algebra.star.freeMathlib.Algebra.Star.Free

This file has been ported!

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2020 Eric Weiser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Weiser
 -/
-import Mathbin.Algebra.Star.Basic
-import Mathbin.Algebra.FreeAlgebra
+import Algebra.Star.Basic
+import Algebra.FreeAlgebra
 
 #align_import algebra.star.free from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
 
Diff
@@ -26,8 +26,7 @@ namespace FreeMonoid
 
 variable {α : Type _}
 
-instance : StarSemigroup (FreeMonoid α)
-    where
+instance : StarMul (FreeMonoid α) where
   unit := List.reverse
   star_involutive := List.reverse_reverse
   star_hMul := List.reverse_append
Diff
@@ -30,7 +30,7 @@ instance : StarSemigroup (FreeMonoid α)
     where
   unit := List.reverse
   star_involutive := List.reverse_reverse
-  star_mul := List.reverse_append
+  star_hMul := List.reverse_append
 
 #print FreeMonoid.star_of /-
 @[simp]
@@ -65,7 +65,7 @@ instance : StarRing (FreeAlgebra R X)
     · intros; simp only [lift_ι_apply, MulOpposite.unop_op]
     · intros; simp only [*, map_mul, MulOpposite.unop_mul]
     · intros; simp only [*, map_add, MulOpposite.unop_add]
-  star_mul a b := by simp only [Function.comp_apply, map_mul, MulOpposite.unop_mul]
+  star_hMul a b := by simp only [Function.comp_apply, map_mul, MulOpposite.unop_mul]
   star_add a b := by simp only [Function.comp_apply, map_add, MulOpposite.unop_add]
 
 #print FreeAlgebra.star_ι /-
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2020 Eric Weiser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Weiser
-
-! This file was ported from Lean 3 source module algebra.star.free
-! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Star.Basic
 import Mathbin.Algebra.FreeAlgebra
 
+#align_import algebra.star.free from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
+
 /-!
 # A *-algebra structure on the free algebra.
 
Diff
@@ -35,16 +35,20 @@ instance : StarSemigroup (FreeMonoid α)
   star_involutive := List.reverse_reverse
   star_mul := List.reverse_append
 
+#print FreeMonoid.star_of /-
 @[simp]
 theorem star_of (x : α) : star (of x) = of x :=
   rfl
 #align free_monoid.star_of FreeMonoid.star_of
+-/
 
+#print FreeMonoid.star_one /-
 /-- Note that `star_one` is already a global simp lemma, but this one works with dsimp too -/
 @[simp]
 theorem star_one : star (1 : FreeMonoid α) = 1 :=
   rfl
 #align free_monoid.star_one FreeMonoid.star_one
+-/
 
 end FreeMonoid
 
@@ -67,19 +71,25 @@ instance : StarRing (FreeAlgebra R X)
   star_mul a b := by simp only [Function.comp_apply, map_mul, MulOpposite.unop_mul]
   star_add a b := by simp only [Function.comp_apply, map_add, MulOpposite.unop_add]
 
+#print FreeAlgebra.star_ι /-
 @[simp]
 theorem star_ι (x : X) : star (ι R x) = ι R x := by simp [star, Star.star]
 #align free_algebra.star_ι FreeAlgebra.star_ι
+-/
 
+#print FreeAlgebra.star_algebraMap /-
 @[simp]
 theorem star_algebraMap (r : R) : star (algebraMap R (FreeAlgebra R X) r) = algebraMap R _ r := by
   simp [star, Star.star]
 #align free_algebra.star_algebra_map FreeAlgebra.star_algebraMap
+-/
 
+#print FreeAlgebra.starHom /-
 /-- `star` as an `alg_equiv` -/
 def starHom : FreeAlgebra R X ≃ₐ[R] (FreeAlgebra R X)ᵐᵒᵖ :=
   { starRingEquiv with commutes' := fun r => by simp [star_algebra_map] }
 #align free_algebra.star_hom FreeAlgebra.starHom
+-/
 
 end FreeAlgebra
 
Diff
@@ -60,10 +60,10 @@ instance : StarRing (FreeAlgebra R X)
     unfold Star.star
     simp only [Function.comp_apply]
     refine' FreeAlgebra.induction R X _ _ _ _ x
-    · intros ; simp only [AlgHom.commutes, MulOpposite.algebraMap_apply, MulOpposite.unop_op]
-    · intros ; simp only [lift_ι_apply, MulOpposite.unop_op]
-    · intros ; simp only [*, map_mul, MulOpposite.unop_mul]
-    · intros ; simp only [*, map_add, MulOpposite.unop_add]
+    · intros; simp only [AlgHom.commutes, MulOpposite.algebraMap_apply, MulOpposite.unop_op]
+    · intros; simp only [lift_ι_apply, MulOpposite.unop_op]
+    · intros; simp only [*, map_mul, MulOpposite.unop_mul]
+    · intros; simp only [*, map_add, MulOpposite.unop_add]
   star_mul a b := by simp only [Function.comp_apply, map_mul, MulOpposite.unop_mul]
   star_add a b := by simp only [Function.comp_apply, map_add, MulOpposite.unop_add]
 
Diff
@@ -35,23 +35,11 @@ instance : StarSemigroup (FreeMonoid α)
   star_involutive := List.reverse_reverse
   star_mul := List.reverse_append
 
-/- warning: free_monoid.star_of -> FreeMonoid.star_of is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (x : α), Eq.{succ u1} (FreeMonoid.{u1} α) (Star.star.{u1} (FreeMonoid.{u1} α) (InvolutiveStar.toHasStar.{u1} (FreeMonoid.{u1} α) (StarSemigroup.toHasInvolutiveStar.{u1} (FreeMonoid.{u1} α) (Monoid.toSemigroup.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (FreeMonoid.starSemigroup.{u1} α))) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u1} α x)
-but is expected to have type
-  forall {α : Type.{u1}} (x : α), Eq.{succ u1} (FreeMonoid.{u1} α) (Star.star.{u1} (FreeMonoid.{u1} α) (InvolutiveStar.toStar.{u1} (FreeMonoid.{u1} α) (StarSemigroup.toInvolutiveStar.{u1} (FreeMonoid.{u1} α) (Monoid.toSemigroup.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (FreeMonoid.instStarSemigroupFreeMonoidToSemigroupToMonoidToRightCancelMonoidInstCancelMonoidFreeMonoid.{u1} α))) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u1} α x)
-Case conversion may be inaccurate. Consider using '#align free_monoid.star_of FreeMonoid.star_ofₓ'. -/
 @[simp]
 theorem star_of (x : α) : star (of x) = of x :=
   rfl
 #align free_monoid.star_of FreeMonoid.star_of
 
-/- warning: free_monoid.star_one -> FreeMonoid.star_one is a dubious translation:
-lean 3 declaration is
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 /-- Note that `star_one` is already a global simp lemma, but this one works with dsimp too -/
 @[simp]
 theorem star_one : star (1 : FreeMonoid α) = 1 :=
@@ -79,30 +67,15 @@ instance : StarRing (FreeAlgebra R X)
   star_mul a b := by simp only [Function.comp_apply, map_mul, MulOpposite.unop_mul]
   star_add a b := by simp only [Function.comp_apply, map_add, MulOpposite.unop_add]
 
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 @[simp]
 theorem star_ι (x : X) : star (ι R x) = ι R x := by simp [star, Star.star]
 #align free_algebra.star_ι FreeAlgebra.star_ι
 
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 @[simp]
 theorem star_algebraMap (r : R) : star (algebraMap R (FreeAlgebra R X) r) = algebraMap R _ r := by
   simp [star, Star.star]
 #align free_algebra.star_algebra_map FreeAlgebra.star_algebraMap
 
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 /-- `star` as an `alg_equiv` -/
 def starHom : FreeAlgebra R X ≃ₐ[R] (FreeAlgebra R X)ᵐᵒᵖ :=
   { starRingEquiv with commutes' := fun r => by simp [star_algebra_map] }
Diff
@@ -72,14 +72,10 @@ instance : StarRing (FreeAlgebra R X)
     unfold Star.star
     simp only [Function.comp_apply]
     refine' FreeAlgebra.induction R X _ _ _ _ x
-    · intros
-      simp only [AlgHom.commutes, MulOpposite.algebraMap_apply, MulOpposite.unop_op]
-    · intros
-      simp only [lift_ι_apply, MulOpposite.unop_op]
-    · intros
-      simp only [*, map_mul, MulOpposite.unop_mul]
-    · intros
-      simp only [*, map_add, MulOpposite.unop_add]
+    · intros ; simp only [AlgHom.commutes, MulOpposite.algebraMap_apply, MulOpposite.unop_op]
+    · intros ; simp only [lift_ι_apply, MulOpposite.unop_op]
+    · intros ; simp only [*, map_mul, MulOpposite.unop_mul]
+    · intros ; simp only [*, map_add, MulOpposite.unop_add]
   star_mul a b := by simp only [Function.comp_apply, map_mul, MulOpposite.unop_mul]
   star_add a b := by simp only [Function.comp_apply, map_add, MulOpposite.unop_add]
 
Diff
@@ -94,10 +94,7 @@ theorem star_ι (x : X) : star (ι R x) = ι R x := by simp [star, Star.star]
 #align free_algebra.star_ι FreeAlgebra.star_ι
 
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(Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))))) (algebraMap.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) r)
+<too large>
 Case conversion may be inaccurate. Consider using '#align free_algebra.star_algebra_map FreeAlgebra.star_algebraMapₓ'. -/
 @[simp]
 theorem star_algebraMap (r : R) : star (algebraMap R (FreeAlgebra R X) r) = algebraMap R _ r := by
Diff
@@ -97,7 +97,7 @@ theorem star_ι (x : X) : star (ι R x) = ι R x := by simp [star, Star.star]
 lean 3 declaration is
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 but is expected to have type
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_inst_1 X) r) (Semiring.toNonAssocSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))))) (StarRing.toStarAddMonoid.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (Semiring.toNonUnitalSemiring.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) (FreeAlgebra.instStarRingFreeAlgebraToNonUnitalSemiringInstSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))) (FunLike.coe.{max (succ u2) (succ u1), succ u2, max (succ u2) (succ u1)} (RingHom.{u2, max u1 u2} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (fun 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u1, u2, max u2 u1} (RingHom.{u2, max u1 u2} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u1 u2} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) 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u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))))) (algebraMap.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) r)
+  forall {R : Type.{u2}} [_inst_1 : CommSemiring.{u2} R] {X : Type.{u1}} (r : R), Eq.{max (succ u2) (succ u1)} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (Star.star.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (InvolutiveStar.toStar.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (StarAddMonoid.toInvolutiveStar.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (AddMonoidWithOne.toAddMonoid.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (AddCommMonoidWithOne.toAddMonoidWithOne.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) r) (NonAssocSemiring.toAddCommMonoidWithOne.{max u2 u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R 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(_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u1 u2} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u1 u2} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u1 u2} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u1 u2} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))))) (algebraMap.{u2, max u1 u2} R (FreeAlgebra.{u2, u1} R _inst_1 X) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) r)) (FunLike.coe.{max (succ u2) (succ (max u2 u1)), succ u2, succ (max u2 u1)} (RingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => FreeAlgebra.{u2, u1} R _inst_1 X) _x) (MulHomClass.toFunLike.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (NonUnitalNonAssocSemiring.toMul.{u2} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)))) (NonUnitalNonAssocSemiring.toMul.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))) (NonUnitalRingHomClass.toMulHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u2} R (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) (RingHomClass.toNonUnitalRingHomClass.{max u2 u1, u2, max u2 u1} (RingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X))) R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) (RingHom.instRingHomClassRingHom.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) (Semiring.toNonAssocSemiring.{u2} R (CommSemiring.toSemiring.{u2} R _inst_1)) (Semiring.toNonAssocSemiring.{max u2 u1} (FreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X)))))) (algebraMap.{u2, max u2 u1} R (FreeAlgebra.{u2, u1} R _inst_1 X) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u2, u1} R _inst_1 X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u2, u1} R _inst_1 X)) r)
 Case conversion may be inaccurate. Consider using '#align free_algebra.star_algebra_map FreeAlgebra.star_algebraMapₓ'. -/
 @[simp]
 theorem star_algebraMap (r : R) : star (algebraMap R (FreeAlgebra R X) r) = algebraMap R _ r := by
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Weiser
 
 ! This file was ported from Lean 3 source module algebra.star.free
-! leanprover-community/mathlib commit 07c3cf2d851866ff7198219ed3fedf42e901f25c
+! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.FreeAlgebra
 /-!
 # A *-algebra structure on the free algebra.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Reversing words gives a *-structure on the free monoid or on the free algebra on a type.
 
 ## Implementation note
Diff
@@ -105,7 +105,7 @@ theorem star_algebraMap (r : R) : star (algebraMap R (FreeAlgebra R X) r) = alge
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {X : Type.{u2}}, AlgEquiv.{u1, max u1 u2, max u1 u2} R (FreeAlgebra.{u1, u2} R _inst_1 X) (MulOpposite.{max u1 u2} (FreeAlgebra.{u1, u2} R _inst_1 X)) _inst_1 (FreeAlgebra.semiring.{u1, u2} R _inst_1 X) (MulOpposite.semiring.{max u1 u2} (FreeAlgebra.{u1, u2} R _inst_1 X) (FreeAlgebra.semiring.{u1, u2} R _inst_1 X)) (FreeAlgebra.algebra.{u1, u2} R _inst_1 X) (MulOpposite.algebra.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R _inst_1 X) _inst_1 (FreeAlgebra.semiring.{u1, u2} R _inst_1 X) (FreeAlgebra.algebra.{u1, u2} R _inst_1 X))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {X : Type.{u2}}, AlgEquiv.{u1, max u2 u1, max u2 u1} R (FreeAlgebra.{u1, u2} R _inst_1 X) (MulOpposite.{max u2 u1} (FreeAlgebra.{u1, u2} R _inst_1 X)) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R _inst_1 X) (MulOpposite.instSemiringMulOpposite.{max u1 u2} (FreeAlgebra.{u1, u2} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R _inst_1 X)) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R _inst_1 X) (MulOpposite.instAlgebraMulOppositeInstSemiringMulOpposite.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R _inst_1 X) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R _inst_1 X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R _inst_1 X))
+  forall {R : Type.{u1}} [_inst_1 : CommSemiring.{u1} R] {X : Type.{u2}}, AlgEquiv.{u1, max u2 u1, max u2 u1} R (FreeAlgebra.{u1, u2} R _inst_1 X) (MulOpposite.{max u2 u1} (FreeAlgebra.{u1, u2} R _inst_1 X)) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R _inst_1 X) (MulOpposite.semiring.{max u1 u2} (FreeAlgebra.{u1, u2} R _inst_1 X) (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R _inst_1 X)) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R _inst_1 X) (MulOpposite.instAlgebraMulOppositeSemiring.{u1, max u1 u2} R (FreeAlgebra.{u1, u2} R _inst_1 X) _inst_1 (FreeAlgebra.instSemiringFreeAlgebra.{u1, u2} R _inst_1 X) (FreeAlgebra.instAlgebraFreeAlgebraInstSemiringFreeAlgebra.{u1, u2} R _inst_1 X))
 Case conversion may be inaccurate. Consider using '#align free_algebra.star_hom FreeAlgebra.starHomₓ'. -/
 /-- `star` as an `alg_equiv` -/
 def starHom : FreeAlgebra R X ≃ₐ[R] (FreeAlgebra R X)ᵐᵒᵖ :=
Diff
@@ -32,11 +32,23 @@ instance : StarSemigroup (FreeMonoid α)
   star_involutive := List.reverse_reverse
   star_mul := List.reverse_append
 
+/- warning: free_monoid.star_of -> FreeMonoid.star_of is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (x : α), Eq.{succ u1} (FreeMonoid.{u1} α) (Star.star.{u1} (FreeMonoid.{u1} α) (InvolutiveStar.toHasStar.{u1} (FreeMonoid.{u1} α) (StarSemigroup.toHasInvolutiveStar.{u1} (FreeMonoid.{u1} α) (Monoid.toSemigroup.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (FreeMonoid.starSemigroup.{u1} α))) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u1} α x)
+but is expected to have type
+  forall {α : Type.{u1}} (x : α), Eq.{succ u1} (FreeMonoid.{u1} α) (Star.star.{u1} (FreeMonoid.{u1} α) (InvolutiveStar.toStar.{u1} (FreeMonoid.{u1} α) (StarSemigroup.toInvolutiveStar.{u1} (FreeMonoid.{u1} α) (Monoid.toSemigroup.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (FreeMonoid.instStarSemigroupFreeMonoidToSemigroupToMonoidToRightCancelMonoidInstCancelMonoidFreeMonoid.{u1} α))) (FreeMonoid.of.{u1} α x)) (FreeMonoid.of.{u1} α x)
+Case conversion may be inaccurate. Consider using '#align free_monoid.star_of FreeMonoid.star_ofₓ'. -/
 @[simp]
 theorem star_of (x : α) : star (of x) = of x :=
   rfl
 #align free_monoid.star_of FreeMonoid.star_of
 
+/- warning: free_monoid.star_one -> FreeMonoid.star_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}}, Eq.{succ u1} (FreeMonoid.{u1} α) (Star.star.{u1} (FreeMonoid.{u1} α) (InvolutiveStar.toHasStar.{u1} (FreeMonoid.{u1} α) (StarSemigroup.toHasInvolutiveStar.{u1} (FreeMonoid.{u1} α) (Monoid.toSemigroup.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α)))) (FreeMonoid.starSemigroup.{u1} α))) (OfNat.ofNat.{u1} (FreeMonoid.{u1} α) 1 (OfNat.mk.{u1} (FreeMonoid.{u1} α) 1 (One.one.{u1} (FreeMonoid.{u1} α) (MulOneClass.toHasOne.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α))))))))) (OfNat.ofNat.{u1} (FreeMonoid.{u1} α) 1 (OfNat.mk.{u1} (FreeMonoid.{u1} α) 1 (One.one.{u1} (FreeMonoid.{u1} α) (MulOneClass.toHasOne.{u1} (FreeMonoid.{u1} α) (Monoid.toMulOneClass.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.cancelMonoid.{u1} α))))))))
+but is expected to have type
+  forall {α : Type.{u1}}, Eq.{succ u1} (FreeMonoid.{u1} α) (Star.star.{u1} (FreeMonoid.{u1} α) (InvolutiveStar.toStar.{u1} (FreeMonoid.{u1} α) (StarSemigroup.toInvolutiveStar.{u1} (FreeMonoid.{u1} α) (Monoid.toSemigroup.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toMonoid.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))) (FreeMonoid.instStarSemigroupFreeMonoidToSemigroupToMonoidToRightCancelMonoidInstCancelMonoidFreeMonoid.{u1} α))) (OfNat.ofNat.{u1} (FreeMonoid.{u1} α) 1 (One.toOfNat1.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toOne.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))))) (OfNat.ofNat.{u1} (FreeMonoid.{u1} α) 1 (One.toOfNat1.{u1} (FreeMonoid.{u1} α) (RightCancelMonoid.toOne.{u1} (FreeMonoid.{u1} α) (CancelMonoid.toRightCancelMonoid.{u1} (FreeMonoid.{u1} α) (FreeMonoid.instCancelMonoidFreeMonoid.{u1} α)))))
+Case conversion may be inaccurate. Consider using '#align free_monoid.star_one FreeMonoid.star_oneₓ'. -/
 /-- Note that `star_one` is already a global simp lemma, but this one works with dsimp too -/
 @[simp]
 theorem star_one : star (1 : FreeMonoid α) = 1 :=
@@ -68,15 +80,33 @@ instance : StarRing (FreeAlgebra R X)
   star_mul a b := by simp only [Function.comp_apply, map_mul, MulOpposite.unop_mul]
   star_add a b := by simp only [Function.comp_apply, map_add, MulOpposite.unop_add]
 
+/- warning: free_algebra.star_ι -> FreeAlgebra.star_ι is a dubious translation:
+lean 3 declaration is
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 @[simp]
 theorem star_ι (x : X) : star (ι R x) = ι R x := by simp [star, Star.star]
 #align free_algebra.star_ι FreeAlgebra.star_ι
 
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+Case conversion may be inaccurate. Consider using '#align free_algebra.star_algebra_map FreeAlgebra.star_algebraMapₓ'. -/
 @[simp]
 theorem star_algebraMap (r : R) : star (algebraMap R (FreeAlgebra R X) r) = algebraMap R _ r := by
   simp [star, Star.star]
 #align free_algebra.star_algebra_map FreeAlgebra.star_algebraMap
 
+/- warning: free_algebra.star_hom -> FreeAlgebra.starHom is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align free_algebra.star_hom FreeAlgebra.starHomₓ'. -/
 /-- `star` as an `alg_equiv` -/
 def starHom : FreeAlgebra R X ≃ₐ[R] (FreeAlgebra R X)ᵐᵒᵖ :=
   { starRingEquiv with commutes' := fun r => by simp [star_algebra_map] }

Changes in mathlib4

mathlib3
mathlib4
chore: classify dsimp cannot prove this porting notes (#10676)

Classifies by adding issue number (#10675) to porting notes claiming dsimp cannot prove this.

Diff
@@ -34,7 +34,7 @@ theorem star_of (x : α) : star (of x) = of x :=
 #align free_monoid.star_of FreeMonoid.star_of
 
 /-- Note that `star_one` is already a global simp lemma, but this one works with dsimp too -/
-@[simp, nolint simpNF] -- Porting note: dsimp cannot prove this
+@[simp, nolint simpNF] -- Porting note (#10675): dsimp cannot prove this
 theorem star_one : star (1 : FreeMonoid α) = 1 :=
   rfl
 #align free_monoid.star_one FreeMonoid.star_one
refactor(Algebra/Star/*): Allow for star operation on non-associative algebras (#6562)

Typically a * operation on a mathematical structure R equipped with a multiplication is an involutive anti-automorphism i.e.

∀ r s : R, star (r * s) = star s * star r

Currently mathlib defines a class StarSemigroup to be a semigroup satisfying this property. However, the requirement for the multiplication to be associative is unnecessarily restrictive. There are important classes of star-algebra which are not associative (e.g. JB*-algebras).

This PR removes the requirement for a StarSemigroup to be a semigroup, merely requiring it to have a multiplication.

I've changed the name from StarSemigroup to StarMul since it's no longer a semigroup.

Zulip discussion

Previously opened as a mathlib PR https://github.com/leanprover-community/mathlib/pull/17949

Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

Diff
@@ -23,7 +23,7 @@ namespace FreeMonoid
 
 variable {α : Type*}
 
-instance : StarSemigroup (FreeMonoid α) where
+instance : StarMul (FreeMonoid α) where
   star := List.reverse
   star_involutive := List.reverse_reverse
   star_mul := List.reverse_append
chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

Diff
@@ -21,7 +21,7 @@ to avoid importing `Algebra.Star.Basic` into the entire hierarchy.
 
 namespace FreeMonoid
 
-variable {α : Type _}
+variable {α : Type*}
 
 instance : StarSemigroup (FreeMonoid α) where
   star := List.reverse
@@ -43,7 +43,7 @@ end FreeMonoid
 
 namespace FreeAlgebra
 
-variable {R : Type _} [CommSemiring R] {X : Type _}
+variable {R : Type*} [CommSemiring R] {X : Type*}
 
 /-- The star ring formed by reversing the elements of products -/
 instance : StarRing (FreeAlgebra R X) where
chore: script to replace headers with #align_import statements (#5979)

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

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2020 Eric Wieser. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Wieser
-
-! This file was ported from Lean 3 source module algebra.star.free
-! leanprover-community/mathlib commit 07c3cf2d851866ff7198219ed3fedf42e901f25c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Star.Basic
 import Mathlib.Algebra.FreeAlgebra
 
+#align_import algebra.star.free from "leanprover-community/mathlib"@"07c3cf2d851866ff7198219ed3fedf42e901f25c"
+
 /-!
 # A *-algebra structure on the free algebra.
 
feat: port Algebra.Star.Free (#3007)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

Dependencies 8 + 456

457 files ported (98.3%)
189643 lines ported (98.4%)
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The unported dependencies are