algebra.star.pi | Mathlib porting status

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

9abfa6f0

(last sync)

refactor(linear_algebra/matrix/hermitian): golf and generalize (#18565)

A handful of these results can be proven trivially using results about is_self_adjoint. This also generalizes the typeclass arguments throughout the file, though largely in a mathematically meaningless way.

Diff

@@ -29,6 +29,9 @@ instance [Π i, has_star (f i)] : has_star (Π i, f i) :=
 
 lemma star_def [Π i, has_star (f i)] (x : Π i, f i) : star x = λ i, star (x i) := rfl
 
+instance [Π i, has_star (f i)] [∀ i, has_trivial_star (f i)] : has_trivial_star (Π i, f i) :=
+{ star_trivial  := λ _, funext $ λ _, star_trivial _ }
+
 instance [Π i, has_involutive_star (f i)] : has_involutive_star (Π i, f i) :=
 { star_involutive := λ _, funext $ λ _, star_star _ }

247a102b

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

9abfa6f0

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ 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.Algebra.Star.Basic
-import Mathbin.Algebra.Ring.Pi
+import Algebra.Star.Basic
+import Algebra.Ring.Pi
 
 #align_import algebra.star.pi from "leanprover-community/mathlib"@"9abfa6f0727d5adc99067e325e15d1a9de17fd8e"

9abfa6f0

bump to nightly-2023-09-02-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

a4ca67cb

Diff

@@ -50,14 +50,14 @@ instance [∀ i, Star (f i)] [∀ i, TrivialStar (f i)] : TrivialStar (∀ i, f
 instance [∀ i, InvolutiveStar (f i)] : InvolutiveStar (∀ i, f i)
     where star_involutive _ := funext fun _ => star_star _
 
-instance [∀ i, Semigroup (f i)] [∀ i, StarSemigroup (f i)] : StarSemigroup (∀ i, f i)
+instance [∀ i, Semigroup (f i)] [∀ i, StarMul (f i)] : StarMul (∀ i, f i)
     where star_hMul _ _ := funext fun _ => star_hMul _ _
 
 instance [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] : StarAddMonoid (∀ i, f i)
     where star_add _ _ := funext fun _ => star_add _ _
 
 instance [∀ i, NonUnitalSemiring (f i)] [∀ i, StarRing (f i)] : StarRing (∀ i, f i) :=
-  { Pi.starAddMonoid, (Pi.starSemigroup : StarSemigroup (∀ i, f i)) with }
+  { Pi.starAddMonoid, (Pi.starSemigroup : StarMul (∀ i, f i)) with }
 
 instance {R : Type w} [∀ i, SMul R (f i)] [Star R] [∀ i, Star (f i)] [∀ i, StarModule R (f i)] :
     StarModule R (∀ i, f i) where star_smul r x := funext fun i => star_smul r (x i)

9abfa6f0

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -51,7 +51,7 @@ instance [∀ i, InvolutiveStar (f i)] : InvolutiveStar (∀ i, f i)
     where star_involutive _ := funext fun _ => star_star _
 
 instance [∀ i, Semigroup (f i)] [∀ i, StarSemigroup (f i)] : StarSemigroup (∀ i, f i)
-    where star_mul _ _ := funext fun _ => star_mul _ _
+    where star_hMul _ _ := funext fun _ => star_hMul _ _
 
 instance [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] : StarAddMonoid (∀ i, f i)
     where star_add _ _ := funext fun _ => star_add _ _

9abfa6f0

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 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 algebra.star.pi
-! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
-! 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.Ring.Pi
 
+#align_import algebra.star.pi from "leanprover-community/mathlib"@"9abfa6f0727d5adc99067e325e15d1a9de17fd8e"
+
 /-!
 # `star` on pi types

9abfa6f0

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -65,10 +65,12 @@ instance [∀ i, NonUnitalSemiring (f i)] [∀ i, StarRing (f i)] : StarRing (
 instance {R : Type w} [∀ i, SMul R (f i)] [Star R] [∀ i, Star (f i)] [∀ i, StarModule R (f i)] :
     StarModule R (∀ i, f i) where star_smul r x := funext fun i => star_smul r (x i)
 
+#print Pi.single_star /-
 theorem single_star [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] [DecidableEq I] (i : I)
     (a : f i) : Pi.single i (star a) = star (Pi.single i a) :=
   single_op (fun i => @star (f i) _) (fun i => star_zero _) i a
 #align pi.single_star Pi.single_star
+-/
 
 end Pi
 
@@ -81,9 +83,11 @@ theorem update_star [∀ i, Star (f i)] [DecidableEq I] (h : ∀ i : I, f i) (i
 #align function.update_star Function.update_star
 -/
 
+#print Function.star_sum_elim /-
 theorem star_sum_elim {I J α : Type _} (x : I → α) (y : J → α) [Star α] :
     star (Sum.elim x y) = Sum.elim (star x) (star y) := by ext x; cases x <;> simp
 #align function.star_sum_elim Function.star_sum_elim
+-/
 
 end Function

9abfa6f0

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -65,12 +65,6 @@ instance [∀ i, NonUnitalSemiring (f i)] [∀ i, StarRing (f i)] : StarRing (
 instance {R : Type w} [∀ i, SMul R (f i)] [Star R] [∀ i, Star (f i)] [∀ i, StarModule R (f i)] :
     StarModule R (∀ i, f i) where star_smul r x := funext fun i => star_smul r (x i)
 
-/- warning: pi.single_star -> Pi.single_star is a dubious translation:
-lean 3 declaration is
-  forall {I : Type.{u1}} {f : I -> Type.{u2}} [_inst_1 : forall (i : I), AddMonoid.{u2} (f i)] [_inst_2 : forall (i : I), StarAddMonoid.{u2} (f i) (_inst_1 i)] [_inst_3 : DecidableEq.{succ u1} I] (i : I) (a : f i), Eq.{max (succ u1) (succ u2)} (forall (i : I), f i) (Pi.single.{u1, u2} I (fun (i : I) => f i) (fun (a : I) (b : I) => _inst_3 a b) (fun (i : I) => AddZeroClass.toHasZero.{u2} (f i) (AddMonoid.toAddZeroClass.{u2} (f i) (_inst_1 i))) i (Star.star.{u2} (f i) (InvolutiveStar.toHasStar.{u2} (f i) (StarAddMonoid.toHasInvolutiveStar.{u2} (f i) (_inst_1 i) (_inst_2 i))) a)) (Star.star.{max u1 u2} (forall (i : I), f i) (Pi.hasStar.{u1, u2} I (fun (i : I) => f i) (fun (i : I) => InvolutiveStar.toHasStar.{u2} (f i) (StarAddMonoid.toHasInvolutiveStar.{u2} (f i) (_inst_1 i) (_inst_2 i)))) (Pi.single.{u1, u2} I (fun (i : I) => f i) (fun (a : I) (b : I) => _inst_3 a b) (fun (i : I) => AddZeroClass.toHasZero.{u2} (f i) (AddMonoid.toAddZeroClass.{u2} (f i) (_inst_1 i))) i a))
-but is expected to have type
-  forall {I : Type.{u1}} {f : I -> Type.{u2}} [_inst_1 : forall (i : I), AddMonoid.{u2} (f i)] [_inst_2 : forall (i : I), StarAddMonoid.{u2} (f i) (_inst_1 i)] [_inst_3 : DecidableEq.{succ u1} I] (i : I) (a : f i), Eq.{max (succ u1) (succ u2)} (forall (i : I), f i) (Pi.single.{u1, u2} I f (fun (a : I) (b : I) => _inst_3 a b) (fun (i : I) => AddMonoid.toZero.{u2} (f i) (_inst_1 i)) i (Star.star.{u2} (f i) (InvolutiveStar.toStar.{u2} (f i) (StarAddMonoid.toInvolutiveStar.{u2} (f i) (_inst_1 i) (_inst_2 i))) a)) (Star.star.{max u2 u1} (forall (i : I), f i) (Pi.instStarForAll.{u1, u2} I (fun (i : I) => f i) (fun (i : I) => InvolutiveStar.toStar.{u2} (f i) (StarAddMonoid.toInvolutiveStar.{u2} (f i) (_inst_1 i) (_inst_2 i)))) (Pi.single.{u1, u2} I f (fun (a : I) (b : I) => _inst_3 a b) (fun (i : I) => AddMonoid.toZero.{u2} (f i) (_inst_1 i)) i a))
-Case conversion may be inaccurate. Consider using '#align pi.single_star Pi.single_starₓ'. -/
 theorem single_star [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] [DecidableEq I] (i : I)
     (a : f i) : Pi.single i (star a) = star (Pi.single i a) :=
   single_op (fun i => @star (f i) _) (fun i => star_zero _) i a
@@ -87,12 +81,6 @@ theorem update_star [∀ i, Star (f i)] [DecidableEq I] (h : ∀ i : I, f i) (i
 #align function.update_star Function.update_star
 -/
 
-/- warning: function.star_sum_elim -> Function.star_sum_elim is a dubious translation:
-lean 3 declaration is
-  forall {I : Type.{u1}} {J : Type.{u2}} {α : Type.{u3}} (x : I -> α) (y : J -> α) [_inst_1 : Star.{u3} α], Eq.{succ (max (max u1 u2) u3)} ((Sum.{u1, u2} I J) -> α) (Star.star.{max (max u1 u2) u3} ((Sum.{u1, u2} I J) -> α) (Pi.hasStar.{max u1 u2, u3} (Sum.{u1, u2} I J) (fun (ᾰ : Sum.{u1, u2} I J) => α) (fun (i : Sum.{u1, u2} I J) => _inst_1)) (Sum.elim.{u1, u2, succ u3} I J α x y)) (Sum.elim.{u1, u2, succ u3} I J α (Star.star.{max u1 u3} (I -> α) (Pi.hasStar.{u1, u3} I (fun (ᾰ : I) => α) (fun (i : I) => _inst_1)) x) (Star.star.{max u2 u3} (J -> α) (Pi.hasStar.{u2, u3} J (fun (ᾰ : J) => α) (fun (i : J) => _inst_1)) y))
-but is expected to have type
-  forall {I : Type.{u3}} {J : Type.{u2}} {α : Type.{u1}} (x : I -> α) (y : J -> α) [_inst_1 : Star.{u1} α], Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((Sum.{u3, u2} I J) -> α) (Star.star.{max (max u3 u2) u1} ((Sum.{u3, u2} I J) -> α) (Pi.instStarForAll.{max u3 u2, u1} (Sum.{u3, u2} I J) (fun (ᾰ : Sum.{u3, u2} I J) => α) (fun (i : Sum.{u3, u2} I J) => _inst_1)) (Sum.elim.{u3, u2, succ u1} I J α x y)) (Sum.elim.{u3, u2, succ u1} I J α (Star.star.{max u3 u1} (I -> α) (Pi.instStarForAll.{u3, u1} I (fun (ᾰ : I) => α) (fun (i : I) => _inst_1)) x) (Star.star.{max u1 u2} (J -> α) (Pi.instStarForAll.{u2, u1} J (fun (ᾰ : J) => α) (fun (i : J) => _inst_1)) y))
-Case conversion may be inaccurate. Consider using '#align function.star_sum_elim Function.star_sum_elimₓ'. -/
 theorem star_sum_elim {I J α : Type _} (x : I → α) (y : J → α) [Star α] :
     star (Sum.elim x y) = Sum.elim (star x) (star y) := by ext x; cases x <;> simp
 #align function.star_sum_elim Function.star_sum_elim

9abfa6f0

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -94,10 +94,7 @@ but is expected to have type
   forall {I : Type.{u3}} {J : Type.{u2}} {α : Type.{u1}} (x : I -> α) (y : J -> α) [_inst_1 : Star.{u1} α], Eq.{max (max (succ u3) (succ u2)) (succ u1)} ((Sum.{u3, u2} I J) -> α) (Star.star.{max (max u3 u2) u1} ((Sum.{u3, u2} I J) -> α) (Pi.instStarForAll.{max u3 u2, u1} (Sum.{u3, u2} I J) (fun (ᾰ : Sum.{u3, u2} I J) => α) (fun (i : Sum.{u3, u2} I J) => _inst_1)) (Sum.elim.{u3, u2, succ u1} I J α x y)) (Sum.elim.{u3, u2, succ u1} I J α (Star.star.{max u3 u1} (I -> α) (Pi.instStarForAll.{u3, u1} I (fun (ᾰ : I) => α) (fun (i : I) => _inst_1)) x) (Star.star.{max u1 u2} (J -> α) (Pi.instStarForAll.{u2, u1} J (fun (ᾰ : J) => α) (fun (i : J) => _inst_1)) y))
 Case conversion may be inaccurate. Consider using '#align function.star_sum_elim Function.star_sum_elimₓ'. -/
 theorem star_sum_elim {I J α : Type _} (x : I → α) (y : J → α) [Star α] :
-    star (Sum.elim x y) = Sum.elim (star x) (star y) :=
-  by
-  ext x
-  cases x <;> simp
+    star (Sum.elim x y) = Sum.elim (star x) (star y) := by ext x; cases x <;> simp
 #align function.star_sum_elim Function.star_sum_elim
 
 end Function

9abfa6f0

bump to nightly-2023-03-21-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/290a7ba01fbcab1b64757bdaa270d28f4dcede35

c67df486

Diff

@@ -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 algebra.star.pi
-! leanprover-community/mathlib commit be24ec5de6701447e5df5ca75400ffee19d65659
+! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -47,6 +47,9 @@ theorem star_def [∀ i, Star (f i)] (x : ∀ i, f i) : star x = fun i => star (
 #align pi.star_def Pi.star_def
 -/
 
+instance [∀ i, Star (f i)] [∀ i, TrivialStar (f i)] : TrivialStar (∀ i, f i)
+    where star_trivial _ := funext fun _ => star_trivial _
+
 instance [∀ i, InvolutiveStar (f i)] : InvolutiveStar (∀ i, f i)
     where star_involutive _ := funext fun _ => star_star _

be24ec5d

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

9abfa6f0

feat: Every star ring is a Nat-star module (#9470)

and other basic star lemmas

From LeanAPAP

83b4d8db

Diff

@@ -61,6 +61,12 @@ theorem single_star [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] [Decid
   single_op (fun i => @star (f i) _) (fun _ => star_zero _) i a
 #align pi.single_star Pi.single_star
 
+open scoped ComplexConjugate
+
+@[simp]
+lemma conj_apply {ι : Type*} {α : ι → Type*} [∀ i, CommSemiring (α i)] [∀ i, StarRing (α i)]
+    (f : ∀ i, α i) (i : ι) : conj f i = conj (f i) := rfl
+
 end Pi
 
 namespace Function

9abfa6f0

style: fix wrapping of where (#7149)

084cfb35

Diff

@@ -37,24 +37,24 @@ theorem star_def [∀ i, Star (f i)] (x : ∀ i, f i) : star x = fun i => star (
   rfl
 #align pi.star_def Pi.star_def
 
-instance [∀ i, Star (f i)] [∀ i, TrivialStar (f i)] : TrivialStar (∀ i, f i)
-    where star_trivial _ := funext fun _ => star_trivial _
+instance [∀ i, Star (f i)] [∀ i, TrivialStar (f i)] : TrivialStar (∀ i, f i) where
+  star_trivial _ := funext fun _ => star_trivial _
 
-instance [∀ i, InvolutiveStar (f i)] : InvolutiveStar (∀ i, f i)
-    where star_involutive _ := funext fun _ => star_star _
+instance [∀ i, InvolutiveStar (f i)] : InvolutiveStar (∀ i, f i) where
+  star_involutive _ := funext fun _ => star_star _
 
-instance [∀ i, Mul (f i)] [∀ i, StarMul (f i)] : StarMul (∀ i, f i)
-    where star_mul _ _ := funext fun _ => star_mul _ _
+instance [∀ i, Mul (f i)] [∀ i, StarMul (f i)] : StarMul (∀ i, f i) where
+  star_mul _ _ := funext fun _ => star_mul _ _
 
-instance [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] : StarAddMonoid (∀ i, f i)
-    where star_add _ _ := funext fun _ => star_add _ _
+instance [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] : StarAddMonoid (∀ i, f i) where
+  star_add _ _ := funext fun _ => star_add _ _
 
 instance [∀ i, NonUnitalSemiring (f i)] [∀ i, StarRing (f i)] : StarRing (∀ i, f i)
   where star_add _ _ := funext fun _ => star_add _ _
 
 instance {R : Type w} [∀ i, SMul R (f i)] [Star R] [∀ i, Star (f i)]
-    [∀ i, StarModule R (f i)] : StarModule R (∀ i, f i)
-    where star_smul r x := funext fun i => star_smul r (x i)
+    [∀ i, StarModule R (f i)] : StarModule R (∀ i, f i) where
+  star_smul r x := funext fun i => star_smul r (x i)
 
 theorem single_star [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] [DecidableEq I] (i : I)
     (a : f i) : Pi.single i (star a) = star (Pi.single i a) :=

9abfa6f0

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>

85c04e73

Diff

@@ -43,7 +43,7 @@ instance [∀ i, Star (f i)] [∀ i, TrivialStar (f i)] : TrivialStar (∀ i, f
 instance [∀ i, InvolutiveStar (f i)] : InvolutiveStar (∀ i, f i)
     where star_involutive _ := funext fun _ => star_star _
 
-instance [∀ i, Semigroup (f i)] [∀ i, StarSemigroup (f i)] : StarSemigroup (∀ i, f i)
+instance [∀ i, Mul (f i)] [∀ i, StarMul (f i)] : StarMul (∀ i, f i)
     where star_mul _ _ := funext fun _ => star_mul _ _
 
 instance [∀ i, AddMonoid (f i)] [∀ i, StarAddMonoid (f i)] : StarAddMonoid (∀ i, f i)

9abfa6f0

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.

32de3f67

Diff

@@ -70,7 +70,7 @@ theorem update_star [∀ i, Star (f i)] [DecidableEq I] (h : ∀ i : I, f i) (i
   funext fun j => (apply_update (fun _ => star) h i a j).symm
 #align function.update_star Function.update_star
 
-theorem star_sum_elim {I J α : Type _} (x : I → α) (y : J → α) [Star α] :
+theorem star_sum_elim {I J α : Type*} (x : I → α) (y : J → α) [Star α] :
     star (Sum.elim x y) = Sum.elim (star x) (star y) := by
   ext x; cases x <;> simp only [Pi.star_apply, Sum.elim_inl, Sum.elim_inr]
 #align function.star_sum_elim Function.star_sum_elim

9abfa6f0

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 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 algebra.star.pi
-! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
-! 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.Ring.Pi
 
+#align_import algebra.star.pi from "leanprover-community/mathlib"@"9abfa6f0727d5adc99067e325e15d1a9de17fd8e"
+
 /-!
 # `star` on pi types

9abfa6f0

chore: sync Mathlib.Algebra.Star.Pi (#3081)

076068bc

Diff

@@ -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 algebra.star.pi
-! leanprover-community/mathlib commit 247a102b14f3cebfee126293341af5f6bed00237
+! leanprover-community/mathlib commit 9abfa6f0727d5adc99067e325e15d1a9de17fd8e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -40,6 +40,9 @@ theorem star_def [∀ i, Star (f i)] (x : ∀ i, f i) : star x = fun i => star (
   rfl
 #align pi.star_def Pi.star_def
 
+instance [∀ i, Star (f i)] [∀ i, TrivialStar (f i)] : TrivialStar (∀ i, f i)
+    where star_trivial _ := funext fun _ => star_trivial _
+
 instance [∀ i, InvolutiveStar (f i)] : InvolutiveStar (∀ i, f i)
     where star_involutive _ := funext fun _ => star_star _

247a102b

feat: port Algebra.Star.Pi (#1432)

09130624

`algebra.star.pi` ⟷ `Mathlib.Algebra.Star.Pi`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 175

algebra.star.pi ⟷ Mathlib.Algebra.Star.Pi

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 175

`algebra.star.pi` ⟷ `Mathlib.Algebra.Star.Pi`