algebra.group.type_tags | Mathlib porting status

(last sync)

refactor(algebra/group/defs): use is_left_cancel_mul etc (#17884)

The Lean 4 version is here: leanprover-community/mathlib4#945.

Diff

@@ -124,21 +124,35 @@ instance [add_comm_semigroup α] : comm_semigroup (multiplicative α) :=
 { mul_comm := @add_comm _ _,
   ..multiplicative.semigroup }
 
+instance [has_mul α] [is_left_cancel_mul α] : is_left_cancel_add (additive α) :=
+{ add_left_cancel := @mul_left_cancel α _ _ }
+
+instance [has_add α] [is_left_cancel_add α] : is_left_cancel_mul (multiplicative α) :=
+{ mul_left_cancel := @add_left_cancel α _ _ }
+
+instance [has_mul α] [is_right_cancel_mul α] : is_right_cancel_add (additive α) :=
+{ add_right_cancel := @mul_right_cancel α _ _ }
+
+instance [has_add α] [is_right_cancel_add α] : is_right_cancel_mul (multiplicative α) :=
+{ mul_right_cancel := @add_right_cancel α _ _ }
+
+instance [has_mul α] [is_cancel_mul α] : is_cancel_add (additive α) :=
+{ ..additive.is_left_cancel_add, ..additive.is_right_cancel_add }
+
+instance [has_add α] [is_cancel_add α] : is_cancel_mul (multiplicative α) :=
+{ ..multiplicative.is_left_cancel_mul, ..multiplicative.is_right_cancel_mul }
+
 instance [left_cancel_semigroup α] : add_left_cancel_semigroup (additive α) :=
-{ add_left_cancel := @mul_left_cancel _ _,
-  ..additive.add_semigroup }
+{ ..additive.add_semigroup, ..additive.is_left_cancel_add }
 
 instance [add_left_cancel_semigroup α] : left_cancel_semigroup (multiplicative α) :=
-{ mul_left_cancel := @add_left_cancel _ _,
-  ..multiplicative.semigroup }
+{ ..multiplicative.semigroup, ..multiplicative.is_left_cancel_mul }
 
 instance [right_cancel_semigroup α] : add_right_cancel_semigroup (additive α) :=
-{ add_right_cancel := @mul_right_cancel _ _,
-  ..additive.add_semigroup }
+{ ..additive.add_semigroup, ..additive.is_right_cancel_add }
 
 instance [add_right_cancel_semigroup α] : right_cancel_semigroup (multiplicative α) :=
-{ mul_right_cancel := @add_right_cancel _ _,
-  ..multiplicative.semigroup }
+{ ..multiplicative.semigroup, ..multiplicative.is_right_cancel_mul }
 
 instance [has_one α] : has_zero (additive α) := ⟨additive.of_mul 1⟩

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
-import Algebra.Hom.Group
+import Algebra.Group.Hom.Defs
 import Logic.Equiv.Defs
 import Data.Finite.Defs

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
-import Mathbin.Algebra.Hom.Group
-import Mathbin.Logic.Equiv.Defs
-import Mathbin.Data.Finite.Defs
+import Algebra.Hom.Group
+import Logic.Equiv.Defs
+import Data.Finite.Defs
 
 #align_import algebra.group.type_tags from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -216,13 +216,13 @@ instance [Mul α] [IsLeftCancelMul α] : IsLeftCancelAdd (Additive α)
     where add_left_cancel := @mul_left_cancel α _ _
 
 instance [Add α] [IsLeftCancelAdd α] : IsLeftCancelMul (Multiplicative α)
-    where mul_left_cancel := @add_left_cancel α _ _
+    where hMul_left_cancel := @add_left_cancel α _ _
 
 instance [Mul α] [IsRightCancelMul α] : IsRightCancelAdd (Additive α)
     where add_right_cancel := @mul_right_cancel α _ _
 
 instance [Add α] [IsRightCancelAdd α] : IsRightCancelMul (Multiplicative α)
-    where mul_right_cancel := @add_right_cancel α _ _
+    where hMul_right_cancel := @add_right_cancel α _ _
 
 instance [Mul α] [IsCancelMul α] : IsCancelAdd (Additive α) :=
   { Additive.isLeftCancelAdd, Additive.isRightCancelAdd with }
@@ -451,7 +451,7 @@ instance [DivInvMonoid α] : SubNegMonoid (Additive α) :=
 instance [SubNegMonoid α] : DivInvMonoid (Multiplicative α) :=
   { Multiplicative.hasInv, Multiplicative.div,
     Multiplicative.monoid with
-    div_eq_mul_inv := @sub_eq_add_neg α _
+    div_eq_hMul_inv := @sub_eq_add_neg α _
     zpow := @SubNegMonoid.zsmul α _
     zpow_zero' := SubNegMonoid.zsmul_zero'
     zpow_succ' := SubNegMonoid.zsmul_succ'
@@ -467,7 +467,7 @@ instance [SubtractionMonoid α] : DivisionMonoid (Multiplicative α) :=
   { Multiplicative.divInvMonoid,
     Multiplicative.hasInvolutiveInv with
     mul_inv_rev := @neg_add_rev _ _
-    inv_eq_of_mul := @neg_eq_of_add_eq_zero_right _ _ }
+    inv_eq_of_hMul := @neg_eq_of_add_eq_zero_right _ _ }
 
 instance [DivisionCommMonoid α] : SubtractionCommMonoid (Additive α) :=
   { Additive.subtractionMonoid, Additive.addCommSemigroup with }
@@ -479,7 +479,7 @@ instance [Group α] : AddGroup (Additive α) :=
   { Additive.subNegMonoid with add_left_neg := @mul_left_inv α _ }
 
 instance [AddGroup α] : Group (Multiplicative α) :=
-  { Multiplicative.divInvMonoid with mul_left_inv := @add_left_neg α _ }
+  { Multiplicative.divInvMonoid with hMul_left_inv := @add_left_neg α _ }
 
 instance [CommGroup α] : AddCommGroup (Additive α) :=
   { Additive.addGroup, Additive.addCommMonoid with }

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module algebra.group.type_tags
-! leanprover-community/mathlib commit 448144f7ae193a8990cb7473c9e9a01990f64ac7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Hom.Group
 import Mathbin.Logic.Equiv.Defs
 import Mathbin.Data.Finite.Defs
 
+#align_import algebra.group.type_tags from "leanprover-community/mathlib"@"448144f7ae193a8990cb7473c9e9a01990f64ac7"
+
 /-!
 # Type tags that turn additive structures into multiplicative, and vice versa

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -502,12 +502,8 @@ def AddMonoidHom.toMultiplicative [AddZeroClass α] [AddZeroClass β] :
     where
   toFun f := ⟨fun a => ofAdd (f a.toAdd), f.2, f.3⟩
   invFun f := ⟨fun a => (f (ofAdd a)).toAdd, f.2, f.3⟩
-  left_inv x := by
-    ext
-    rfl
-  right_inv x := by
-    ext
-    rfl
+  left_inv x := by ext; rfl
+  right_inv x := by ext; rfl
 #align add_monoid_hom.to_multiplicative AddMonoidHom.toMultiplicative
 -/
 
@@ -518,12 +514,8 @@ def MonoidHom.toAdditive [MulOneClass α] [MulOneClass β] : (α →* β) ≃ (A
     where
   toFun f := ⟨fun a => ofMul (f a.toMul), f.2, f.3⟩
   invFun f := ⟨fun a => (f (ofMul a)).toMul, f.2, f.3⟩
-  left_inv x := by
-    ext
-    rfl
-  right_inv x := by
-    ext
-    rfl
+  left_inv x := by ext; rfl
+  right_inv x := by ext; rfl
 #align monoid_hom.to_additive MonoidHom.toAdditive
 -/
 
@@ -535,12 +527,8 @@ def AddMonoidHom.toMultiplicative' [MulOneClass α] [AddZeroClass β] :
     where
   toFun f := ⟨fun a => ofAdd (f (ofMul a)), f.2, f.3⟩
   invFun f := ⟨fun a => (f a.toMul).toAdd, f.2, f.3⟩
-  left_inv x := by
-    ext
-    rfl
-  right_inv x := by
-    ext
-    rfl
+  left_inv x := by ext; rfl
+  right_inv x := by ext; rfl
 #align add_monoid_hom.to_multiplicative' AddMonoidHom.toMultiplicative'
 -/
 
@@ -561,12 +549,8 @@ def AddMonoidHom.toMultiplicative'' [AddZeroClass α] [MulOneClass β] :
     where
   toFun f := ⟨fun a => (f a.toAdd).toMul, f.2, f.3⟩
   invFun f := ⟨fun a => ofMul (f (ofAdd a)), f.2, f.3⟩
-  left_inv x := by
-    ext
-    rfl
-  right_inv x := by
-    ext
-    rfl
+  left_inv x := by ext; rfl
+  right_inv x := by ext; rfl
 #align add_monoid_hom.to_multiplicative'' AddMonoidHom.toMultiplicative''
 -/

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

feat(Algebra/Group): Miscellaneous lemmas (#9387)

From LeanAPAP, LeanCamCombi and PFR

fabcf9d9

Diff

@@ -67,6 +67,12 @@ theorem toMul_symm_eq : (@toMul α).symm = ofMul :=
   rfl
 #align additive.to_mul_symm_eq Additive.toMul_symm_eq
 
+@[simp]
+protected lemma «forall» {p : Additive α → Prop} : (∀ a, p a) ↔ ∀ a, p (ofMul a) := Iff.rfl
+
+@[simp]
+protected lemma «exists» {p : Additive α → Prop} : (∃ a, p a) ↔ ∃ a, p (ofMul a) := Iff.rfl
+
 end Additive
 
 namespace Multiplicative
@@ -90,6 +96,12 @@ theorem toAdd_symm_eq : (@toAdd α).symm = ofAdd :=
   rfl
 #align multiplicative.to_add_symm_eq Multiplicative.toAdd_symm_eq
 
+@[simp]
+protected lemma «forall» {p : Multiplicative α → Prop} : (∀ a, p a) ↔ ∀ a, p (ofAdd a) := Iff.rfl
+
+@[simp]
+protected lemma «exists» {p : Multiplicative α → Prop} : (∃ a, p a) ↔ ∃ a, p (ofAdd a) := Iff.rfl
+
 end Multiplicative
 
 open Additive (ofMul toMul)
@@ -458,6 +470,10 @@ def AddMonoidHom.toMultiplicative [AddZeroClass α] [AddZeroClass β] :
 #align add_monoid_hom.to_multiplicative_symm_apply_apply AddMonoidHom.toMultiplicative_symm_apply_apply
 #align add_monoid_hom.to_multiplicative_apply_apply AddMonoidHom.toMultiplicative_apply_apply
 
+@[simp, norm_cast]
+lemma AddMonoidHom.coe_toMultiplicative [AddZeroClass α] [AddZeroClass β] (f : α →+ β) :
+    ⇑(toMultiplicative f) = ofAdd ∘ f ∘ toAdd := rfl
+
 /-- Reinterpret `α →* β` as `Additive α →+ Additive β`. -/
 @[simps]
 def MonoidHom.toAdditive [MulOneClass α] [MulOneClass β] :
@@ -478,6 +494,10 @@ def MonoidHom.toAdditive [MulOneClass α] [MulOneClass β] :
 #align monoid_hom.to_additive_symm_apply_apply MonoidHom.toAdditive_symm_apply_apply
 #align monoid_hom.to_additive_apply_apply MonoidHom.toAdditive_apply_apply
 
+@[simp, norm_cast]
+lemma MonoidHom.coe_toMultiplicative [MulOneClass α] [MulOneClass β] (f : α →* β) :
+    ⇑(toAdditive f) = ofMul ∘ f ∘ toMul := rfl
+
 /-- Reinterpret `Additive α →+ β` as `α →* Multiplicative β`. -/
 @[simps]
 def AddMonoidHom.toMultiplicative' [MulOneClass α] [AddZeroClass β] :
@@ -498,6 +518,10 @@ def AddMonoidHom.toMultiplicative' [MulOneClass α] [AddZeroClass β] :
 #align add_monoid_hom.to_multiplicative'_apply_apply AddMonoidHom.toMultiplicative'_apply_apply
 #align add_monoid_hom.to_multiplicative'_symm_apply_apply AddMonoidHom.toMultiplicative'_symm_apply_apply
 
+@[simp, norm_cast]
+lemma AddMonoidHom.coe_toMultiplicative' [MulOneClass α] [AddZeroClass β] (f : Additive α →+ β) :
+    ⇑(toMultiplicative' f) = ofAdd ∘ f ∘ ofMul := rfl
+
 /-- Reinterpret `α →* Multiplicative β` as `Additive α →+ β`. -/
 @[simps!]
 def MonoidHom.toAdditive' [MulOneClass α] [AddZeroClass β] :
@@ -507,6 +531,10 @@ def MonoidHom.toAdditive' [MulOneClass α] [AddZeroClass β] :
 #align monoid_hom.to_additive'_symm_apply_apply MonoidHom.toAdditive'_symm_apply_apply
 #align monoid_hom.to_additive'_apply_apply MonoidHom.toAdditive'_apply_apply
 
+@[simp, norm_cast]
+lemma MonoidHom.coe_toAdditive' [MulOneClass α] [AddZeroClass β] (f : α →* Multiplicative β) :
+    ⇑(toAdditive' f) = toAdd ∘ f ∘ toMul := rfl
+
 /-- Reinterpret `α →+ Additive β` as `Multiplicative α →* β`. -/
 @[simps]
 def AddMonoidHom.toMultiplicative'' [AddZeroClass α] [MulOneClass β] :
@@ -527,6 +555,10 @@ def AddMonoidHom.toMultiplicative'' [AddZeroClass α] [MulOneClass β] :
 #align add_monoid_hom.to_multiplicative''_symm_apply_apply AddMonoidHom.toMultiplicative''_symm_apply_apply
 #align add_monoid_hom.to_multiplicative''_apply_apply AddMonoidHom.toMultiplicative''_apply_apply
 
+@[simp, norm_cast]
+lemma AddMonoidHom.coe_toMultiplicative'' [AddZeroClass α] [MulOneClass β] (f : α →+ Additive β) :
+    ⇑(toMultiplicative'' f) = toMul ∘ f ∘ toAdd := rfl
+
 /-- Reinterpret `Multiplicative α →* β` as `α →+ Additive β`. -/
 @[simps!]
 def MonoidHom.toAdditive'' [AddZeroClass α] [MulOneClass β] :
@@ -536,6 +568,10 @@ def MonoidHom.toAdditive'' [AddZeroClass α] [MulOneClass β] :
 #align monoid_hom.to_additive''_symm_apply_apply MonoidHom.toAdditive''_symm_apply_apply
 #align monoid_hom.to_additive''_apply_apply MonoidHom.toAdditive''_apply_apply
 
+@[simp, norm_cast]
+lemma MonoidHom.coe_toAdditive'' [AddZeroClass α] [MulOneClass β] (f : Multiplicative α →* β) :
+    ⇑(toAdditive'' f) = ofMul ∘ f ∘ ofAdd := rfl
+
 /-- If `α` has some multiplicative structure and coerces to a function,
 then `Additive α` should also coerce to the same function.

chore: Move Int and Nat cast lemmas (#9503)

Part of #9411

e1b05c51

Diff

@@ -5,7 +5,6 @@ Authors: Mario Carneiro
 -/
 import Mathlib.Algebra.Group.Hom.Defs
 import Mathlib.Data.Finite.Defs
-import Mathlib.Logic.Equiv.Defs
 import Mathlib.Logic.Nontrivial.Basic
 
 #align_import algebra.group.type_tags from "leanprover-community/mathlib"@"2e0975f6a25dd3fbfb9e41556a77f075f6269748"

chore: tidy various files (#8560)

8c4338d2

Diff

@@ -142,13 +142,13 @@ instance [h : DecidableEq α] : DecidableEq (Multiplicative α) := h
 
 instance [h : DecidableEq α] : DecidableEq (Additive α) := h
 
-instance instNontrivialAdditive [Nontrivial α] : Nontrivial (Additive α) :=
+instance Additive.instNontrivial [Nontrivial α] : Nontrivial (Additive α) :=
   ofMul.injective.nontrivial
-#align additive.nontrivial instNontrivialAdditive
+#align additive.nontrivial Additive.instNontrivial
 
-instance instNontrivialMultiplicative [Nontrivial α] : Nontrivial (Multiplicative α) :=
+instance Multiplicative.instNontrivial [Nontrivial α] : Nontrivial (Multiplicative α) :=
   ofAdd.injective.nontrivial
-#align multiplicative.nontrivial instNontrivialMultiplicative
+#align multiplicative.nontrivial Multiplicative.instNontrivial
 
 instance Additive.add [Mul α] : Add (Additive α) where
   add x y := ofMul (toMul x * toMul y)

chore: add some Unique instances (#8500)

The aim is to remove some extraneous Nonempty assumptions in Algebra/DirectLimit.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>

9a4ae4a9

Diff

@@ -116,12 +116,18 @@ theorem ofMul_toMul (x : Additive α) : ofMul (toMul x) = x :=
   rfl
 #align of_mul_to_mul ofMul_toMul
 
+instance [Subsingleton α] : Subsingleton (Additive α) := toMul.injective.subsingleton
+instance [Subsingleton α] : Subsingleton (Multiplicative α) := toAdd.injective.subsingleton
+
 instance [Inhabited α] : Inhabited (Additive α) :=
   ⟨ofMul default⟩
 
 instance [Inhabited α] : Inhabited (Multiplicative α) :=
   ⟨ofAdd default⟩
 
+instance [Unique α] : Unique (Additive α) := toMul.unique
+instance [Unique α] : Unique (Multiplicative α) := toAdd.unique
+
 instance [Finite α] : Finite (Additive α) :=
   Finite.of_equiv α (by rfl)

style: add missing spaces around colons (#8293)

This is not exhaustive

c488ddff

Diff

@@ -128,9 +128,9 @@ instance [Finite α] : Finite (Additive α) :=
 instance [Finite α] : Finite (Multiplicative α) :=
   Finite.of_equiv α (by rfl)
 
-instance [h: Infinite α] : Infinite (Additive α) := h
+instance [h : Infinite α] : Infinite (Additive α) := h
 
-instance [h: Infinite α] : Infinite (Multiplicative α) := h
+instance [h : Infinite α] : Infinite (Multiplicative α) := h
 
 instance [h : DecidableEq α] : DecidableEq (Multiplicative α) := h

refactor(Algebra/Hom): transpose Hom and file name (#8095)

I believe the file defining a type of morphisms belongs alongside the file defining the structure this morphism works on. So I would like to reorganize the files in the Mathlib.Algebra.Hom folder so that e.g. Mathlib.Algebra.Hom.Ring becomes Mathlib.Algebra.Ring.Hom and Mathlib.Algebra.Hom.NonUnitalAlg becomes Mathlib.Algebra.Algebra.NonUnitalHom.

While fixing the imports I went ahead and sorted them for good luck.

The full list of changes is: renamed: Mathlib/Algebra/Hom/NonUnitalAlg.lean -> Mathlib/Algebra/Algebra/NonUnitalHom.lean renamed: Mathlib/Algebra/Hom/Aut.lean -> Mathlib/Algebra/Group/Aut.lean renamed: Mathlib/Algebra/Hom/Commute.lean -> Mathlib/Algebra/Group/Commute/Hom.lean renamed: Mathlib/Algebra/Hom/Embedding.lean -> Mathlib/Algebra/Group/Embedding.lean renamed: Mathlib/Algebra/Hom/Equiv/Basic.lean -> Mathlib/Algebra/Group/Equiv/Basic.lean renamed: Mathlib/Algebra/Hom/Equiv/TypeTags.lean -> Mathlib/Algebra/Group/Equiv/TypeTags.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/Basic.lean -> Mathlib/Algebra/Group/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/GroupWithZero.lean -> Mathlib/Algebra/GroupWithZero/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Freiman.lean -> Mathlib/Algebra/Group/Freiman.lean renamed: Mathlib/Algebra/Hom/Group/Basic.lean -> Mathlib/Algebra/Group/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Group/Defs.lean -> Mathlib/Algebra/Group/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/GroupAction.lean -> Mathlib/GroupTheory/GroupAction/Hom.lean renamed: Mathlib/Algebra/Hom/GroupInstances.lean -> Mathlib/Algebra/Group/Hom/Instances.lean renamed: Mathlib/Algebra/Hom/Iterate.lean -> Mathlib/Algebra/GroupPower/IterateHom.lean renamed: Mathlib/Algebra/Hom/Centroid.lean -> Mathlib/Algebra/Ring/CentroidHom.lean renamed: Mathlib/Algebra/Hom/Ring/Basic.lean -> Mathlib/Algebra/Ring/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Ring/Defs.lean -> Mathlib/Algebra/Ring/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/Units.lean -> Mathlib/Algebra/Group/Units/Hom.lean

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Reorganizing.20.60Mathlib.2EAlgebra.2EHom.60

92fe122e

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
-import Mathlib.Algebra.Hom.Group.Defs
-import Mathlib.Logic.Nontrivial.Basic
-import Mathlib.Logic.Equiv.Defs
+import Mathlib.Algebra.Group.Hom.Defs
 import Mathlib.Data.Finite.Defs
+import Mathlib.Logic.Equiv.Defs
+import Mathlib.Logic.Nontrivial.Basic
 
 #align_import algebra.group.type_tags from "leanprover-community/mathlib"@"2e0975f6a25dd3fbfb9e41556a77f075f6269748"

feat: add DecidableEq instances for Multiplicative and Additive (#8072)

056e7257

Diff

@@ -132,6 +132,10 @@ instance [h: Infinite α] : Infinite (Additive α) := h
 
 instance [h: Infinite α] : Infinite (Multiplicative α) := h
 
+instance [h : DecidableEq α] : DecidableEq (Multiplicative α) := h
+
+instance [h : DecidableEq α] : DecidableEq (Additive α) := h
+
 instance instNontrivialAdditive [Nontrivial α] : Nontrivial (Additive α) :=
   ofMul.injective.nontrivial
 #align additive.nontrivial instNontrivialAdditive

chore(Algebra/Group/TypeTags): lemmas about pow and smul (#7862)

Half of these lemmas already existed, but were a long way from the definition that define the operators. For the ones that did exist, the #aligns have been kept.

The new lemmas are all @[simp] since that matches the corresponding add/mul lemmas. This makes some lemmas about Int and Nat not simp-normal any more (they disagree on commutativity), but that doesn't seem to matter.

55c25193

Diff

@@ -267,6 +267,24 @@ instance Multiplicative.monoid [h : AddMonoid α] : Monoid (Multiplicative α) :
     npow_zero := @AddMonoid.nsmul_zero α h
     npow_succ := @AddMonoid.nsmul_succ α h }
 
+@[simp]
+theorem ofMul_pow [Monoid α] (n : ℕ) (a : α) : ofMul (a ^ n) = n • ofMul a :=
+  rfl
+#align of_mul_pow ofMul_pow
+
+@[simp]
+theorem toMul_nsmul [Monoid α] (n : ℕ) (a : Additive α) : toMul (n • a) = toMul a ^ n :=
+  rfl
+
+@[simp]
+theorem ofAdd_nsmul [AddMonoid α] (n : ℕ) (a : α) : ofAdd (n • a) = ofAdd a ^ n :=
+  rfl
+#align of_add_nsmul ofAdd_nsmul
+
+@[simp]
+theorem toAdd_pow [AddMonoid α] (a : Multiplicative α) (n : ℕ) : toAdd (a ^ n) = n • toAdd a :=
+  rfl
+
 instance Additive.addLeftCancelMonoid [LeftCancelMonoid α] : AddLeftCancelMonoid (Additive α) :=
   { Additive.addMonoid, Additive.addLeftCancelSemigroup with }
 
@@ -363,6 +381,24 @@ instance Multiplicative.divInvMonoid [SubNegMonoid α] : DivInvMonoid (Multiplic
     zpow_succ' := @SubNegMonoid.zsmul_succ' α _
     zpow_neg' := @SubNegMonoid.zsmul_neg' α _ }
 
+@[simp]
+theorem ofMul_zpow [DivInvMonoid α] (z : ℤ) (a : α) : ofMul (a ^ z) = z • ofMul a :=
+  rfl
+#align of_mul_zpow ofMul_zpow
+
+@[simp]
+theorem toMul_zsmul [DivInvMonoid α] (z : ℤ) (a : Additive α) : toMul (z • a) = toMul a ^ z :=
+  rfl
+
+@[simp]
+theorem ofAdd_zsmul [SubNegMonoid α] (z : ℤ) (a : α) : ofAdd (z • a) = ofAdd a ^ z :=
+  rfl
+#align of_add_zsmul ofAdd_zsmul
+
+@[simp]
+theorem toAdd_zpow [SubNegMonoid α] (a : Multiplicative α) (z : ℤ) : toAdd (a ^ z) = z • toAdd a :=
+  rfl
+
 instance Additive.subtractionMonoid [DivisionMonoid α] : SubtractionMonoid (Additive α) :=
   { Additive.subNegMonoid, Additive.involutiveNeg with
     neg_add_rev := @mul_inv_rev α _

perf: remove overspecified fields (#6965)

This removes redundant field values of the form add := add for smaller terms and less unfolding during unification.

A list of all files containing a structure instance of the form { a1, ... with x1 := val, ... } where some xi is a field of some aj was generated by modifying the structure instance elaboration algorithm to print such overlaps to stdout in a custom toolchain.

Using that toolchain, I went through each file on the list and attempted to remove algebraic fields that overlapped and were redundant, eg add := add and not toFun (though some other ones did creep in). If things broke (which was the case in a couple of cases), I did not push further and reverted.

It is possible that pushing harder and trying to remove all redundant overlaps will yield further improvements.

12150475

Diff

@@ -257,39 +257,35 @@ instance Multiplicative.mulOneClass [AddZeroClass α] : MulOneClass (Multiplicat
 
 instance Additive.addMonoid [h : Monoid α] : AddMonoid (Additive α) :=
   { Additive.addZeroClass, Additive.addSemigroup with
-    zero := 0
-    add := (· + ·)
     nsmul := @Monoid.npow α h
     nsmul_zero := @Monoid.npow_zero α h
     nsmul_succ := @Monoid.npow_succ α h }
 
 instance Multiplicative.monoid [h : AddMonoid α] : Monoid (Multiplicative α) :=
   { Multiplicative.mulOneClass, Multiplicative.semigroup with
-    one := 1
-    mul := (· * ·)
     npow := @AddMonoid.nsmul α h
     npow_zero := @AddMonoid.nsmul_zero α h
     npow_succ := @AddMonoid.nsmul_succ α h }
 
 instance Additive.addLeftCancelMonoid [LeftCancelMonoid α] : AddLeftCancelMonoid (Additive α) :=
-  { Additive.addMonoid, Additive.addLeftCancelSemigroup with zero := 0, add := (· + ·) }
+  { Additive.addMonoid, Additive.addLeftCancelSemigroup with }
 
 instance Multiplicative.leftCancelMonoid [AddLeftCancelMonoid α] :
     LeftCancelMonoid (Multiplicative α) :=
-  { Multiplicative.monoid, Multiplicative.leftCancelSemigroup with one := 1, mul := (· * ·) }
+  { Multiplicative.monoid, Multiplicative.leftCancelSemigroup with }
 
 instance Additive.addRightCancelMonoid [RightCancelMonoid α] : AddRightCancelMonoid (Additive α) :=
-  { Additive.addMonoid, Additive.addRightCancelSemigroup with zero := 0, add := (· + ·) }
+  { Additive.addMonoid, Additive.addRightCancelSemigroup with }
 
 instance Multiplicative.rightCancelMonoid [AddRightCancelMonoid α] :
     RightCancelMonoid (Multiplicative α) :=
-  { Multiplicative.monoid, Multiplicative.rightCancelSemigroup with one := 1, mul := (· * ·) }
+  { Multiplicative.monoid, Multiplicative.rightCancelSemigroup with }
 
 instance Additive.addCommMonoid [CommMonoid α] : AddCommMonoid (Additive α) :=
-  { Additive.addMonoid, Additive.addCommSemigroup with zero := 0, add := (· + ·) }
+  { Additive.addMonoid, Additive.addCommSemigroup with }
 
 instance Multiplicative.commMonoid [AddCommMonoid α] : CommMonoid (Multiplicative α) :=
-  { Multiplicative.monoid, Multiplicative.commSemigroup with one := 1, mul := (· * ·) }
+  { Multiplicative.monoid, Multiplicative.commSemigroup with }
 
 instance Additive.neg [Inv α] : Neg (Additive α) :=
   ⟨fun x => ofAdd (toMul x)⁻¹⟩

refactor: split Algebra.Hom.Group and Algebra.Hom.Ring (#7094)

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

260cb506

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
-import Mathlib.Algebra.Hom.Group
+import Mathlib.Algebra.Hom.Group.Defs
 import Mathlib.Logic.Nontrivial.Basic
 import Mathlib.Logic.Equiv.Defs
 import Mathlib.Data.Finite.Defs

feat: split Logic.Nontrivial (#6959)

This continues reducing the import requirements for the basic algebraic hierarchy.

In combination with #6954 #6955 #6956 #6957, this reduces the imports for Mathlib.Algebra.Field.Defs from

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

560425d2

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
 import Mathlib.Algebra.Hom.Group
+import Mathlib.Logic.Nontrivial.Basic
 import Mathlib.Logic.Equiv.Defs
 import Mathlib.Data.Finite.Defs

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

@@ -38,12 +38,12 @@ variable {α : Type u} {β : Type v}
 
 /-- If `α` carries some multiplicative structure, then `Additive α` carries the corresponding
 additive structure. -/
-def Additive (α : Type _) := α
+def Additive (α : Type*) := α
 #align additive Additive
 
 /-- If `α` carries some additive structure, then `Multiplicative α` carries the corresponding
 multiplicative structure. -/
-def Multiplicative (α : Type _) := α
+def Multiplicative (α : Type*) := α
 #align multiplicative Multiplicative
 
 namespace Additive
@@ -217,7 +217,7 @@ theorem ofMul_one [One α] : @Additive.ofMul α 1 = 0 := rfl
 #align of_mul_one ofMul_one
 
 @[simp]
-theorem ofMul_eq_zero {A : Type _} [One A] {x : A} : Additive.ofMul x = 0 ↔ x = 1 := Iff.rfl
+theorem ofMul_eq_zero {A : Type*} [One A] {x : A} : Additive.ofMul x = 0 ↔ x = 1 := Iff.rfl
 #align of_mul_eq_zero ofMul_eq_zero
 
 @[simp]
@@ -233,7 +233,7 @@ theorem ofAdd_zero [Zero α] : @Multiplicative.ofAdd α 0 = 1 :=
 #align of_add_zero ofAdd_zero
 
 @[simp]
-theorem ofAdd_eq_one {A : Type _} [Zero A] {x : A} : Multiplicative.ofAdd x = 1 ↔ x = 0 :=
+theorem ofAdd_eq_one {A : Type*} [Zero A] {x : A} : Multiplicative.ofAdd x = 1 ↔ x = 0 :=
   Iff.rfl
 #align of_add_eq_one ofAdd_eq_one
 
@@ -500,7 +500,7 @@ then `Additive α` should also coerce to the same function.
 This allows `Additive` to be used on bundled function types with a multiplicative structure, which
 is often used for composition, without affecting the behavior of the function itself.
 -/
-instance Additive.coeToFun {α : Type _} {β : α → Sort _} [CoeFun α β] :
+instance Additive.coeToFun {α : Type*} {β : α → Sort*} [CoeFun α β] :
     CoeFun (Additive α) fun a => β (toMul a) :=
   ⟨fun a => CoeFun.coe (toMul a)⟩
 #align additive.has_coe_to_fun Additive.coeToFun
@@ -511,7 +511,7 @@ then `Multiplicative α` should also coerce to the same function.
 This allows `Multiplicative` to be used on bundled function types with an additive structure, which
 is often used for composition, without affecting the behavior of the function itself.
 -/
-instance Multiplicative.coeToFun {α : Type _} {β : α → Sort _} [CoeFun α β] :
+instance Multiplicative.coeToFun {α : Type*} {β : α → Sort*} [CoeFun α β] :
     CoeFun (Multiplicative α) fun a => β (toAdd a) :=
   ⟨fun a => CoeFun.coe (toAdd a)⟩
 #align multiplicative.has_coe_to_fun Multiplicative.coeToFun

chore: ensure all instances referred to directly have explicit names (#6423)

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

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

65a35f78

Diff

@@ -131,11 +131,11 @@ instance [h: Infinite α] : Infinite (Additive α) := h
 
 instance [h: Infinite α] : Infinite (Multiplicative α) := h
 
-instance [Nontrivial α] : Nontrivial (Additive α) :=
+instance instNontrivialAdditive [Nontrivial α] : Nontrivial (Additive α) :=
   ofMul.injective.nontrivial
 #align additive.nontrivial instNontrivialAdditive
 
-instance [Nontrivial α] : Nontrivial (Multiplicative α) :=
+instance instNontrivialMultiplicative [Nontrivial α] : Nontrivial (Multiplicative α) :=
   ofAdd.injective.nontrivial
 #align multiplicative.nontrivial instNontrivialMultiplicative

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

@@ -2,16 +2,13 @@
 Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module algebra.group.type_tags
-! leanprover-community/mathlib commit 2e0975f6a25dd3fbfb9e41556a77f075f6269748
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Hom.Group
 import Mathlib.Logic.Equiv.Defs
 import Mathlib.Data.Finite.Defs
 
+#align_import algebra.group.type_tags from "leanprover-community/mathlib"@"2e0975f6a25dd3fbfb9e41556a77f075f6269748"
+
 /-!
 # Type tags that turn additive structures into multiplicative, and vice versa

chore: update SHA sums (#2201)

All these changes in Mathlib 3 were backported from this repository or were forward-ported earler.

Port status pages

Relevant PRs

Topology.Basic: #1957
Order.Filter.Basic: #1953
Order.Basic: #1738
Algebra.Group.TypeTags: #945

5d18ee9b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 
 ! This file was ported from Lean 3 source module algebra.group.type_tags
-! leanprover-community/mathlib commit 6eb334bd8f3433d5b08ba156b8ec3e6af47e1904
+! leanprover-community/mathlib commit 2e0975f6a25dd3fbfb9e41556a77f075f6269748
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

feat: require @[simps!] if simps runs in expensive mode (#1885)

This does not change the behavior of simps, just raises a linter error if you run simps in a more expensive mode without writing !.
Fixed some incorrect occurrences of to_additive, simps. Will do that systematically in future PR.
Fix port of OmegaCompletePartialOrder.ContinuousHom.ofMono a bit

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

52c04a34

Diff

@@ -460,7 +460,7 @@ def AddMonoidHom.toMultiplicative' [MulOneClass α] [AddZeroClass β] :
 #align add_monoid_hom.to_multiplicative'_symm_apply_apply AddMonoidHom.toMultiplicative'_symm_apply_apply
 
 /-- Reinterpret `α →* Multiplicative β` as `Additive α →+ β`. -/
-@[simps]
+@[simps!]
 def MonoidHom.toAdditive' [MulOneClass α] [AddZeroClass β] :
     (α →* Multiplicative β) ≃ (Additive α →+ β) :=
   AddMonoidHom.toMultiplicative'.symm
@@ -489,7 +489,7 @@ def AddMonoidHom.toMultiplicative'' [AddZeroClass α] [MulOneClass β] :
 #align add_monoid_hom.to_multiplicative''_apply_apply AddMonoidHom.toMultiplicative''_apply_apply
 
 /-- Reinterpret `Multiplicative α →* β` as `α →+ Additive β`. -/
-@[simps]
+@[simps!]
 def MonoidHom.toAdditive'' [AddZeroClass α] [MulOneClass β] :
     (Multiplicative α →* β) ≃ (α →+ Additive β) :=
   AddMonoidHom.toMultiplicative''.symm

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -416,6 +416,8 @@ def AddMonoidHom.toMultiplicative [AddZeroClass α] [AddZeroClass β] :
   left_inv _ := rfl
   right_inv _ := rfl
 #align add_monoid_hom.to_multiplicative AddMonoidHom.toMultiplicative
+#align add_monoid_hom.to_multiplicative_symm_apply_apply AddMonoidHom.toMultiplicative_symm_apply_apply
+#align add_monoid_hom.to_multiplicative_apply_apply AddMonoidHom.toMultiplicative_apply_apply
 
 /-- Reinterpret `α →* β` as `Additive α →+ Additive β`. -/
 @[simps]
@@ -434,6 +436,8 @@ def MonoidHom.toAdditive [MulOneClass α] [MulOneClass β] :
   left_inv _ := rfl
   right_inv _ := rfl
 #align monoid_hom.to_additive MonoidHom.toAdditive
+#align monoid_hom.to_additive_symm_apply_apply MonoidHom.toAdditive_symm_apply_apply
+#align monoid_hom.to_additive_apply_apply MonoidHom.toAdditive_apply_apply
 
 /-- Reinterpret `Additive α →+ β` as `α →* Multiplicative β`. -/
 @[simps]
@@ -452,6 +456,8 @@ def AddMonoidHom.toMultiplicative' [MulOneClass α] [AddZeroClass β] :
   left_inv _ := rfl
   right_inv _ := rfl
 #align add_monoid_hom.to_multiplicative' AddMonoidHom.toMultiplicative'
+#align add_monoid_hom.to_multiplicative'_apply_apply AddMonoidHom.toMultiplicative'_apply_apply
+#align add_monoid_hom.to_multiplicative'_symm_apply_apply AddMonoidHom.toMultiplicative'_symm_apply_apply
 
 /-- Reinterpret `α →* Multiplicative β` as `Additive α →+ β`. -/
 @[simps]
@@ -459,6 +465,8 @@ def MonoidHom.toAdditive' [MulOneClass α] [AddZeroClass β] :
     (α →* Multiplicative β) ≃ (Additive α →+ β) :=
   AddMonoidHom.toMultiplicative'.symm
 #align monoid_hom.to_additive' MonoidHom.toAdditive'
+#align monoid_hom.to_additive'_symm_apply_apply MonoidHom.toAdditive'_symm_apply_apply
+#align monoid_hom.to_additive'_apply_apply MonoidHom.toAdditive'_apply_apply
 
 /-- Reinterpret `α →+ Additive β` as `Multiplicative α →* β`. -/
 @[simps]
@@ -477,6 +485,8 @@ def AddMonoidHom.toMultiplicative'' [AddZeroClass α] [MulOneClass β] :
   left_inv _ := rfl
   right_inv _ := rfl
 #align add_monoid_hom.to_multiplicative'' AddMonoidHom.toMultiplicative''
+#align add_monoid_hom.to_multiplicative''_symm_apply_apply AddMonoidHom.toMultiplicative''_symm_apply_apply
+#align add_monoid_hom.to_multiplicative''_apply_apply AddMonoidHom.toMultiplicative''_apply_apply
 
 /-- Reinterpret `Multiplicative α →* β` as `α →+ Additive β`. -/
 @[simps]
@@ -484,6 +494,8 @@ def MonoidHom.toAdditive'' [AddZeroClass α] [MulOneClass β] :
     (Multiplicative α →* β) ≃ (α →+ Additive β) :=
   AddMonoidHom.toMultiplicative''.symm
 #align monoid_hom.to_additive'' MonoidHom.toAdditive''
+#align monoid_hom.to_additive''_symm_apply_apply MonoidHom.toAdditive''_symm_apply_apply
+#align monoid_hom.to_additive''_apply_apply MonoidHom.toAdditive''_apply_apply
 
 /-- If `α` has some multiplicative structure and coerces to a function,
 then `Additive α` should also coerce to the same function.

feat: implement basic version of tauto tactic (#1081)

Adds a basic version of the tauto tactic, mostly a line-by-line translation of the Lean 3 version.

As per this zulip discussion, makes tauto always-classical and eliminates tauto!.
Does not yet add any symmetry-based logic or the fancy union-find datastructure from https://github.com/leanprover-community/mathlib/pull/180.
Adds a andThenOnSubgoals tactic combinator in Mathlib.Tactic.Basic.

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

3f9ce172

Diff

@@ -130,10 +130,8 @@ instance [Finite α] : Finite (Additive α) :=
 instance [Finite α] : Finite (Multiplicative α) :=
   Finite.of_equiv α (by rfl)
 
--- Porting note: the mathlib3 proof is `by tauto`
 instance [h: Infinite α] : Infinite (Additive α) := h
 
--- Porting note: the mathlib3 proof is `by tauto`
 instance [h: Infinite α] : Infinite (Multiplicative α) := h
 
 instance [Nontrivial α] : Nontrivial (Additive α) :=