linear_algebra.free_algebra ⟷ Mathlib.LinearAlgebra.FreeAlgebra

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

@@ -5,7 +5,7 @@ Authors: Eric Wieser
 -/
 import LinearAlgebra.Basis
 import Algebra.FreeAlgebra
-import LinearAlgebra.Dimension
+import LinearAlgebra.Dimension.Basic
 import LinearAlgebra.FinsuppVectorSpace
 
 #align_import linear_algebra.free_algebra from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
 -/
-import Mathbin.LinearAlgebra.Basis
-import Mathbin.Algebra.FreeAlgebra
-import Mathbin.LinearAlgebra.Dimension
-import Mathbin.LinearAlgebra.FinsuppVectorSpace
+import LinearAlgebra.Basis
+import Algebra.FreeAlgebra
+import LinearAlgebra.Dimension
+import LinearAlgebra.FinsuppVectorSpace
 
 #align_import linear_algebra.free_algebra from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 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.free_algebra
-! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Basis
 import Mathbin.Algebra.FreeAlgebra
 import Mathbin.LinearAlgebra.Dimension
 import Mathbin.LinearAlgebra.FinsuppVectorSpace
 
+#align_import linear_algebra.free_algebra from "leanprover-community/mathlib"@"814d76e2247d5ba8bc024843552da1278bfe9e5c"
+
 /-!
 # Linear algebra properties of `free_algebra R X`
 

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

@@ -28,6 +28,7 @@ universe u v
 
 namespace FreeAlgebra
 
+#print FreeAlgebra.basisFreeMonoid /-
 /-- The `free_monoid X` basis on the `free_algebra R X`,
 mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * xₙ` -/
 @[simps]
@@ -36,12 +37,15 @@ noncomputable def basisFreeMonoid (R : Type u) (X : Type v) [CommRing R] :
   Finsupp.basisSingleOne.map
     (equivMonoidAlgebraFreeMonoid.symm.toLinearEquiv : _ ≃ₗ[R] FreeAlgebra R X)
 #align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoid
+-/
 
+#print FreeAlgebra.rank_eq /-
 -- TODO: generalize to `X : Type v`
 theorem rank_eq {K : Type u} {X : Type max u v} [Field K] :
     Module.rank K (FreeAlgebra K X) = Cardinal.mk (List X) :=
   (Cardinal.lift_inj.mp (basisFreeMonoid K X).mk_eq_rank).symm
 #align free_algebra.rank_eq FreeAlgebra.rank_eq
+-/
 
 end FreeAlgebra
 

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

@@ -28,12 +28,6 @@ universe u v
 
 namespace FreeAlgebra
 
-/- warning: free_algebra.basis_free_monoid -> FreeAlgebra.basisFreeMonoid is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u1}) (X : Type.{u2}) [_inst_1 : CommRing.{u1} R], Basis.{u2, u1, max u1 u2} (FreeMonoid.{u2} X) R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonUnitalNonAssocRing.toAddCommGroup.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.ring.{u2, u1} X R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommRing.toCommSemiring.{u1} R _inst_1) (FreeAlgebra.semiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.algebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X))
-but is expected to have type
-  forall (R : Type.{u1}) (X : Type.{u2}) [_inst_1 : CommRing.{u1} R], Basis.{u2, u1, max u2 u1} (FreeMonoid.{u2} X) R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{u2, u1} X R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommRing.toCommSemiring.{u1} R _inst_1) (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X))
-Case conversion may be inaccurate. Consider using '#align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoidₓ'. -/
 /-- The `free_monoid X` basis on the `free_algebra R X`,
 mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * xₙ` -/
 @[simps]
@@ -43,12 +37,6 @@ noncomputable def basisFreeMonoid (R : Type u) (X : Type v) [CommRing R] :
     (equivMonoidAlgebraFreeMonoid.symm.toLinearEquiv : _ ≃ₗ[R] FreeAlgebra R X)
 #align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoid
 
-/- warning: free_algebra.rank_eq -> FreeAlgebra.rank_eq is a dubious translation:
-lean 3 declaration is
-  forall {K : Type.{u1}} {X : Type.{max u1 u2}} [_inst_1 : Field.{u1} K], Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonUnitalNonAssocRing.toAddCommGroup.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.ring.{max u1 u2, u1} X K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))))) (Algebra.toModule.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (FreeAlgebra.semiring.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.algebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X))) (Cardinal.mk.{max u1 u2} (List.{max u1 u2} X))
-but is expected to have type
-  forall {K : Type.{u1}} {X : Type.{max u1 u2}} [_inst_1 : Field.{u1} K], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{max u1 u2, u1} X K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))))) (Algebra.toModule.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (FreeAlgebra.instSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X))) (Cardinal.mk.{max u1 u2} (List.{max u1 u2} X))
-Case conversion may be inaccurate. Consider using '#align free_algebra.rank_eq FreeAlgebra.rank_eqₓ'. -/
 -- TODO: generalize to `X : Type v`
 theorem rank_eq {K : Type u} {X : Type max u v} [Field K] :
     Module.rank K (FreeAlgebra K X) = Cardinal.mk (List X) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -47,7 +47,7 @@ noncomputable def basisFreeMonoid (R : Type u) (X : Type v) [CommRing R] :
 lean 3 declaration is
   forall {K : Type.{u1}} {X : Type.{max u1 u2}} [_inst_1 : Field.{u1} K], Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonUnitalNonAssocRing.toAddCommGroup.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.ring.{max u1 u2, u1} X K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))))) (Algebra.toModule.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (FreeAlgebra.semiring.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.algebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X))) (Cardinal.mk.{max u1 u2} (List.{max u1 u2} X))
 but is expected to have type
-  forall {K : Type.{u1}} {X : Type.{max u1 u2}} [_inst_1 : Field.{u1} K], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{max u1 u2, u1} X K (Field.toCommRing.{u1} K _inst_1)))))) (Algebra.toModule.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (FreeAlgebra.instSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X))) (Cardinal.mk.{max u1 u2} (List.{max u1 u2} X))
+  forall {K : Type.{u1}} {X : Type.{max u1 u2}} [_inst_1 : Field.{u1} K], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{max u1 u2, u1} X K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))))) (Algebra.toModule.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (FreeAlgebra.instSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X))) (Cardinal.mk.{max u1 u2} (List.{max u1 u2} X))
 Case conversion may be inaccurate. Consider using '#align free_algebra.rank_eq FreeAlgebra.rank_eqₓ'. -/
 -- TODO: generalize to `X : Type v`
 theorem rank_eq {K : Type u} {X : Type max u v} [Field K] :

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

@@ -32,7 +32,7 @@ namespace FreeAlgebra
 lean 3 declaration is
   forall (R : Type.{u1}) (X : Type.{u2}) [_inst_1 : CommRing.{u1} R], Basis.{u2, u1, max u1 u2} (FreeMonoid.{u2} X) R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonUnitalNonAssocRing.toAddCommGroup.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.ring.{u2, u1} X R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommRing.toCommSemiring.{u1} R _inst_1) (FreeAlgebra.semiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.algebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X))
 but is expected to have type
-  forall (R : Type.{u1}) (X : Type.{u2}) [_inst_1 : CommRing.{u1} R], Basis.{u2, u1, max u2 u1} (FreeMonoid.{u2} X) R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{u2, u1} X R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommRing.toCommSemiring.{u1} R _inst_1) (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X))
+  forall (R : Type.{u1}) (X : Type.{u2}) [_inst_1 : CommRing.{u1} R], Basis.{u2, u1, max u2 u1} (FreeMonoid.{u2} X) R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{u2, u1} X R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommRing.toCommSemiring.{u1} R _inst_1) (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X))
 Case conversion may be inaccurate. Consider using '#align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoidₓ'. -/
 /-- The `free_monoid X` basis on the `free_algebra R X`,
 mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * xₙ` -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

@@ -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.free_algebra
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
+! leanprover-community/mathlib commit 814d76e2247d5ba8bc024843552da1278bfe9e5c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.LinearAlgebra.FinsuppVectorSpace
 /-!
 # Linear algebra properties of `free_algebra R X`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file provides a `free_monoid X` basis on the `free_algebra R X`, and uses it to show the
 dimension of the algebra is the cardinality of `list X`
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/c9236f47f5b9df573443aa499c0d3968769628b7

@@ -25,6 +25,12 @@ universe u v
 
 namespace FreeAlgebra
 
+/- warning: free_algebra.basis_free_monoid -> FreeAlgebra.basisFreeMonoid is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u1}) (X : Type.{u2}) [_inst_1 : CommRing.{u1} R], Basis.{u2, u1, max u1 u2} (FreeMonoid.{u2} X) R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (AddCommGroup.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonUnitalNonAssocRing.toAddCommGroup.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.ring.{u2, u1} X R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommRing.toCommSemiring.{u1} R _inst_1) (FreeAlgebra.semiring.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.algebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X))
+but is expected to have type
+  forall (R : Type.{u1}) (X : Type.{u2}) [_inst_1 : CommRing.{u1} R], Basis.{u2, u1, max u2 u1} (FreeMonoid.{u2} X) R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R _inst_1)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{u2, u1} X R _inst_1))))) (Algebra.toModule.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (CommRing.toCommSemiring.{u1} R _inst_1) (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R (CommRing.toCommSemiring.{u1} R _inst_1) X))
+Case conversion may be inaccurate. Consider using '#align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoidₓ'. -/
 /-- The `free_monoid X` basis on the `free_algebra R X`,
 mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * xₙ` -/
 @[simps]
@@ -34,6 +40,12 @@ noncomputable def basisFreeMonoid (R : Type u) (X : Type v) [CommRing R] :
     (equivMonoidAlgebraFreeMonoid.symm.toLinearEquiv : _ ≃ₗ[R] FreeAlgebra R X)
 #align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoid
 
+/- warning: free_algebra.rank_eq -> FreeAlgebra.rank_eq is a dubious translation:
+lean 3 declaration is
+  forall {K : Type.{u1}} {X : Type.{max u1 u2}} [_inst_1 : Field.{u1} K], Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toSemiring.{u1} K (DivisionRing.toRing.{u1} K (Field.toDivisionRing.{u1} K _inst_1))) (AddCommGroup.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonUnitalNonAssocRing.toAddCommGroup.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.ring.{max u1 u2, u1} X K (EuclideanDomain.toCommRing.{u1} K (Field.toEuclideanDomain.{u1} K _inst_1))))))) (Algebra.toModule.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (FreeAlgebra.semiring.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.algebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X))) (Cardinal.mk.{max u1 u2} (List.{max u1 u2} X))
+but is expected to have type
+  forall {K : Type.{u1}} {X : Type.{max u1 u2}} [_inst_1 : Field.{u1} K], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} (Module.rank.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (DivisionSemiring.toSemiring.{u1} K (Semifield.toDivisionSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1))) (NonUnitalNonAssocSemiring.toAddCommMonoid.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (NonAssocRing.toNonUnitalNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Ring.toNonAssocRing.{max u1 u2} (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instRingFreeAlgebraToCommSemiring.{max u1 u2, u1} X K (Field.toCommRing.{u1} K _inst_1)))))) (Algebra.toModule.{u1, max u1 u2} K (FreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) (FreeAlgebra.instSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, max u1 u2} K (Semifield.toCommSemiring.{u1} K (Field.toSemifield.{u1} K _inst_1)) X))) (Cardinal.mk.{max u1 u2} (List.{max u1 u2} X))
+Case conversion may be inaccurate. Consider using '#align free_algebra.rank_eq FreeAlgebra.rank_eqₓ'. -/
 -- TODO: generalize to `X : Type v`
 theorem rank_eq {K : Type u} {X : Type max u v} [Field K] :
     Module.rank K (FreeAlgebra K X) = Cardinal.mk (List X) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

@@ -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.free_algebra
-! leanprover-community/mathlib commit 59628387770d82eb6f6dd7b7107308aa2509ec95
+! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -35,10 +35,10 @@ noncomputable def basisFreeMonoid (R : Type u) (X : Type v) [CommRing R] :
 #align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoid
 
 -- TODO: generalize to `X : Type v`
-theorem dim_eq {K : Type u} {X : Type max u v} [Field K] :
+theorem rank_eq {K : Type u} {X : Type max u v} [Field K] :
     Module.rank K (FreeAlgebra K X) = Cardinal.mk (List X) :=
-  (Cardinal.lift_inj.mp (basisFreeMonoid K X).mk_eq_dim).symm
-#align free_algebra.dim_eq FreeAlgebra.dim_eq
+  (Cardinal.lift_inj.mp (basisFreeMonoid K X).mk_eq_rank).symm
+#align free_algebra.rank_eq FreeAlgebra.rank_eq
 
 end FreeAlgebra
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

@@ -4,12 +4,13 @@ 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.free_algebra
-! leanprover-community/mathlib commit cd3434749bf1f6a8155cb53b2705f08b74371f2a
+! leanprover-community/mathlib commit 59628387770d82eb6f6dd7b7107308aa2509ec95
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.LinearAlgebra.Basis
 import Mathbin.Algebra.FreeAlgebra
+import Mathbin.LinearAlgebra.Dimension
 import Mathbin.LinearAlgebra.FinsuppVectorSpace
 
 /-!

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

The files Mathlib.LinearAlgebra.FreeModule.Rank, Mathlib.LinearAlgebra.FreeModule.Finite.Rank, Mathlib.LinearAlgebra.Dimension and Mathlib.LinearAlgebra.Finrank were reorganized into a folder Mathlib.LinearAlgebra.Dimension, containing the following files

• Basic.lean: Contains the definition of Module.rank.
• Finrank.lean: Contains the definition of FiniteDimensional.finrank.
• StrongRankCondition.lean: Contains results about rank and finrank over rings satisfying strong rank condition
• Free.lean: Contains results about rank and finrank of free modules
• Finite.lean: Contains conditions or consequences for rank to be finite or zero
• Constructions.lean: Contains the calculation of the rank of various constructions.
• DivisionRing.lean: Contains results about rank and finrank of spaces over division rings.
• LinearMap.lean: Contains results about LinearMap.rank

API changes: IsNoetherian.rank_lt_aleph0 and FiniteDimensional.rank_lt_aleph0 are replaced with rank_lt_aleph0. Module.Free.finite_basis was renamed to Module.Finite.finite_basis. FiniteDimensional.finrank_eq_rank was renamed to finrank_eq_rank. rank_eq_cardinal_basis and rank_eq_cardinal_basis' were removed in favour of Basis.mk_eq_mk and Basis.mk_eq_mk''.

Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>

@@ -5,7 +5,6 @@ Authors: Eric Wieser
 -/
 import Mathlib.LinearAlgebra.Basis
 import Mathlib.Algebra.FreeAlgebra
-import Mathlib.LinearAlgebra.Dimension
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -43,7 +43,7 @@ end
 
 theorem rank_eq [CommRing R] [Nontrivial R] :
     Module.rank R (FreeAlgebra R X) = Cardinal.lift.{u} (Cardinal.mk (List X)) := by
-  rw [←(Basis.mk_eq_rank'.{_,_,_,u} (basisFreeMonoid R X)).trans (Cardinal.lift_id _),
+  rw [← (Basis.mk_eq_rank'.{_,_,_,u} (basisFreeMonoid R X)).trans (Cardinal.lift_id _),
     Cardinal.lift_umax'.{v,u}, FreeMonoid]
 #align free_algebra.rank_eq FreeAlgebra.rank_eq
 

The main result here is Basis.tensorAlgebra (b : Basis κ R M) : Basis (FreeMonoid κ) R (TensorAlgebra R M) from which everything else follows without much work.

@@ -7,6 +7,7 @@ import Mathlib.LinearAlgebra.Basis
 import Mathlib.Algebra.FreeAlgebra
 import Mathlib.LinearAlgebra.Dimension
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
+import Mathlib.LinearAlgebra.FreeModule.StrongRankCondition
 
 #align_import linear_algebra.free_algebra from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
 
@@ -22,21 +23,28 @@ universe u v
 
 namespace FreeAlgebra
 
+variable (R : Type u) (X : Type v)
+
+section
+variable [CommSemiring R]
+
 /-- The `FreeMonoid X` basis on the `FreeAlgebra R X`,
 mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * xₙ` -/
 -- @[simps]
-noncomputable def basisFreeMonoid (R : Type u) (X : Type v) [CommRing R] :
-    Basis (FreeMonoid X) R (FreeAlgebra R X) :=
+noncomputable def basisFreeMonoid : Basis (FreeMonoid X) R (FreeAlgebra R X) :=
   Finsupp.basisSingleOne.map (equivMonoidAlgebraFreeMonoid (R := R) (X := X)).symm.toLinearEquiv
 #align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoid
 
--- TODO: generalize to `X : Type v`
-theorem rank_eq {K : Type u} {X : Type max u v} [Field K] :
-    Module.rank K (FreeAlgebra K X) = Cardinal.mk (List X) :=
-  -- Porting note: the type class inference was no longer automatic.
-  -- was: (Cardinal.lift_inj.mp (basisFreeMonoid K X).mk_eq_rank).symm
-  Cardinal.lift_inj.mp (@Basis.mk_eq_rank _ _ _ _ _ _ (inferInstance : Module K (FreeAlgebra K X))
-  (basisFreeMonoid K X)).symm
+instance : Module.Free R (FreeAlgebra R X) :=
+  have : Module.Free R (MonoidAlgebra R (FreeMonoid X)) := Module.Free.finsupp _ _ _
+  Module.Free.of_equiv (equivMonoidAlgebraFreeMonoid (R := R) (X := X)).symm.toLinearEquiv
+
+end
+
+theorem rank_eq [CommRing R] [Nontrivial R] :
+    Module.rank R (FreeAlgebra R X) = Cardinal.lift.{u} (Cardinal.mk (List X)) := by
+  rw [←(Basis.mk_eq_rank'.{_,_,_,u} (basisFreeMonoid R X)).trans (Cardinal.lift_id _),
+    Cardinal.lift_umax'.{v,u}, FreeMonoid]
 #align free_algebra.rank_eq FreeAlgebra.rank_eq
 
 end FreeAlgebra

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 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.free_algebra
-! leanprover-community/mathlib commit 039a089d2a4b93c761b234f3e5f5aeb752bac60f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.LinearAlgebra.Basis
 import Mathlib.Algebra.FreeAlgebra
 import Mathlib.LinearAlgebra.Dimension
 import Mathlib.LinearAlgebra.FinsuppVectorSpace
 
+#align_import linear_algebra.free_algebra from "leanprover-community/mathlib"@"039a089d2a4b93c761b234f3e5f5aeb752bac60f"
+
 /-!
 # Linear algebra properties of `FreeAlgebra R X`
 

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -25,7 +25,6 @@ universe u v
 
 namespace FreeAlgebra
 
-set_option synthInstance.etaExperiment true in
 /-- The `FreeMonoid X` basis on the `FreeAlgebra R X`,
 mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * xₙ` -/
 -- @[simps]

This is to fix timeouts in https://github.com/leanprover-community/mathlib4/pull/3552.

See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/!4.233552.20.28LinearAlgebra.2EMatrix.2EToLin.29.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -25,6 +25,7 @@ universe u v
 
 namespace FreeAlgebra
 
+set_option synthInstance.etaExperiment true in
 /-- The `FreeMonoid X` basis on the `FreeAlgebra R X`,
 mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * xₙ` -/
 -- @[simps]

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -31,7 +31,6 @@ mapping `[x₁, x₂, ..., xₙ]` to the "monomial" `1 • x₁ * x₂ * ⋯ * x
 noncomputable def basisFreeMonoid (R : Type u) (X : Type v) [CommRing R] :
     Basis (FreeMonoid X) R (FreeAlgebra R X) :=
   Finsupp.basisSingleOne.map (equivMonoidAlgebraFreeMonoid (R := R) (X := X)).symm.toLinearEquiv
-
 #align free_algebra.basis_free_monoid FreeAlgebra.basisFreeMonoid
 
 -- TODO: generalize to `X : Type v`