A).symm
-    ≪≫ₗ LinearMap.toBilin).toLinearMap
+    ≪≫ₗ (TensorProduct.lift.equiv A (M₁ ⊗[R] M₂) (M₁ ⊗[R] M₂) A).symm).toLinearMap
   ∘ₗ TensorProduct.AlgebraTensorModule.dualDistrib R _ _ _
   ∘ₗ (TensorProduct.AlgebraTensorModule.congr
-    (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv A _ _ _)
-    (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)).toLinearMap
-#align bilin_form.tensor_distrib BilinForm.tensorDistrib
+    (TensorProduct.lift.equiv A M₁ M₁ A)
+    (TensorProduct.lift.equiv R _ _ _)).toLinearMap
+#align bilin_form.tensor_distrib LinearMap.BilinForm.tensorDistrib
 
 -- TODO: make the RHS `MulOpposite.op (B₂ m₂ m₂') • B₁ m₁ m₁'` so that this has a nicer defeq for
 -- `R = A` of `B₁ m₁ m₁' * B₂ m₂ m₂'`, as it did before the generalization in #6306.
@@ -61,27 +63,26 @@ theorem tensorDistrib_tmul (B₁ : BilinForm A M₁) (B₂ : BilinForm R M₂) (
     tensorDistrib R A (B₁ ⊗ₜ B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂')
       = B₂ m₂ m₂' • B₁ m₁ m₁' :=
   rfl
-#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ
+#align bilin_form.tensor_distrib_tmul LinearMap.BilinForm.tensorDistrib_tmulₓ
 
 /-- The tensor product of two bilinear forms, a shorthand for dot notation. -/
 @[reducible]
 protected def tmul (B₁ : BilinForm A M₁) (B₂ : BilinForm R M₂) : BilinForm A (M₁ ⊗[R] M₂) :=
   tensorDistrib R A (B₁ ⊗ₜ[R] B₂)
-#align bilin_form.tmul BilinForm.tmul
+#align bilin_form.tmul LinearMap.BilinForm.tmul
 
 attribute [ext] TensorProduct.ext in
 /-- A tensor product of symmetric bilinear forms is symmetric. -/
-lemma IsSymm.tmul {B₁ : BilinForm A M₁} {B₂ : BilinForm R M₂}
+lemma _root_.LinearMap.IsSymm.tmul {B₁ : BilinForm A M₁} {B₂ : BilinForm R M₂}
     (hB₁ : B₁.IsSymm) (hB₂ : B₂.IsSymm) : (B₁.tmul B₂).IsSymm := by
-  rw [isSymm_iff_flip R]
-  apply toLin.injective
+  rw [LinearMap.isSymm_iff_eq_flip]
   ext x₁ x₂ y₁ y₂
-  exact (congr_arg₂ (HSMul.hSMul) (hB₂ x₂ y₂) (hB₁ x₁ y₁)).symm
+  exact congr_arg₂ (HSMul.hSMul) (hB₂ x₂ y₂) (hB₁ x₁ y₁)
 
 variable (A) in
 /-- The base change of a bilinear form. -/
 protected def baseChange (B : BilinForm R M₂) : BilinForm A (A ⊗[R] M₂) :=
-  BilinForm.tmul (R := R) (A := A) (M₁ := A) (M₂ := M₂) (LinearMap.toBilin <| LinearMap.mul A A) B
+  BilinForm.tmul (R := R) (A := A) (M₁ := A) (M₂ := M₂) (LinearMap.mul A A) B
 
 @[simp]
 theorem baseChange_tmul (B₂ : BilinForm R M₂) (a : A) (m₂ : M₂)
@@ -116,12 +117,11 @@ noncomputable def tensorDistribEquiv :
     BilinForm R M₁ ⊗[R] BilinForm R M₂ ≃ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
   -- the same `LinearEquiv`s as from `tensorDistrib`,
   -- but with the inner linear map also as an equiv
-  TensorProduct.congr (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
-    (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _) ≪≫ₗ
+  TensorProduct.congr (TensorProduct.lift.equiv R _ _ _) (TensorProduct.lift.equiv R _ _ _) ≪≫ₗ
   TensorProduct.dualDistribEquiv R (M₁ ⊗ M₁) (M₂ ⊗ M₂) ≪≫ₗ
   (TensorProduct.tensorTensorTensorComm R _ _ _ _).dualMap ≪≫ₗ
-  (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ LinearMap.toBilin
-#align bilin_form.tensor_distrib_equiv BilinForm.tensorDistribEquiv
+  (TensorProduct.lift.equiv R _ _ _).symm
+#align bilin_form.tensor_distrib_equiv LinearMap.BilinForm.tensorDistribEquiv
 
 -- this is a dsimp lemma
 @[simp, nolint simpNF]
@@ -137,7 +137,6 @@ variable (R M₁ M₂) in
 theorem tensorDistribEquiv_toLinearMap :
     (tensorDistribEquiv R (M₁ := M₁) (M₂ := M₂)).toLinearMap = tensorDistrib R R := by
   ext B₁ B₂ : 3
-  apply toLin.injective
   ext
   exact mul_comm _ _
 
@@ -145,8 +144,10 @@ theorem tensorDistribEquiv_toLinearMap :
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
     tensorDistribEquiv R (M₁ := M₁) (M₂ := M₂) B = tensorDistrib R R B :=
   DFunLike.congr_fun (tensorDistribEquiv_toLinearMap R M₁ M₂) B
-#align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_apply
+#align bilin_form.tensor_distrib_equiv_apply LinearMap.BilinForm.tensorDistribEquiv_apply
 
 end CommRing
 
 end BilinForm
+
+end LinearMap

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -144,7 +144,7 @@ theorem tensorDistribEquiv_toLinearMap :
 @[simp]
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
     tensorDistribEquiv R (M₁ := M₁) (M₂ := M₂) B = tensorDistrib R R B :=
-  FunLike.congr_fun (tensorDistribEquiv_toLinearMap R M₁ M₂) B
+  DFunLike.congr_fun (tensorDistribEquiv_toLinearMap R M₁ M₂) B
 #align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_apply
 
 end CommRing

Also renamed BilinearForm.restrictSymm to BilinearForm.IsSymm.restrict.

@@ -3,7 +3,7 @@ Copyright (c) 2023 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathlib.LinearAlgebra.BilinearForm
+import Mathlib.LinearAlgebra.BilinearForm.Properties
 import Mathlib.LinearAlgebra.TensorProduct
 import Mathlib.LinearAlgebra.TensorProduct.Tower
 

More principled version of #7281.

@@ -21,6 +21,7 @@ import Mathlib.LinearAlgebra.TensorProduct.Tower
 
 -/
 
+suppress_compilation
 
 universe u v w uι uR uA uM₁ uM₂
 

This generalizes the existing BilinForm.tensorDistrib to be heterogenous in the rings it uses, such that a base change,

protected def baseChange (B : BilinForm R M₂) :
  BilinForm A (A ⊗[R] M₂) :=

falls out as a special case. I do not attempt to generalize BilinForm.tensorDistribEquiv.

Unfortunately, this changes the defeq as

-(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂'
+(B₁.tmul B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₂ m₂ m₂' • B₁ m₁ m₁'

We could fix this by using the right action instead, but that's a lot of work for a very minorly annoying defeq.

This also breaks the defeq of tensorDistribEquiv B = tensorDistrib B; though the reason is more complicated than the scalar action issue above. It would be fixed if we defined all the homogenous operations on tensor products as special cases of the heterogenous ones, but that's also a lot of work for a very small win.

This is a port of work from https://github.com/pygae/lean-ga/pull/31, and almost at the end of the path to a base change of quadratic forms and clifford algebras.

This was independently developed at the Leiden workshop as BilinForm.baseChange, though the results there are not sorry-free.

@@ -5,6 +5,7 @@ Authors: Eric Wieser
 -/
 import Mathlib.LinearAlgebra.BilinearForm
 import Mathlib.LinearAlgebra.TensorProduct
+import Mathlib.LinearAlgebra.TensorProduct.Tower
 
 #align_import linear_algebra.bilinear_form.tensor_product from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
 
@@ -21,52 +22,76 @@ import Mathlib.LinearAlgebra.TensorProduct
 -/
 
 
-universe u v w
+universe u v w uι uR uA uM₁ uM₂
 
-variable {ι : Type*} {R : Type*} {M₁ M₂ : Type*}
+variable {ι : Type uι} {R : Type uR} {A : Type uA} {M₁ : Type uM₁} {M₂ : Type uM₂}
 
 open TensorProduct
 
 namespace BilinForm
 
 section CommSemiring
-
-variable [CommSemiring R]
-
+variable [CommSemiring R] [CommSemiring A]
 variable [AddCommMonoid M₁] [AddCommMonoid M₂]
-
-variable [Module R M₁] [Module R M₂]
-
-/-- The tensor product of two bilinear forms injects into bilinear forms on tensor products. -/
-def tensorDistrib : BilinForm R M₁ ⊗[R] BilinForm R M₂ →ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
-  ((TensorProduct.tensorTensorTensorComm R _ _ _ _).dualMap ≪≫ₗ
-    (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ LinearMap.toBilin).toLinearMap ∘ₗ
-  TensorProduct.dualDistrib R _ _ ∘ₗ
-  (TensorProduct.congr (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)
+variable [Algebra R A] [Module R M₁] [Module A M₁]
+variable [SMulCommClass R A M₁] [SMulCommClass A R M₁] [IsScalarTower R A M₁]
+variable [Module R M₂]
+
+variable (R A) in
+/-- The tensor product of two bilinear forms injects into bilinear forms on tensor products.
+
+Note this is heterobasic; the bilinear form on the left can take values in an (commutative) algebra
+over the ring in which the right bilinear form is valued. -/
+def tensorDistrib : BilinForm A M₁ ⊗[R] BilinForm R M₂ →ₗ[A] BilinForm A (M₁ ⊗[R] M₂) :=
+  ((TensorProduct.AlgebraTensorModule.tensorTensorTensorComm R A M₁ M₂ M₁ M₂).dualMap
+    ≪≫ₗ (TensorProduct.lift.equiv A (M₁ ⊗[R] M₂) (M₁ ⊗[R] M₂) A).symm
+    ≪≫ₗ LinearMap.toBilin).toLinearMap
+  ∘ₗ TensorProduct.AlgebraTensorModule.dualDistrib R _ _ _
+  ∘ₗ (TensorProduct.AlgebraTensorModule.congr
+    (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv A _ _ _)
     (BilinForm.toLin ≪≫ₗ TensorProduct.lift.equiv R _ _ _)).toLinearMap
 #align bilin_form.tensor_distrib BilinForm.tensorDistrib
 
+-- TODO: make the RHS `MulOpposite.op (B₂ m₂ m₂') • B₁ m₁ m₁'` so that this has a nicer defeq for
+-- `R = A` of `B₁ m₁ m₁' * B₂ m₂ m₂'`, as it did before the generalization in #6306.
 @[simp]
-theorem tensorDistrib_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
+theorem tensorDistrib_tmul (B₁ : BilinForm A M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
     (m₁' : M₁) (m₂' : M₂) :
-    tensorDistrib (R := R) (B₁ ⊗ₜ B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂') = B₁ m₁ m₁' * B₂ m₂ m₂' :=
+    tensorDistrib R A (B₁ ⊗ₜ B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂')
+      = B₂ m₂ m₂' • B₁ m₁ m₁' :=
   rfl
-#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmul
+#align bilin_form.tensor_distrib_tmul BilinForm.tensorDistrib_tmulₓ
 
 /-- The tensor product of two bilinear forms, a shorthand for dot notation. -/
 @[reducible]
-protected def tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) : BilinForm R (M₁ ⊗[R] M₂) :=
-  tensorDistrib (R := R) (B₁ ⊗ₜ[R] B₂)
+protected def tmul (B₁ : BilinForm A M₁) (B₂ : BilinForm R M₂) : BilinForm A (M₁ ⊗[R] M₂) :=
+  tensorDistrib R A (B₁ ⊗ₜ[R] B₂)
 #align bilin_form.tmul BilinForm.tmul
 
 attribute [ext] TensorProduct.ext in
 /-- A tensor product of symmetric bilinear forms is symmetric. -/
-lemma IsSymm.tmul {B₁ : BilinForm R M₁} {B₂ : BilinForm R M₂}
+lemma IsSymm.tmul {B₁ : BilinForm A M₁} {B₂ : BilinForm R M₂}
     (hB₁ : B₁.IsSymm) (hB₂ : B₂.IsSymm) : (B₁.tmul B₂).IsSymm := by
   rw [isSymm_iff_flip R]
   apply toLin.injective
   ext x₁ x₂ y₁ y₂
-  exact (congr_arg₂ (HMul.hMul) (hB₁ x₁ y₁) (hB₂ x₂ y₂)).symm
+  exact (congr_arg₂ (HSMul.hSMul) (hB₂ x₂ y₂) (hB₁ x₁ y₁)).symm
+
+variable (A) in
+/-- The base change of a bilinear form. -/
+protected def baseChange (B : BilinForm R M₂) : BilinForm A (A ⊗[R] M₂) :=
+  BilinForm.tmul (R := R) (A := A) (M₁ := A) (M₂ := M₂) (LinearMap.toBilin <| LinearMap.mul A A) B
+
+@[simp]
+theorem baseChange_tmul (B₂ : BilinForm R M₂) (a : A) (m₂ : M₂)
+    (a' : A) (m₂' : M₂) :
+    B₂.baseChange A (a ⊗ₜ m₂) (a' ⊗ₜ m₂') = (B₂ m₂ m₂') • (a * a') :=
+  rfl
+
+variable (A) in
+/-- The base change of a symmetric bilinear form is symmetric. -/
+lemma IsSymm.baseChange {B₂ : BilinForm R M₂} (hB₂ : B₂.IsSymm) : (B₂.baseChange A).IsSymm :=
+  IsSymm.tmul mul_comm hB₂
 
 end CommSemiring
 
@@ -84,6 +109,7 @@ variable [Module.Free R M₂] [Module.Finite R M₂]
 
 variable [Nontrivial R]
 
+variable (R) in
 /-- `tensorDistrib` as an equivalence. -/
 noncomputable def tensorDistribEquiv :
     BilinForm R M₁ ⊗[R] BilinForm R M₂ ≃ₗ[R] BilinForm R (M₁ ⊗[R] M₂) :=
@@ -96,10 +122,28 @@ noncomputable def tensorDistribEquiv :
   (TensorProduct.lift.equiv R _ _ _).symm ≪≫ₗ LinearMap.toBilin
 #align bilin_form.tensor_distrib_equiv BilinForm.tensorDistribEquiv
 
+-- this is a dsimp lemma
+@[simp, nolint simpNF]
+theorem tensorDistribEquiv_tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) (m₁ : M₁) (m₂ : M₂)
+    (m₁' : M₁) (m₂' : M₂) :
+    tensorDistribEquiv R (M₁ := M₁) (M₂ := M₂) (B₁ ⊗ₜ[R] B₂) (m₁ ⊗ₜ m₂) (m₁' ⊗ₜ m₂')
+      = B₁ m₁ m₁' * B₂ m₂ m₂' :=
+  rfl
+
+variable (R M₁ M₂) in
+-- TODO: make this `rfl`
+@[simp]
+theorem tensorDistribEquiv_toLinearMap :
+    (tensorDistribEquiv R (M₁ := M₁) (M₂ := M₂)).toLinearMap = tensorDistrib R R := by
+  ext B₁ B₂ : 3
+  apply toLin.injective
+  ext
+  exact mul_comm _ _
+
 @[simp]
 theorem tensorDistribEquiv_apply (B : BilinForm R M₁ ⊗ BilinForm R M₂) :
-    tensorDistribEquiv (R := R) (M₁ := M₁) (M₂ := M₂) B = tensorDistrib (R := R) B :=
-  rfl
+    tensorDistribEquiv R (M₁ := M₁) (M₂ := M₂) B = tensorDistrib R R B :=
+  FunLike.congr_fun (tensorDistribEquiv_toLinearMap R M₁ M₂) B
 #align bilin_form.tensor_distrib_equiv_apply BilinForm.tensorDistribEquiv_apply
 
 end CommRing

@@ -59,6 +59,15 @@ protected def tmul (B₁ : BilinForm R M₁) (B₂ : BilinForm R M₂) : BilinFo
   tensorDistrib (R := R) (B₁ ⊗ₜ[R] B₂)
 #align bilin_form.tmul BilinForm.tmul
 
+attribute [ext] TensorProduct.ext in
+/-- A tensor product of symmetric bilinear forms is symmetric. -/
+lemma IsSymm.tmul {B₁ : BilinForm R M₁} {B₂ : BilinForm R M₂}
+    (hB₁ : B₁.IsSymm) (hB₂ : B₂.IsSymm) : (B₁.tmul B₂).IsSymm := by
+  rw [isSymm_iff_flip R]
+  apply toLin.injective
+  ext x₁ x₂ y₁ y₂
+  exact (congr_arg₂ (HMul.hMul) (hB₁ x₁ y₁) (hB₂ x₂ y₂)).symm
+
 end CommSemiring
 
 section CommRing

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

This has nice performance benefits.

@@ -23,7 +23,7 @@ import Mathlib.LinearAlgebra.TensorProduct
 
 universe u v w
 
-variable {ι : Type _} {R : Type _} {M₁ M₂ : Type _}
+variable {ι : Type*} {R : Type*} {M₁ M₂ : Type*}
 
 open TensorProduct
 

• 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) 2023 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.bilinear_form.tensor_product
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.BilinearForm
 import Mathlib.LinearAlgebra.TensorProduct
 
+#align_import linear_algebra.bilinear_form.tensor_product from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # The bilinear form on a tensor product