linear_algebra.free_module.basic ⟷ Mathlib.LinearAlgebra.FreeModule.Basic

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

@@ -4,10 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
 import LinearAlgebra.DirectSum.Finsupp
-import Logic.Small.Basic
+import Logic.Small.Defs
 import LinearAlgebra.StdBasis
 import LinearAlgebra.FinsuppVectorSpace
-import LinearAlgebra.TensorProductBasis
+import LinearAlgebra.TensorProduct.Basis
 
 #align_import linear_algebra.free_module.basic from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 

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

@@ -41,7 +41,7 @@ section Basic
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 #print Module.Free /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
   exists_basis : Nonempty (Σ I : Type v, Basis I R M)

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

@@ -41,7 +41,7 @@ section Basic
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 #print Module.Free /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
   exists_basis : Nonempty (Σ I : Type v, Basis I R M)

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

@@ -3,11 +3,11 @@ Copyright (c) 2021 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathbin.LinearAlgebra.DirectSum.Finsupp
-import Mathbin.Logic.Small.Basic
-import Mathbin.LinearAlgebra.StdBasis
-import Mathbin.LinearAlgebra.FinsuppVectorSpace
-import Mathbin.LinearAlgebra.TensorProductBasis
+import LinearAlgebra.DirectSum.Finsupp
+import Logic.Small.Basic
+import LinearAlgebra.StdBasis
+import LinearAlgebra.FinsuppVectorSpace
+import LinearAlgebra.TensorProductBasis
 
 #align_import linear_algebra.free_module.basic from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
 
@@ -41,7 +41,7 @@ section Basic
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 #print Module.Free /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
   exists_basis : Nonempty (Σ I : Type v, Basis I R M)

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module linear_algebra.free_module.basic
-! 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.DirectSum.Finsupp
 import Mathbin.Logic.Small.Basic
@@ -14,6 +9,8 @@ import Mathbin.LinearAlgebra.StdBasis
 import Mathbin.LinearAlgebra.FinsuppVectorSpace
 import Mathbin.LinearAlgebra.TensorProductBasis
 
+#align_import linear_algebra.free_module.basic from "leanprover-community/mathlib"@"19cb3751e5e9b3d97adb51023949c50c13b5fdfd"
+
 /-!
 
 # Free modules

mathlib commit https://github.com/leanprover-community/mathlib/commit/4e24c4bfcff371c71f7ba22050308aa17815626c

@@ -220,7 +220,7 @@ instance (priority := 100) of_subsingleton' [Subsingleton R] : Module.Free R N :
 #print Module.Free.dfinsupp /-
 instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (Π₀ i, M i) :=
-  of_basis <| Dfinsupp.basis fun i => chooseBasis R (M i)
+  of_basis <| DFinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
 -/
 

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

@@ -44,7 +44,7 @@ section Basic
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 #print Module.Free /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
   exists_basis : Nonempty (Σ I : Type v, Basis I R M)
@@ -106,10 +106,12 @@ noncomputable def chooseBasis : Basis (ChooseBasisIndex R M) R M :=
 #align module.free.choose_basis Module.Free.chooseBasis
 -/
 
+#print Module.Free.repr /-
 /-- The isomorphism `M ≃ₗ[R] (choose_basis_index R M →₀ R)`. -/
 noncomputable def repr : M ≃ₗ[R] ChooseBasisIndex R M →₀ R :=
   (chooseBasis R M).repr
 #align module.free.repr Module.Free.repr
+-/
 
 #print Module.Free.constr /-
 /-- The universal property of free modules: giving a functon `(choose_basis_index R M) → N`, for `N`
@@ -126,10 +128,12 @@ noncomputable def constr {S : Type z} [Semiring S] [Module S N] [SMulCommClass R
 #align module.free.constr Module.Free.constr
 -/
 
+#print Module.Free.noZeroSMulDivisors /-
 instance (priority := 100) noZeroSMulDivisors [NoZeroDivisors R] : NoZeroSMulDivisors R M :=
   let ⟨⟨_, b⟩⟩ := exists_basis R M
   b.NoZeroSMulDivisors
 #align module.free.no_zero_smul_divisors Module.Free.noZeroSMulDivisors
+-/
 
 instance [Nontrivial M] : Nonempty (Module.Free.ChooseBasisIndex R M) :=
   (Module.Free.chooseBasis R M).index_nonempty
@@ -160,9 +164,11 @@ instance self : Module.Free R R :=
 #align module.free.self Module.Free.self
 -/
 
+#print Module.Free.prod /-
 instance prod [Module.Free R N] : Module.Free R (M × N) :=
   of_basis <| (chooseBasis R M).Prod (chooseBasis R N)
 #align module.free.prod Module.Free.prod
+-/
 
 #print Module.Free.pi /-
 /-- The product of finitely many free modules is free. -/
@@ -190,25 +196,33 @@ instance function [Finite ι] : Module.Free R (ι → M) :=
 #align module.free.function Module.Free.function
 -/
 
+#print Module.Free.finsupp /-
 instance finsupp : Module.Free R (ι →₀ M) :=
   of_basis (Finsupp.basis fun i => chooseBasis R M)
 #align module.free.finsupp Module.Free.finsupp
+-/
 
 variable {ι}
 
+#print Module.Free.of_subsingleton /-
 instance (priority := 100) of_subsingleton [Subsingleton N] : Module.Free R N :=
   of_basis (Basis.empty N : Basis PEmpty R N)
 #align module.free.of_subsingleton Module.Free.of_subsingleton
+-/
 
+#print Module.Free.of_subsingleton' /-
 instance (priority := 100) of_subsingleton' [Subsingleton R] : Module.Free R N :=
   letI := Module.subsingleton R N
   Module.Free.of_subsingleton R N
 #align module.free.of_subsingleton' Module.Free.of_subsingleton'
+-/
 
+#print Module.Free.dfinsupp /-
 instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (Π₀ i, M i) :=
   of_basis <| Dfinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
+-/
 
 #print Module.Free.directSum /-
 instance directSum {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
@@ -225,11 +239,13 @@ variable [CommRing R] [AddCommGroup M] [Module R M] [Module.Free R M]
 
 variable [AddCommGroup N] [Module R N] [Module.Free R N]
 
+#print Module.Free.tensor /-
 instance tensor : Module.Free R (M ⊗[R] N) :=
   let ⟨bM⟩ := exists_basis R M
   let ⟨bN⟩ := exists_basis R N
   of_basis (bM.2.TensorProduct bN.2)
 #align module.free.tensor Module.Free.tensor
+-/
 
 end CommRing
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -210,10 +210,12 @@ instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (
   of_basis <| Dfinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
 
+#print Module.Free.directSum /-
 instance directSum {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (⨁ i, M i) :=
   Module.Free.dfinsupp R M
 #align module.free.direct_sum Module.Free.directSum
+-/
 
 end Semiring
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -44,7 +44,7 @@ section Basic
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 #print Module.Free /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
   exists_basis : Nonempty (Σ I : Type v, Basis I R M)

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -47,7 +47,7 @@ variable [Semiring R] [AddCommMonoid M] [Module R M]
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
-  exists_basis : Nonempty (ΣI : Type v, Basis I R M)
+  exists_basis : Nonempty (Σ I : Type v, Basis I R M)
 #align module.free Module.Free
 -/
 

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

@@ -37,7 +37,7 @@ universe u v w z
 
 variable {ι : Type _} (R : Type u) (M : Type v) (N : Type z)
 
-open TensorProduct DirectSum BigOperators
+open scoped TensorProduct DirectSum BigOperators
 
 section Basic
 

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

@@ -106,12 +106,6 @@ noncomputable def chooseBasis : Basis (ChooseBasisIndex R M) R M :=
 #align module.free.choose_basis Module.Free.chooseBasis
 -/
 
-/- warning: module.free.repr -> Module.Free.repr is a dubious translation:
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-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3], LinearEquiv.{u1, u1, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (Finsupp.{u2, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u2, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))
-Case conversion may be inaccurate. Consider using '#align module.free.repr Module.Free.reprₓ'. -/
 /-- The isomorphism `M ≃ₗ[R] (choose_basis_index R M →₀ R)`. -/
 noncomputable def repr : M ≃ₗ[R] ChooseBasisIndex R M →₀ R :=
   (chooseBasis R M).repr
@@ -132,12 +126,6 @@ noncomputable def constr {S : Type z} [Semiring S] [Module S N] [SMulCommClass R
 #align module.free.constr Module.Free.constr
 -/
 
-/- warning: module.free.no_zero_smul_divisors -> Module.Free.noZeroSMulDivisors is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_7 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))], NoZeroSMulDivisors.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))
-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_7 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))], NoZeroSMulDivisors.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))
-Case conversion may be inaccurate. Consider using '#align module.free.no_zero_smul_divisors Module.Free.noZeroSMulDivisorsₓ'. -/
 instance (priority := 100) noZeroSMulDivisors [NoZeroDivisors R] : NoZeroSMulDivisors R M :=
   let ⟨⟨_, b⟩⟩ := exists_basis R M
   b.NoZeroSMulDivisors
@@ -172,12 +160,6 @@ instance self : Module.Free R R :=
 #align module.free.self Module.Free.self
 -/
 
-/- warning: module.free.prod -> Module.Free.prod is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u1, u3} R N _inst_1 _inst_5] [_inst_7 : Module.Free.{u1, u3} R N _inst_1 _inst_5 _inst_6], Module.Free.{u1, max u2 u3} R (Prod.{u2, u3} M N) _inst_1 (Prod.addCommMonoid.{u2, u3} M N _inst_2 _inst_5) (Prod.module.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_5 _inst_3 _inst_6)
-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u1, u3} R N _inst_1 _inst_5] [_inst_7 : Module.Free.{u1, u3} R N _inst_1 _inst_5 _inst_6], Module.Free.{u1, max u3 u2} R (Prod.{u2, u3} M N) _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M N _inst_2 _inst_5) (Prod.module.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_5 _inst_3 _inst_6)
-Case conversion may be inaccurate. Consider using '#align module.free.prod Module.Free.prodₓ'. -/
 instance prod [Module.Free R N] : Module.Free R (M × N) :=
   of_basis <| (chooseBasis R M).Prod (chooseBasis R N)
 #align module.free.prod Module.Free.prod
@@ -208,56 +190,26 @@ instance function [Finite ι] : Module.Free R (ι → M) :=
 #align module.free.function Module.Free.function
 -/
 
-/- warning: module.free.finsupp -> Module.Free.finsupp is a dubious translation:
-lean 3 declaration is
-  forall (ι : Type.{u3}) (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3], Module.Free.{u1, max u3 u2} R (Finsupp.{u3, u2} ι M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι M _inst_2) (Finsupp.module.{u3, u2, u1} ι M R _inst_1 _inst_2 _inst_3)
-but is expected to have type
-  forall (ι : Type.{u3}) (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3], Module.Free.{u1, max u2 u3} R (Finsupp.{u3, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι M _inst_2) (Finsupp.module.{u3, u2, u1} ι M R _inst_1 _inst_2 _inst_3)
-Case conversion may be inaccurate. Consider using '#align module.free.finsupp Module.Free.finsuppₓ'. -/
 instance finsupp : Module.Free R (ι →₀ M) :=
   of_basis (Finsupp.basis fun i => chooseBasis R M)
 #align module.free.finsupp Module.Free.finsupp
 
 variable {ι}
 
-/- warning: module.free.of_subsingleton -> Module.Free.of_subsingleton is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ z} N], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
-but is expected to have type
-  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ z} N], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
-Case conversion may be inaccurate. Consider using '#align module.free.of_subsingleton Module.Free.of_subsingletonₓ'. -/
 instance (priority := 100) of_subsingleton [Subsingleton N] : Module.Free R N :=
   of_basis (Basis.empty N : Basis PEmpty R N)
 #align module.free.of_subsingleton Module.Free.of_subsingleton
 
-/- warning: module.free.of_subsingleton' -> Module.Free.of_subsingleton' is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ u} R], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
-but is expected to have type
-  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ u} R], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
-Case conversion may be inaccurate. Consider using '#align module.free.of_subsingleton' Module.Free.of_subsingleton'ₓ'. -/
 instance (priority := 100) of_subsingleton' [Subsingleton R] : Module.Free R N :=
   letI := Module.subsingleton R N
   Module.Free.of_subsingleton R N
 #align module.free.of_subsingleton' Module.Free.of_subsingleton'
 
-/- warning: module.free.dfinsupp -> Module.Free.dfinsupp is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u2 u3} R (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_7 i))))) _inst_1 (Dfinsupp.addCommMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.module.{u2, u3, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u3 u2} R (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_7 i)))) _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.module.{u2, u3, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
-Case conversion may be inaccurate. Consider using '#align module.free.dfinsupp Module.Free.dfinsuppₓ'. -/
 instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (Π₀ i, M i) :=
   of_basis <| Dfinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
 
-/- warning: module.free.direct_sum -> Module.Free.directSum is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u2 u3} R (DirectSum.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) _inst_1 (DirectSum.addCommMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (DirectSum.module.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
-but is expected to have type
-  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u3 u2} R (DirectSum.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) _inst_1 (instAddCommMonoidDirectSum.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (DirectSum.instModuleDirectSumInstAddCommMonoidDirectSum.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
-Case conversion may be inaccurate. Consider using '#align module.free.direct_sum Module.Free.directSumₓ'. -/
 instance directSum {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (⨁ i, M i) :=
   Module.Free.dfinsupp R M
@@ -271,12 +223,6 @@ variable [CommRing R] [AddCommGroup M] [Module R M] [Module.Free R M]
 
 variable [AddCommGroup N] [Module R N] [Module.Free R N]
 
-/- warning: module.free.tensor -> Module.Free.tensor is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Module.Free.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_5 : AddCommGroup.{u3} N] [_inst_6 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5)] [_inst_7 : Module.Free.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_6], Module.Free.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6)
-but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Module.Free.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_5 : AddCommGroup.{u3} N] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5)] [_inst_7 : Module.Free.{u1, u3} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_6], Module.Free.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6)
-Case conversion may be inaccurate. Consider using '#align module.free.tensor Module.Free.tensorₓ'. -/
 instance tensor : Module.Free R (M ⊗[R] N) :=
   let ⟨bM⟩ := exists_basis R M
   let ⟨bN⟩ := exists_basis R N

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -275,7 +275,7 @@ variable [AddCommGroup N] [Module R N] [Module.Free R N]
 lean 3 declaration is
   forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Module.Free.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_5 : AddCommGroup.{u3} N] [_inst_6 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5)] [_inst_7 : Module.Free.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_6], Module.Free.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6)
 but is expected to have type
-  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Module.Free.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_5 : AddCommGroup.{u3} N] [_inst_6 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5)] [_inst_7 : Module.Free.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_6], Module.Free.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6)
+  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Module.Free.{u1, u2} R M (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_5 : AddCommGroup.{u3} N] [_inst_6 : Module.{u1, u3} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5)] [_inst_7 : Module.Free.{u1, u3} R N (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_6], Module.Free.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6)
 Case conversion may be inaccurate. Consider using '#align module.free.tensor Module.Free.tensorₓ'. -/
 instance tensor : Module.Free R (M ⊗[R] N) :=
   let ⟨bM⟩ := exists_basis R M

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

@@ -44,7 +44,7 @@ section Basic
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
 #print Module.Free /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
   exists_basis : Nonempty (ΣI : Type v, Basis I R M)

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: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.basic
-! leanprover-community/mathlib commit 4e7e7009099d4a88a750de710909b95487bf0124
+! leanprover-community/mathlib commit 19cb3751e5e9b3d97adb51023949c50c13b5fdfd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.LinearAlgebra.TensorProductBasis
 
 # Free modules
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We introduce a class `module.free R M`, for `R` a `semiring` and `M` an `R`-module and we provide
 several basic instances for this class.
 

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

@@ -40,12 +40,15 @@ section Basic
 
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
+#print Module.Free /-
 /- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`exists_basis] [] -/
 /-- `module.free R M` is the statement that the `R`-module `M` is free.-/
 class Module.Free : Prop where
   exists_basis : Nonempty (ΣI : Type v, Basis I R M)
 #align module.free Module.Free
+-/
 
+#print Module.free_def /-
 /- If `M` fits in universe `w`, then freeness is equivalent to existence of a basis in that
 universe.
 
@@ -57,17 +60,22 @@ theorem Module.free_def [Small.{w} M] : Module.Free R M ↔ ∃ I : Type w, None
       ⟨(Basis.reindexRange h.exists_basis.some.2).reindex (equivShrink _)⟩⟩,
     fun h => ⟨(nonempty_sigma.2 h).map fun ⟨i, b⟩ => ⟨Set.range b, b.reindexRange⟩⟩⟩
 #align module.free_def Module.free_def
+-/
 
+#print Module.free_iff_set /-
 theorem Module.free_iff_set : Module.Free R M ↔ ∃ S : Set M, Nonempty (Basis S R M) :=
   ⟨fun h => ⟨Set.range h.exists_basis.some.2, ⟨Basis.reindexRange h.exists_basis.some.2⟩⟩,
     fun ⟨S, hS⟩ => ⟨nonempty_sigma.2 ⟨S, hS⟩⟩⟩
 #align module.free_iff_set Module.free_iff_set
+-/
 
 variable {R M}
 
+#print Module.Free.of_basis /-
 theorem Module.Free.of_basis {ι : Type w} (b : Basis ι R M) : Module.Free R M :=
   (Module.free_def R M).2 ⟨Set.range b, ⟨b.reindexRange⟩⟩
 #align module.free.of_basis Module.Free.of_basis
+-/
 
 end Basic
 
@@ -79,23 +87,34 @@ variable (R M) [Semiring R] [AddCommMonoid M] [Module R M] [Module.Free R M]
 
 variable [AddCommMonoid N] [Module R N]
 
+#print Module.Free.ChooseBasisIndex /-
 /-- If `module.free R M` then `choose_basis_index R M` is the `ι` which indexes the basis
   `ι → M`. -/
 def ChooseBasisIndex :=
   (exists_basis R M).some.1
 #align module.free.choose_basis_index Module.Free.ChooseBasisIndex
+-/
 
+#print Module.Free.chooseBasis /-
 /-- If `module.free R M` then `choose_basis : ι → M` is the basis.
 Here `ι = choose_basis_index R M`. -/
 noncomputable def chooseBasis : Basis (ChooseBasisIndex R M) R M :=
   (exists_basis R M).some.2
 #align module.free.choose_basis Module.Free.chooseBasis
+-/
 
+/- warning: module.free.repr -> Module.Free.repr is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3], LinearEquiv.{u1, u1, u2, max u2 u1} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (Finsupp.{u2, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))) _inst_2 (Finsupp.addCommMonoid.{u2, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3], LinearEquiv.{u1, u1, u2, max u1 u2} R R _inst_1 _inst_1 (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHom.id.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)) (RingHomInvPair.ids.{u1} R _inst_1) (RingHomInvPair.ids.{u1} R _inst_1) M (Finsupp.{u2, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))) _inst_2 (Finsupp.addCommMonoid.{u2, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) _inst_3 (Finsupp.module.{u2, u1, u1} (Module.Free.ChooseBasisIndex.{u1, u2} R M _inst_1 _inst_2 _inst_3 _inst_4) R R _inst_1 (NonUnitalNonAssocSemiring.toAddCommMonoid.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (Semiring.toModule.{u1} R _inst_1))
+Case conversion may be inaccurate. Consider using '#align module.free.repr Module.Free.reprₓ'. -/
 /-- The isomorphism `M ≃ₗ[R] (choose_basis_index R M →₀ R)`. -/
 noncomputable def repr : M ≃ₗ[R] ChooseBasisIndex R M →₀ R :=
   (chooseBasis R M).repr
 #align module.free.repr Module.Free.repr
 
+#print Module.Free.constr /-
 /-- The universal property of free modules: giving a functon `(choose_basis_index R M) → N`, for `N`
 an `R`-module, is the same as giving an `R`-linear map `M →ₗ[R] N`.
 
@@ -108,7 +127,14 @@ noncomputable def constr {S : Type z} [Semiring S] [Module S N] [SMulCommClass R
     (ChooseBasisIndex R M → N) ≃ₗ[S] M →ₗ[R] N :=
   Basis.constr (chooseBasis R M) S
 #align module.free.constr Module.Free.constr
+-/
 
+/- warning: module.free.no_zero_smul_divisors -> Module.Free.noZeroSMulDivisors is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_7 : NoZeroDivisors.{u1} R (Distrib.toHasMul.{u1} R (NonUnitalNonAssocSemiring.toDistrib.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))))], NoZeroSMulDivisors.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulZeroClass.toHasSmul.{u1, u2} R M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (SMulWithZero.toSmulZeroClass.{u1, u2} R M (MulZeroClass.toHasZero.{u1} R (MulZeroOneClass.toMulZeroClass.{u1} R (MonoidWithZero.toMulZeroOneClass.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)))) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_7 : NoZeroDivisors.{u1} R (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R _inst_1))) (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1))], NoZeroSMulDivisors.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulZeroClass.toSMul.{u1, u2} R M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (SMulWithZero.toSMulZeroClass.{u1, u2} R M (MonoidWithZero.toZero.{u1} R (Semiring.toMonoidWithZero.{u1} R _inst_1)) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (MulActionWithZero.toSMulWithZero.{u1, u2} R M (Semiring.toMonoidWithZero.{u1} R _inst_1) (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)) (Module.toMulActionWithZero.{u1, u2} R M _inst_1 _inst_2 _inst_3))))
+Case conversion may be inaccurate. Consider using '#align module.free.no_zero_smul_divisors Module.Free.noZeroSMulDivisorsₓ'. -/
 instance (priority := 100) noZeroSMulDivisors [NoZeroDivisors R] : NoZeroSMulDivisors R M :=
   let ⟨⟨_, b⟩⟩ := exists_basis R M
   b.NoZeroSMulDivisors
@@ -119,68 +145,116 @@ instance [Nontrivial M] : Nonempty (Module.Free.ChooseBasisIndex R M) :=
 
 variable {R M N}
 
+#print Module.Free.of_equiv /-
 theorem of_equiv (e : M ≃ₗ[R] N) : Module.Free R N :=
   of_basis <| (chooseBasis R M).map e
 #align module.free.of_equiv Module.Free.of_equiv
+-/
 
+#print Module.Free.of_equiv' /-
 /-- A variation of `of_equiv`: the assumption `module.free R P` here is explicit rather than an
 instance. -/
 theorem of_equiv' {P : Type v} [AddCommMonoid P] [Module R P] (h : Module.Free R P)
     (e : P ≃ₗ[R] N) : Module.Free R N :=
   of_equiv e
 #align module.free.of_equiv' Module.Free.of_equiv'
+-/
 
 variable (R M N)
 
+#print Module.Free.self /-
 /-- The module structure provided by `semiring.to_module` is free. -/
 instance self : Module.Free R R :=
   of_basis (Basis.singleton Unit R)
 #align module.free.self Module.Free.self
+-/
 
+/- warning: module.free.prod -> Module.Free.prod is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u1, u3} R N _inst_1 _inst_5] [_inst_7 : Module.Free.{u1, u3} R N _inst_1 _inst_5 _inst_6], Module.Free.{u1, max u2 u3} R (Prod.{u2, u3} M N) _inst_1 (Prod.addCommMonoid.{u2, u3} M N _inst_2 _inst_5) (Prod.module.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_5 _inst_3 _inst_6)
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3] [_inst_5 : AddCommMonoid.{u3} N] [_inst_6 : Module.{u1, u3} R N _inst_1 _inst_5] [_inst_7 : Module.Free.{u1, u3} R N _inst_1 _inst_5 _inst_6], Module.Free.{u1, max u3 u2} R (Prod.{u2, u3} M N) _inst_1 (Prod.instAddCommMonoidSum.{u2, u3} M N _inst_2 _inst_5) (Prod.module.{u1, u2, u3} R M N _inst_1 _inst_2 _inst_5 _inst_3 _inst_6)
+Case conversion may be inaccurate. Consider using '#align module.free.prod Module.Free.prodₓ'. -/
 instance prod [Module.Free R N] : Module.Free R (M × N) :=
   of_basis <| (chooseBasis R M).Prod (chooseBasis R N)
 #align module.free.prod Module.Free.prod
 
+#print Module.Free.pi /-
 /-- The product of finitely many free modules is free. -/
 instance pi (M : ι → Type _) [Finite ι] [∀ i : ι, AddCommMonoid (M i)] [∀ i : ι, Module R (M i)]
     [∀ i : ι, Module.Free R (M i)] : Module.Free R (∀ i, M i) :=
   let ⟨_⟩ := nonempty_fintype ι
   of_basis <| Pi.basis fun i => choose_basis R (M i)
 #align module.free.pi Module.Free.pi
+-/
 
+#print Module.Free.matrix /-
 /-- The module of finite matrices is free. -/
 instance matrix {m n : Type _} [Finite m] [Finite n] : Module.Free R (Matrix m n M) :=
   Module.Free.pi R _
 #align module.free.matrix Module.Free.matrix
+-/
 
 variable (ι)
 
+#print Module.Free.function /-
 /-- The product of finitely many free modules is free (non-dependent version to help with typeclass
 search). -/
 instance function [Finite ι] : Module.Free R (ι → M) :=
   Free.pi _ _
 #align module.free.function Module.Free.function
+-/
 
+/- warning: module.free.finsupp -> Module.Free.finsupp is a dubious translation:
+lean 3 declaration is
+  forall (ι : Type.{u3}) (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3], Module.Free.{u1, max u3 u2} R (Finsupp.{u3, u2} ι M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2)))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι M _inst_2) (Finsupp.module.{u3, u2, u1} ι M R _inst_1 _inst_2 _inst_3)
+but is expected to have type
+  forall (ι : Type.{u3}) (R : Type.{u1}) (M : Type.{u2}) [_inst_1 : Semiring.{u1} R] [_inst_2 : AddCommMonoid.{u2} M] [_inst_3 : Module.{u1, u2} R M _inst_1 _inst_2] [_inst_4 : Module.Free.{u1, u2} R M _inst_1 _inst_2 _inst_3], Module.Free.{u1, max u2 u3} R (Finsupp.{u3, u2} ι M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_2))) _inst_1 (Finsupp.addCommMonoid.{u3, u2} ι M _inst_2) (Finsupp.module.{u3, u2, u1} ι M R _inst_1 _inst_2 _inst_3)
+Case conversion may be inaccurate. Consider using '#align module.free.finsupp Module.Free.finsuppₓ'. -/
 instance finsupp : Module.Free R (ι →₀ M) :=
   of_basis (Finsupp.basis fun i => chooseBasis R M)
 #align module.free.finsupp Module.Free.finsupp
 
 variable {ι}
 
+/- warning: module.free.of_subsingleton -> Module.Free.of_subsingleton is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ z} N], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
+but is expected to have type
+  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ z} N], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
+Case conversion may be inaccurate. Consider using '#align module.free.of_subsingleton Module.Free.of_subsingletonₓ'. -/
 instance (priority := 100) of_subsingleton [Subsingleton N] : Module.Free R N :=
   of_basis (Basis.empty N : Basis PEmpty R N)
 #align module.free.of_subsingleton Module.Free.of_subsingleton
 
+/- warning: module.free.of_subsingleton' -> Module.Free.of_subsingleton' is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ u} R], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
+but is expected to have type
+  forall (R : Type.{u}) (N : Type.{z}) [_inst_1 : Semiring.{u} R] [_inst_5 : AddCommMonoid.{z} N] [_inst_6 : Module.{u, z} R N _inst_1 _inst_5] [_inst_7 : Subsingleton.{succ u} R], Module.Free.{u, z} R N _inst_1 _inst_5 _inst_6
+Case conversion may be inaccurate. Consider using '#align module.free.of_subsingleton' Module.Free.of_subsingleton'ₓ'. -/
 instance (priority := 100) of_subsingleton' [Subsingleton R] : Module.Free R N :=
   letI := Module.subsingleton R N
   Module.Free.of_subsingleton R N
 #align module.free.of_subsingleton' Module.Free.of_subsingleton'
 
+/- warning: module.free.dfinsupp -> Module.Free.dfinsupp is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u2 u3} R (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddZeroClass.toHasZero.{u3} (M i) (AddMonoid.toAddZeroClass.{u3} (M i) (AddCommMonoid.toAddMonoid.{u3} (M i) (_inst_7 i))))) _inst_1 (Dfinsupp.addCommMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.module.{u2, u3, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u3 u2} R (Dfinsupp.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => AddMonoid.toZero.{u3} ((fun (i : ι) => M i) i) (AddCommMonoid.toAddMonoid.{u3} ((fun (i : ι) => M i) i) (_inst_7 i)))) _inst_1 (Dfinsupp.instAddCommMonoidDfinsuppToZeroToAddMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (Dfinsupp.module.{u2, u3, u1} ι R (fun (i : ι) => M i) _inst_1 (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
+Case conversion may be inaccurate. Consider using '#align module.free.dfinsupp Module.Free.dfinsuppₓ'. -/
 instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (Π₀ i, M i) :=
   of_basis <| Dfinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
 
+/- warning: module.free.direct_sum -> Module.Free.directSum is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u2 u3} R (DirectSum.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) _inst_1 (DirectSum.addCommMonoid.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (DirectSum.module.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
+but is expected to have type
+  forall (R : Type.{u1}) [_inst_1 : Semiring.{u1} R] {ι : Type.{u2}} (M : ι -> Type.{u3}) [_inst_7 : forall (i : ι), AddCommMonoid.{u3} (M i)] [_inst_8 : forall (i : ι), Module.{u1, u3} R (M i) _inst_1 (_inst_7 i)] [_inst_9 : forall (i : ι), Module.Free.{u1, u3} R (M i) _inst_1 (_inst_7 i) (_inst_8 i)], Module.Free.{u1, max u3 u2} R (DirectSum.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) _inst_1 (instAddCommMonoidDirectSum.{u2, u3} ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i)) (DirectSum.instModuleDirectSumInstAddCommMonoidDirectSum.{u1, u2, u3} R _inst_1 ι (fun (i : ι) => M i) (fun (i : ι) => _inst_7 i) (fun (i : ι) => _inst_8 i))
+Case conversion may be inaccurate. Consider using '#align module.free.direct_sum Module.Free.directSumₓ'. -/
 instance directSum {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (⨁ i, M i) :=
   Module.Free.dfinsupp R M
@@ -194,6 +268,12 @@ variable [CommRing R] [AddCommGroup M] [Module R M] [Module.Free R M]
 
 variable [AddCommGroup N] [Module R N] [Module.Free R N]
 
+/- warning: module.free.tensor -> Module.Free.tensor is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Module.Free.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_5 : AddCommGroup.{u3} N] [_inst_6 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5)] [_inst_7 : Module.Free.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_6], Module.Free.{u1, max u2 u3} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (TensorProduct.module.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6)
+but is expected to have type
+  forall (R : Type.{u1}) (M : Type.{u2}) (N : Type.{u3}) [_inst_1 : CommRing.{u1} R] [_inst_2 : AddCommGroup.{u2} M] [_inst_3 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2)] [_inst_4 : Module.Free.{u1, u2} R M (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) _inst_3] [_inst_5 : AddCommGroup.{u3} N] [_inst_6 : Module.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5)] [_inst_7 : Module.Free.{u1, u3} R N (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_6], Module.Free.{u1, max u3 u2} R (TensorProduct.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (TensorProduct.addCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6) (TensorProduct.instModuleTensorProductToSemiringAddCommMonoid.{u1, u2, u3} R (CommRing.toCommSemiring.{u1} R _inst_1) M N (AddCommGroup.toAddCommMonoid.{u2} M _inst_2) (AddCommGroup.toAddCommMonoid.{u3} N _inst_5) _inst_3 _inst_6)
+Case conversion may be inaccurate. Consider using '#align module.free.tensor Module.Free.tensorₓ'. -/
 instance tensor : Module.Free R (M ⊗[R] N) :=
   let ⟨bM⟩ := exists_basis R M
   let ⟨bN⟩ := exists_basis R N
@@ -206,9 +286,11 @@ section DivisionRing
 
 variable [DivisionRing R] [AddCommGroup M] [Module R M]
 
+#print Module.Free.of_divisionRing /-
 instance (priority := 100) of_divisionRing : Module.Free R M :=
   of_basis (Basis.ofVectorSpace R M)
 #align module.free.of_division_ring Module.Free.of_divisionRing
+-/
 
 end DivisionRing
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ec294687917cbc5c73620b4414ae9b5dd9ae1b4

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 
 ! This file was ported from Lean 3 source module linear_algebra.free_module.basic
-! leanprover-community/mathlib commit 5fe298160aa02b0f3cf95690a1265232cdd9563c
+! leanprover-community/mathlib commit 4e7e7009099d4a88a750de710909b95487bf0124
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,7 @@ import Mathbin.LinearAlgebra.DirectSum.Finsupp
 import Mathbin.Logic.Small.Basic
 import Mathbin.LinearAlgebra.StdBasis
 import Mathbin.LinearAlgebra.FinsuppVectorSpace
+import Mathbin.LinearAlgebra.TensorProductBasis
 
 /-!
 
@@ -194,8 +195,9 @@ variable [CommRing R] [AddCommGroup M] [Module R M] [Module.Free R M]
 variable [AddCommGroup N] [Module R N] [Module.Free R N]
 
 instance tensor : Module.Free R (M ⊗[R] N) :=
-  of_equiv' (of_equiv' (Free.finsupp _ R _) (finsuppTensorFinsupp' R _ _).symm)
-    (TensorProduct.congr (chooseBasis R M).repr (chooseBasis R N).repr).symm
+  let ⟨bM⟩ := exists_basis R M
+  let ⟨bN⟩ := exists_basis R N
+  of_basis (bM.2.TensorProduct bN.2)
 #align module.free.tensor Module.Free.tensor
 
 end CommRing

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

@@ -64,9 +64,9 @@ theorem Module.free_iff_set : Module.Free R M ↔ ∃ S : Set M, Nonempty (Basis
 
 variable {R M}
 
-theorem Module.Free.ofBasis {ι : Type w} (b : Basis ι R M) : Module.Free R M :=
+theorem Module.Free.of_basis {ι : Type w} (b : Basis ι R M) : Module.Free R M :=
   (Module.free_def R M).2 ⟨Set.range b, ⟨b.reindexRange⟩⟩
-#align module.free.of_basis Module.Free.ofBasis
+#align module.free.of_basis Module.Free.of_basis
 
 end Basic
 
@@ -118,26 +118,26 @@ instance [Nontrivial M] : Nonempty (Module.Free.ChooseBasisIndex R M) :=
 
 variable {R M N}
 
-theorem ofEquiv (e : M ≃ₗ[R] N) : Module.Free R N :=
-  ofBasis <| (chooseBasis R M).map e
-#align module.free.of_equiv Module.Free.ofEquiv
+theorem of_equiv (e : M ≃ₗ[R] N) : Module.Free R N :=
+  of_basis <| (chooseBasis R M).map e
+#align module.free.of_equiv Module.Free.of_equiv
 
 /-- A variation of `of_equiv`: the assumption `module.free R P` here is explicit rather than an
 instance. -/
-theorem ofEquiv' {P : Type v} [AddCommMonoid P] [Module R P] (h : Module.Free R P) (e : P ≃ₗ[R] N) :
-    Module.Free R N :=
-  ofEquiv e
-#align module.free.of_equiv' Module.Free.ofEquiv'
+theorem of_equiv' {P : Type v} [AddCommMonoid P] [Module R P] (h : Module.Free R P)
+    (e : P ≃ₗ[R] N) : Module.Free R N :=
+  of_equiv e
+#align module.free.of_equiv' Module.Free.of_equiv'
 
 variable (R M N)
 
 /-- The module structure provided by `semiring.to_module` is free. -/
 instance self : Module.Free R R :=
-  ofBasis (Basis.singleton Unit R)
+  of_basis (Basis.singleton Unit R)
 #align module.free.self Module.Free.self
 
 instance prod [Module.Free R N] : Module.Free R (M × N) :=
-  ofBasis <| (chooseBasis R M).Prod (chooseBasis R N)
+  of_basis <| (chooseBasis R M).Prod (chooseBasis R N)
 #align module.free.prod Module.Free.prod
 
 /-- The product of finitely many free modules is free. -/
@@ -161,23 +161,23 @@ instance function [Finite ι] : Module.Free R (ι → M) :=
 #align module.free.function Module.Free.function
 
 instance finsupp : Module.Free R (ι →₀ M) :=
-  ofBasis (Finsupp.basis fun i => chooseBasis R M)
+  of_basis (Finsupp.basis fun i => chooseBasis R M)
 #align module.free.finsupp Module.Free.finsupp
 
 variable {ι}
 
-instance (priority := 100) ofSubsingleton [Subsingleton N] : Module.Free R N :=
-  ofBasis (Basis.empty N : Basis PEmpty R N)
-#align module.free.of_subsingleton Module.Free.ofSubsingleton
+instance (priority := 100) of_subsingleton [Subsingleton N] : Module.Free R N :=
+  of_basis (Basis.empty N : Basis PEmpty R N)
+#align module.free.of_subsingleton Module.Free.of_subsingleton
 
-instance (priority := 100) ofSubsingleton' [Subsingleton R] : Module.Free R N :=
+instance (priority := 100) of_subsingleton' [Subsingleton R] : Module.Free R N :=
   letI := Module.subsingleton R N
-  Module.Free.ofSubsingleton R N
-#align module.free.of_subsingleton' Module.Free.ofSubsingleton'
+  Module.Free.of_subsingleton R N
+#align module.free.of_subsingleton' Module.Free.of_subsingleton'
 
 instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (Π₀ i, M i) :=
-  ofBasis <| Dfinsupp.basis fun i => chooseBasis R (M i)
+  of_basis <| Dfinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
 
 instance directSum {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
@@ -194,7 +194,7 @@ variable [CommRing R] [AddCommGroup M] [Module R M] [Module.Free R M]
 variable [AddCommGroup N] [Module R N] [Module.Free R N]
 
 instance tensor : Module.Free R (M ⊗[R] N) :=
-  ofEquiv' (ofEquiv' (Free.finsupp _ R _) (finsuppTensorFinsupp' R _ _).symm)
+  of_equiv' (of_equiv' (Free.finsupp _ R _) (finsuppTensorFinsupp' R _ _).symm)
     (TensorProduct.congr (chooseBasis R M).repr (chooseBasis R N).repr).symm
 #align module.free.tensor Module.Free.tensor
 
@@ -204,9 +204,9 @@ section DivisionRing
 
 variable [DivisionRing R] [AddCommGroup M] [Module R M]
 
-instance (priority := 100) ofDivisionRing : Module.Free R M :=
-  ofBasis (Basis.ofVectorSpace R M)
-#align module.free.of_division_ring Module.Free.ofDivisionRing
+instance (priority := 100) of_divisionRing : Module.Free R M :=
+  of_basis (Basis.ofVectorSpace R M)
+#align module.free.of_division_ring Module.Free.of_divisionRing
 
 end DivisionRing
 

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

All of these changes appear to be oversights to me.

@@ -37,7 +37,7 @@ class Module.Free : Prop where
   exists_basis : Nonempty <| (I : Type v) × Basis I R M
 #align module.free Module.Free
 
-/- If `M` fits in universe `w`, then freeness is equivalent to existence of a basis in that
+/-- If `M` fits in universe `w`, then freeness is equivalent to existence of a basis in that
 universe.
 
 Note that if `M` does not fit in `w`, the reverse direction of this implication is still true as

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

@@ -32,7 +32,7 @@ section Basic
 
 variable [Semiring R] [AddCommMonoid M] [Module R M]
 
-/-- `Module.Free R M` is the statement that the `R`-module `M` is free.-/
+/-- `Module.Free R M` is the statement that the `R`-module `M` is free. -/
 class Module.Free : Prop where
   exists_basis : Nonempty <| (I : Type v) × Basis I R M
 #align module.free Module.Free

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)

@@ -68,7 +68,6 @@ namespace Module.Free
 section Semiring
 
 variable [Semiring R] [AddCommMonoid M] [Module R M] [Module.Free R M]
-
 variable [AddCommMonoid N] [Module R N]
 
 /-- If `Module.Free R M` then `ChooseBasisIndex R M` is the `ι` which indexes the basis

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: Riccardo Brasca
 -/
 import Mathlib.Data.Finsupp.Fintype
-import Mathlib.LinearAlgebra.TensorProductBasis
+import Mathlib.LinearAlgebra.TensorProduct.Basis
 
 #align_import linear_algebra.free_module.basic from "leanprover-community/mathlib"@"4e7e7009099d4a88a750de710909b95487bf0124"
 

Generalize Basis.tensorProduct and instance Module.Free.tensor to CommSemiring and AddCommMonoid, as a follow-up to #10828.

Plus style fixes:

• tidy up LinearAlgebra.DirectSum.Finsupp.lean:
  • delete unused universe declaration
  • delete duplicate open TensorProduct
  • delete redundant noncomputable annotation and associated comment (due to noncomputable section in the same file)
  • use variable
• delete "typeclass reminders" in "Module.Flat.iff_rTensor_injective'" (no longer needed)
• whitespace fixes
• simplify file structure (section/namespace/open/variable)

Co-authored-by: Richard Copley <rcopley@gmail.com>

@@ -9,7 +9,6 @@ import Mathlib.LinearAlgebra.TensorProductBasis
 #align_import linear_algebra.free_module.basic from "leanprover-community/mathlib"@"4e7e7009099d4a88a750de710909b95487bf0124"
 
 /-!
-
 # Free modules
 
 We introduce a class `Module.Free R M`, for `R` a `Semiring` and `M` an `R`-module and we provide
@@ -20,7 +19,6 @@ Use `Finsupp.total_id_surjective` to prove that any module is the quotient of a
 ## Main definition
 
 * `Module.Free R M` : the class of free `R`-modules.
-
 -/
 
 
@@ -191,11 +189,10 @@ instance directSum {ι : Type*} (M : ι → Type*) [∀ i : ι, AddCommMonoid (M
 
 end Semiring
 
-section CommRing
-
-variable [CommRing R] [AddCommGroup M] [Module R M] [Module.Free R M]
+section CommSemiring
 
-variable [AddCommGroup N] [Module R N] [Module.Free R N]
+variable [CommSemiring R] [AddCommMonoid M] [Module R M] [Module.Free R M]
+  [AddCommMonoid N] [Module R N] [Module.Free R N]
 
 instance tensor : Module.Free R (M ⊗[R] N) :=
   let ⟨bM⟩ := exists_basis (R := R) (M := M)
@@ -203,6 +200,6 @@ instance tensor : Module.Free R (M ⊗[R] N) :=
   of_basis (bM.2.tensorProduct bN.2)
 #align module.free.tensor Module.Free.tensor
 
-end CommRing
+end CommSemiring
 
 end Module.Free

Also fix a typo and remove a now useless maxHeartbeats in Mathlib.NumberTheory.NumberField.Units.

@@ -3,10 +3,7 @@ Copyright (c) 2021 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
 -/
-import Mathlib.LinearAlgebra.DirectSum.Finsupp
-import Mathlib.Logic.Small.Basic
-import Mathlib.LinearAlgebra.StdBasis
-import Mathlib.LinearAlgebra.FinsuppVectorSpace
+import Mathlib.Data.Finsupp.Fintype
 import Mathlib.LinearAlgebra.TensorProductBasis
 
 #align_import linear_algebra.free_module.basic from "leanprover-community/mathlib"@"4e7e7009099d4a88a750de710909b95487bf0124"
@@ -118,6 +115,9 @@ instance (priority := 100) noZeroSMulDivisors [NoZeroDivisors R] : NoZeroSMulDiv
 instance [Nontrivial M] : Nonempty (Module.Free.ChooseBasisIndex R M) :=
   (Module.Free.chooseBasis R M).index_nonempty
 
+theorem infinite [Infinite R] [Nontrivial M] : Infinite M :=
+  (Equiv.infinite_iff (chooseBasis R M).repr.toEquiv).mpr Finsupp.infinite_of_right
+
 variable {R M N}
 
 theorem of_equiv (e : M ≃ₗ[R] N) : Module.Free R N :=

@@ -49,9 +49,6 @@ Note that if `M` does not fit in `w`, the reverse direction of this implication
 `Module.Free.of_basis`. -/
 theorem Module.free_def [Small.{w,v} M] :
     Module.Free R M ↔ ∃ I : Type w, Nonempty (Basis I R M) :=
-  -- Porting note: this is required or Lean cannot solve universe constraints
-  -- The same error presents if inferInstance is called to solve `small`
-  have _small (s : Set M) : Small.{w} ↑s := small_of_injective (fun _ _ => (Subtype.val_inj).mp)
   ⟨fun h =>
     ⟨Shrink (Set.range h.exists_basis.some.2),
       ⟨(Basis.reindexRange h.exists_basis.some.2).reindex (equivShrink _)⟩⟩,

These carry no data so should be harmless.

@@ -157,6 +157,8 @@ instance matrix {m n : Type*} [Finite m] [Finite n] : Module.Free R (Matrix m n
   Module.Free.pi R _
 #align module.free.matrix Module.Free.matrix
 
+instance ulift [Free R M] : Free R (ULift M) := of_equiv ULift.moduleEquiv.symm
+
 variable (ι)
 
 /-- The product of finitely many free modules is free (non-dependent version to help with typeclass

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

This has nice performance benefits.

@@ -29,7 +29,7 @@ Use `Finsupp.total_id_surjective` to prove that any module is the quotient of a
 
 universe u v w z
 
-variable {ι : Type _} (R : Type u) (M : Type v) (N : Type z)
+variable {ι : Type*} (R : Type u) (M : Type v) (N : Type z)
 
 open TensorProduct DirectSum BigOperators
 
@@ -146,14 +146,14 @@ instance prod [Module.Free R N] : Module.Free R (M × N) :=
 #align module.free.prod Module.Free.prod
 
 /-- The product of finitely many free modules is free. -/
-instance pi (M : ι → Type _) [Finite ι] [∀ i : ι, AddCommMonoid (M i)] [∀ i : ι, Module R (M i)]
+instance pi (M : ι → Type*) [Finite ι] [∀ i : ι, AddCommMonoid (M i)] [∀ i : ι, Module R (M i)]
     [∀ i : ι, Module.Free R (M i)] : Module.Free R (∀ i, M i) :=
   let ⟨_⟩ := nonempty_fintype ι
   of_basis <| Pi.basis fun i => chooseBasis R (M i)
 #align module.free.pi Module.Free.pi
 
 /-- The module of finite matrices is free. -/
-instance matrix {m n : Type _} [Finite m] [Finite n] : Module.Free R (Matrix m n M) :=
+instance matrix {m n : Type*} [Finite m] [Finite n] : Module.Free R (Matrix m n M) :=
   Module.Free.pi R _
 #align module.free.matrix Module.Free.matrix
 
@@ -180,12 +180,12 @@ instance (priority := 100) of_subsingleton' [Subsingleton R] : Module.Free R N :
   Module.Free.of_subsingleton R N
 #align module.free.of_subsingleton' Module.Free.of_subsingleton'
 
-instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
+instance dfinsupp {ι : Type*} (M : ι → Type*) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (Π₀ i, M i) :=
   of_basis <| DFinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
 
-instance directSum {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
+instance directSum {ι : Type*} (M : ι → Type*) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (⨁ i, M i) :=
   Module.Free.dfinsupp R M
 #align module.free.direct_sum Module.Free.directSum

This also changes basisFintypeOfFiniteSpans to use Finite rather than Fintype, as it was noncomputable anyway. This means it has to be renamed to basis_finite_of_finite_spans as it now is a proof!

Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -80,9 +80,9 @@ variable [Semiring R] [AddCommMonoid M] [Module R M] [Module.Free R M]
 variable [AddCommMonoid N] [Module R N]
 
 /-- If `Module.Free R M` then `ChooseBasisIndex R M` is the `ι` which indexes the basis
-  `ι → M`. -/
-def ChooseBasisIndex :=
-  (exists_basis (R := R) (M := M)).some.1
+  `ι → M`. Note that this is defined such that this type is finite if `R` is trivial. -/
+def ChooseBasisIndex : Type _ :=
+  ((Module.free_iff_set R M).mp ‹_›).choose
 #align module.free.choose_basis_index Module.Free.ChooseBasisIndex
 
 /-- There is no hope of computing this, but we add the instance anyway to avoid fumbling with
@@ -92,7 +92,7 @@ noncomputable instance : DecidableEq (ChooseBasisIndex R M) := Classical.decEq _
 /-- If `Module.Free R M` then `chooseBasis : ι → M` is the basis.
 Here `ι = ChooseBasisIndex R M`. -/
 noncomputable def chooseBasis : Basis (ChooseBasisIndex R M) R M :=
-  (exists_basis (R := R) (M := M)).some.2
+  ((Module.free_iff_set R M).mp ‹_›).choose_spec.some
 #align module.free.choose_basis Module.Free.chooseBasis
 
 /-- The isomorphism `M ≃ₗ[R] (ChooseBasisIndex R M →₀ R)`. -/

This uncovers a few situations where a lemma was stated with the wrong decidability assumption. The corrected lemmas are strictly more syntactically-general.

This is exhaustive in the LinearAlgebra folder.

Where removal is impractical, this switches to open Classical in to make the intent clear.

@@ -85,6 +85,10 @@ def ChooseBasisIndex :=
   (exists_basis (R := R) (M := M)).some.1
 #align module.free.choose_basis_index Module.Free.ChooseBasisIndex
 
+/-- There is no hope of computing this, but we add the instance anyway to avoid fumbling with
+`open scoped Classical`. -/
+noncomputable instance : DecidableEq (ChooseBasisIndex R M) := Classical.decEq _
+
 /-- If `Module.Free R M` then `chooseBasis : ι → M` is the basis.
 Here `ι = ChooseBasisIndex R M`. -/
 noncomputable def chooseBasis : Basis (ChooseBasisIndex R M) R M :=

This breaks a dependency cycle with Module.Free, which means we can immediately show that all vector spaces are free modules.

The lemmas are moved without modification in this PR. A subsequent PR can use the Module.Free results to golf the vector space ones, and deduplicate the API.

Co-authored-by: Oliver Nash <github@olivernash.org>

@@ -202,14 +202,4 @@ instance tensor : Module.Free R (M ⊗[R] N) :=
 
 end CommRing
 
-section DivisionRing
-
-variable [DivisionRing R] [AddCommGroup M] [Module R M]
-
-instance (priority := 100) of_divisionRing : Module.Free R M :=
-  of_basis (Basis.ofVectorSpace R M)
-#align module.free.of_division_ring Module.Free.of_divisionRing
-
-end DivisionRing
-
 end Module.Free

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca
-
-! This file was ported from Lean 3 source module linear_algebra.free_module.basic
-! leanprover-community/mathlib commit 4e7e7009099d4a88a750de710909b95487bf0124
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.DirectSum.Finsupp
 import Mathlib.Logic.Small.Basic
@@ -14,6 +9,8 @@ import Mathlib.LinearAlgebra.StdBasis
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 import Mathlib.LinearAlgebra.TensorProductBasis
 
+#align_import linear_algebra.free_module.basic from "leanprover-community/mathlib"@"4e7e7009099d4a88a750de710909b95487bf0124"
+
 /-!
 
 # Free modules

See #4354

@@ -181,7 +181,7 @@ instance (priority := 100) of_subsingleton' [Subsingleton R] : Module.Free R N :
 
 instance dfinsupp {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]
     [∀ i : ι, Module R (M i)] [∀ i : ι, Module.Free R (M i)] : Module.Free R (Π₀ i, M i) :=
-  of_basis <| Dfinsupp.basis fun i => chooseBasis R (M i)
+  of_basis <| DFinsupp.basis fun i => chooseBasis R (M i)
 #align module.free.dfinsupp Module.Free.dfinsupp
 
 instance directSum {ι : Type _} (M : ι → Type _) [∀ i : ι, AddCommMonoid (M i)]

These are all doc fixes

@@ -53,7 +53,7 @@ Note that if `M` does not fit in `w`, the reverse direction of this implication
 theorem Module.free_def [Small.{w,v} M] :
     Module.Free R M ↔ ∃ I : Type w, Nonempty (Basis I R M) :=
   -- Porting note: this is required or Lean cannot solve universe constraints
-  -- The same error presents if interInstance is called to solve `small`
+  -- The same error presents if inferInstance is called to solve `small`
   have _small (s : Set M) : Small.{w} ↑s := small_of_injective (fun _ _ => (Subtype.val_inj).mp)
   ⟨fun h =>
     ⟨Shrink (Set.range h.exists_basis.some.2),

Run codespell Mathlib and keep some suggestions.

@@ -99,7 +99,7 @@ noncomputable def repr : M ≃ₗ[R] ChooseBasisIndex R M →₀ R :=
   (chooseBasis R M).repr
 #align module.free.repr Module.Free.repr
 
-/-- The universal property of free modules: giving a functon `(ChooseBasisIndex R M) → N`, for `N`
+/-- The universal property of free modules: giving a function `(ChooseBasisIndex R M) → N`, for `N`
 an `R`-module, is the same as giving an `R`-linear map `M →ₗ[R] N`.
 
 This definition is parameterized over an extra `Semiring S`,

@@ -49,7 +49,7 @@ class Module.Free : Prop where
 universe.
 
 Note that if `M` does not fit in `w`, the reverse direction of this implication is still true as
-`module.free.of_basis`. -/
+`Module.Free.of_basis`. -/
 theorem Module.free_def [Small.{w,v} M] :
     Module.Free R M ↔ ∃ I : Type w, Nonempty (Basis I R M) :=
   -- Porting note: this is required or Lean cannot solve universe constraints
@@ -82,30 +82,30 @@ variable [Semiring R] [AddCommMonoid M] [Module R M] [Module.Free R M]
 
 variable [AddCommMonoid N] [Module R N]
 
-/-- If `module.free R M` then `choose_basis_index R M` is the `ι` which indexes the basis
+/-- If `Module.Free R M` then `ChooseBasisIndex R M` is the `ι` which indexes the basis
   `ι → M`. -/
 def ChooseBasisIndex :=
   (exists_basis (R := R) (M := M)).some.1
 #align module.free.choose_basis_index Module.Free.ChooseBasisIndex
 
-/-- If `module.free R M` then `choose_basis : ι → M` is the basis.
-Here `ι = choose_basis_index R M`. -/
+/-- If `Module.Free R M` then `chooseBasis : ι → M` is the basis.
+Here `ι = ChooseBasisIndex R M`. -/
 noncomputable def chooseBasis : Basis (ChooseBasisIndex R M) R M :=
   (exists_basis (R := R) (M := M)).some.2
 #align module.free.choose_basis Module.Free.chooseBasis
 
-/-- The isomorphism `M ≃ₗ[R] (choose_basis_index R M →₀ R)`. -/
+/-- The isomorphism `M ≃ₗ[R] (ChooseBasisIndex R M →₀ R)`. -/
 noncomputable def repr : M ≃ₗ[R] ChooseBasisIndex R M →₀ R :=
   (chooseBasis R M).repr
 #align module.free.repr Module.Free.repr
 
-/-- The universal property of free modules: giving a functon `(choose_basis_index R M) → N`, for `N`
+/-- The universal property of free modules: giving a functon `(ChooseBasisIndex R M) → N`, for `N`
 an `R`-module, is the same as giving an `R`-linear map `M →ₗ[R] N`.
 
-This definition is parameterized over an extra `semiring S`,
-such that `smul_comm_class R S M'` holds.
+This definition is parameterized over an extra `Semiring S`,
+such that `SMulCommClass R S M'` holds.
 If `R` is commutative, you can set `S := R`; if `R` is not commutative,
-you can recover an `add_equiv` by setting `S := ℕ`.
+you can recover an `AddEquiv` by setting `S := ℕ`.
 See library note [bundled maps over different rings]. -/
 noncomputable def constr {S : Type z} [Semiring S] [Module S N] [SMulCommClass R S N] :
     (ChooseBasisIndex R M → N) ≃ₗ[S] M →ₗ[R] N :=
@@ -126,7 +126,7 @@ theorem of_equiv (e : M ≃ₗ[R] N) : Module.Free R N :=
   of_basis <| (chooseBasis R M).map e
 #align module.free.of_equiv Module.Free.of_equiv
 
-/-- A variation of `of_equiv`: the assumption `module.free R P` here is explicit rather than an
+/-- A variation of `of_equiv`: the assumption `Module.Free R P` here is explicit rather than an
 instance. -/
 theorem of_equiv' {P : Type v} [AddCommMonoid P] [Module R P] (_ : Module.Free R P)
     (e : P ≃ₗ[R] N) : Module.Free R N :=
@@ -135,7 +135,7 @@ theorem of_equiv' {P : Type v} [AddCommMonoid P] [Module R P] (_ : Module.Free R
 
 variable (R M N)
 
-/-- The module structure provided by `semiring.to_module` is free. -/
+/-- The module structure provided by `Semiring.toModule` is free. -/
 instance self : Module.Free R R :=
   of_basis (Basis.singleton Unit R)
 #align module.free.self Module.Free.self
@@ -216,4 +216,3 @@ instance (priority := 100) of_divisionRing : Module.Free R M :=
 end DivisionRing
 
 end Module.Free
-

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>