group_theory.specific_groups.quaternion

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

879155bf

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c2092722

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -215,7 +215,7 @@ theorem a_one_pow_n : (a 1 : QuaternionGroup n) ^ (2 * n) = 1 :=
   by
   rw [a_one_pow, one_def]
   congr 1
-  exact ZMod.nat_cast_self _
+  exact ZMod.natCast_self _
 #align quaternion_group.a_one_pow_n QuaternionGroup.a_one_pow_n
 -/
 
@@ -251,7 +251,7 @@ theorem orderOf_xa [NeZero n] (i : ZMod (2 * n)) : orderOf (xa i) = 4 :=
     injection h with h'
     apply_fun ZMod.val at h'
     apply_fun (· / n) at h'
-    simp only [ZMod.val_nat_cast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
+    simp only [ZMod.val_natCast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
       Nat.div_self (NeZero.pos n)] at h'
     norm_num at h'
   · norm_num
@@ -289,7 +289,7 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n :=
   have h1 : (a 1 : QuaternionGroup n) ^ orderOf (a 1) = 1 := pow_orderOf_eq_one _
   rw [a_one_pow] at h1
   injection h1 with h2
-  rw [← ZMod.val_eq_zero, ZMod.val_nat_cast, Nat.mod_eq_of_lt h] at h2
+  rw [← ZMod.val_eq_zero, ZMod.val_natCast, Nat.mod_eq_of_lt h] at h2
   exact absurd h2.symm (orderOf_pos _).Ne
 #align quaternion_group.order_of_a_one QuaternionGroup.orderOf_a_one
 -/
@@ -299,7 +299,7 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n :=
 -/
 theorem orderOf_a [NeZero n] (i : ZMod (2 * n)) : orderOf (a i) = 2 * n / Nat.gcd (2 * n) i.val :=
   by
-  conv_lhs => rw [← ZMod.nat_cast_zmod_val i]
+  conv_lhs => rw [← ZMod.natCast_zmod_val i]
   rw [← a_one_pow, orderOf_pow, order_of_a_one]
 #align quaternion_group.order_of_a QuaternionGroup.orderOf_a
 -/

c2092722

bump to nightly-2024-04-09-08

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

659ec6f7

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
 -/
 import Data.ZMod.Basic
-import Data.Nat.Defs
+import Algebra.Group.Nat
 import Tactic.IntervalCases
 import GroupTheory.SpecificGroups.Dihedral
 import GroupTheory.SpecificGroups.Cyclic

c2092722

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
 -/
-import Data.Zmod.Basic
-import Data.Nat.Basic
+import Data.ZMod.Basic
+import Data.Nat.Defs
 import Tactic.IntervalCases
 import GroupTheory.SpecificGroups.Dihedral
 import GroupTheory.SpecificGroups.Cyclic
@@ -202,7 +202,7 @@ theorem a_one_pow (k : ℕ) : (a 1 : QuaternionGroup n) ^ k = a k :=
   by
   induction' k with k IH
   · rw [Nat.cast_zero]; rfl
-  · rw [pow_succ, IH, a_mul_a]
+  · rw [pow_succ', IH, a_mul_a]
     congr 1
     norm_cast
     rw [Nat.one_add]
@@ -229,8 +229,8 @@ theorem xa_sq (i : ZMod (2 * n)) : xa i ^ 2 = a n := by simp [sq]
 @[simp]
 theorem xa_pow_four (i : ZMod (2 * n)) : xa i ^ 4 = 1 :=
   by
-  simp only [pow_succ, sq, xa_mul_xa, xa_mul_a, add_sub_cancel, add_sub_assoc, add_sub_cancel',
-    sub_self, add_zero]
+  simp only [pow_succ', sq, xa_mul_xa, xa_mul_a, add_sub_cancel_right, add_sub_assoc,
+    add_sub_cancel_left, sub_self, add_zero]
   norm_cast
   rw [← two_mul]
   simp [one_def]

c2092722

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -247,13 +247,13 @@ theorem orderOf_xa [NeZero n] (i : ZMod (2 * n)) : orderOf (xa i) = 4 :=
   haveI : Fact (Nat.Prime 2) := Fact.mk Nat.prime_two
   apply orderOf_eq_prime_pow
   · intro h
-    simp only [pow_one, xa_sq] at h 
+    simp only [pow_one, xa_sq] at h
     injection h with h'
-    apply_fun ZMod.val at h' 
-    apply_fun (· / n) at h' 
+    apply_fun ZMod.val at h'
+    apply_fun (· / n) at h'
     simp only [ZMod.val_nat_cast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
-      Nat.div_self (NeZero.pos n)] at h' 
-    norm_num at h' 
+      Nat.div_self (NeZero.pos n)] at h'
+    norm_num at h'
   · norm_num
 #align quaternion_group.order_of_xa QuaternionGroup.orderOf_xa
 -/
@@ -287,9 +287,9 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n :=
           (orderOf_dvd_of_pow_eq_one (@a_one_pow_n n))).lt_or_eq.resolve_left
   intro h
   have h1 : (a 1 : QuaternionGroup n) ^ orderOf (a 1) = 1 := pow_orderOf_eq_one _
-  rw [a_one_pow] at h1 
+  rw [a_one_pow] at h1
   injection h1 with h2
-  rw [← ZMod.val_eq_zero, ZMod.val_nat_cast, Nat.mod_eq_of_lt h] at h2 
+  rw [← ZMod.val_eq_zero, ZMod.val_nat_cast, Nat.mod_eq_of_lt h] at h2
   exact absurd h2.symm (orderOf_pos _).Ne
 #align quaternion_group.order_of_a_one QuaternionGroup.orderOf_a_one
 -/

c2092722

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
 -/
-import Mathbin.Data.Zmod.Basic
-import Mathbin.Data.Nat.Basic
-import Mathbin.Tactic.IntervalCases
-import Mathbin.GroupTheory.SpecificGroups.Dihedral
-import Mathbin.GroupTheory.SpecificGroups.Cyclic
+import Data.Zmod.Basic
+import Data.Nat.Basic
+import Tactic.IntervalCases
+import GroupTheory.SpecificGroups.Dihedral
+import GroupTheory.SpecificGroups.Cyclic
 
 #align_import group_theory.specific_groups.quaternion from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"

c2092722

bump to nightly-2023-08-17-09

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

60285dcc

Diff

@@ -108,7 +108,7 @@ instance : Group (QuaternionGroup n) where
     · exact congr_arg a (add_zero i)
     · exact congr_arg xa (add_zero i)
   inv := inv
-  mul_left_inv := by
+  hMul_left_inv := by
     rintro (i | i)
     · exact congr_arg a (neg_add_self i)
     · exact congr_arg a (sub_self (n + i))

c2092722

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
-
-! This file was ported from Lean 3 source module group_theory.specific_groups.quaternion
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Zmod.Basic
 import Mathbin.Data.Nat.Basic
@@ -14,6 +9,8 @@ import Mathbin.Tactic.IntervalCases
 import Mathbin.GroupTheory.SpecificGroups.Dihedral
 import Mathbin.GroupTheory.SpecificGroups.Cyclic
 
+#align_import group_theory.specific_groups.quaternion from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # Quaternion Groups

c2092722

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -118,29 +118,39 @@ instance : Group (QuaternionGroup n) where
 
 variable {n}
 
+#print QuaternionGroup.a_mul_a /-
 @[simp]
 theorem a_mul_a (i j : ZMod (2 * n)) : a i * a j = a (i + j) :=
   rfl
 #align quaternion_group.a_mul_a QuaternionGroup.a_mul_a
+-/
 
+#print QuaternionGroup.a_mul_xa /-
 @[simp]
 theorem a_mul_xa (i j : ZMod (2 * n)) : a i * xa j = xa (j - i) :=
   rfl
 #align quaternion_group.a_mul_xa QuaternionGroup.a_mul_xa
+-/
 
+#print QuaternionGroup.xa_mul_a /-
 @[simp]
 theorem xa_mul_a (i j : ZMod (2 * n)) : xa i * a j = xa (i + j) :=
   rfl
 #align quaternion_group.xa_mul_a QuaternionGroup.xa_mul_a
+-/
 
+#print QuaternionGroup.xa_mul_xa /-
 @[simp]
 theorem xa_mul_xa (i j : ZMod (2 * n)) : xa i * xa j = a (n + j - i) :=
   rfl
 #align quaternion_group.xa_mul_xa QuaternionGroup.xa_mul_xa
+-/
 
+#print QuaternionGroup.one_def /-
 theorem one_def : (1 : QuaternionGroup n) = a 0 :=
   rfl
 #align quaternion_group.one_def QuaternionGroup.one_def
+-/
 
 private def fintype_helper : Sum (ZMod (2 * n)) (ZMod (2 * n)) ≃ QuaternionGroup n
     where
@@ -155,6 +165,7 @@ private def fintype_helper : Sum (ZMod (2 * n)) (ZMod (2 * n)) ≃ QuaternionGro
   left_inv := by rintro (x | x) <;> rfl
   right_inv := by rintro (x | x) <;> rfl
 
+#print QuaternionGroup.quaternionGroupZeroEquivDihedralGroupZero /-
 /-- The special case that more or less by definition `quaternion_group 0` is isomorphic to the
 infinite dihedral group. -/
 def quaternionGroupZeroEquivDihedralGroupZero : QuaternionGroup 0 ≃* DihedralGroup 0
@@ -168,6 +179,7 @@ def quaternionGroupZeroEquivDihedralGroupZero : QuaternionGroup 0 ≃* DihedralG
   right_inv := by rintro (k | k) <;> rfl
   map_mul' := by rintro (k | k) (l | l) <;> · dsimp; simp
 #align quaternion_group.quaternion_group_zero_equiv_dihedral_group_zero QuaternionGroup.quaternionGroupZeroEquivDihedralGroupZero
+-/
 
 /-- If `0 < n`, then `quaternion_group n` is a finite group.
 -/
@@ -187,6 +199,7 @@ theorem card [NeZero n] : Fintype.card (QuaternionGroup n) = 4 * n :=
 #align quaternion_group.card QuaternionGroup.card
 -/
 
+#print QuaternionGroup.a_one_pow /-
 @[simp]
 theorem a_one_pow (k : ℕ) : (a 1 : QuaternionGroup n) ^ k = a k :=
   by
@@ -197,7 +210,9 @@ theorem a_one_pow (k : ℕ) : (a 1 : QuaternionGroup n) ^ k = a k :=
     norm_cast
     rw [Nat.one_add]
 #align quaternion_group.a_one_pow QuaternionGroup.a_one_pow
+-/
 
+#print QuaternionGroup.a_one_pow_n /-
 @[simp]
 theorem a_one_pow_n : (a 1 : QuaternionGroup n) ^ (2 * n) = 1 :=
   by
@@ -205,11 +220,15 @@ theorem a_one_pow_n : (a 1 : QuaternionGroup n) ^ (2 * n) = 1 :=
   congr 1
   exact ZMod.nat_cast_self _
 #align quaternion_group.a_one_pow_n QuaternionGroup.a_one_pow_n
+-/
 
+#print QuaternionGroup.xa_sq /-
 @[simp]
 theorem xa_sq (i : ZMod (2 * n)) : xa i ^ 2 = a n := by simp [sq]
 #align quaternion_group.xa_sq QuaternionGroup.xa_sq
+-/
 
+#print QuaternionGroup.xa_pow_four /-
 @[simp]
 theorem xa_pow_four (i : ZMod (2 * n)) : xa i ^ 4 = 1 :=
   by
@@ -219,7 +238,9 @@ theorem xa_pow_four (i : ZMod (2 * n)) : xa i ^ 4 = 1 :=
   rw [← two_mul]
   simp [one_def]
 #align quaternion_group.xa_pow_four QuaternionGroup.xa_pow_four
+-/
 
+#print QuaternionGroup.orderOf_xa /-
 /-- If `0 < n`, then `xa i` has order 4.
 -/
 @[simp]
@@ -238,7 +259,9 @@ theorem orderOf_xa [NeZero n] (i : ZMod (2 * n)) : orderOf (xa i) = 4 :=
     norm_num at h' 
   · norm_num
 #align quaternion_group.order_of_xa QuaternionGroup.orderOf_xa
+-/
 
+#print QuaternionGroup.quaternionGroup_one_isCyclic /-
 /-- In the special case `n = 1`, `quaternion 1` is a cyclic group (of order `4`). -/
 theorem quaternionGroup_one_isCyclic : IsCyclic (QuaternionGroup 1) :=
   by
@@ -246,7 +269,9 @@ theorem quaternionGroup_one_isCyclic : IsCyclic (QuaternionGroup 1) :=
   rw [card, mul_one]
   exact order_of_xa 0
 #align quaternion_group.quaternion_group_one_is_cyclic QuaternionGroup.quaternionGroup_one_isCyclic
+-/
 
+#print QuaternionGroup.orderOf_a_one /-
 /-- If `0 < n`, then `a 1` has order `2 * n`.
 -/
 @[simp]
@@ -270,7 +295,9 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n :=
   rw [← ZMod.val_eq_zero, ZMod.val_nat_cast, Nat.mod_eq_of_lt h] at h2 
   exact absurd h2.symm (orderOf_pos _).Ne
 #align quaternion_group.order_of_a_one QuaternionGroup.orderOf_a_one
+-/
 
+#print QuaternionGroup.orderOf_a /-
 /-- If `0 < n`, then `a i` has order `(2 * n) / gcd (2 * n) i`.
 -/
 theorem orderOf_a [NeZero n] (i : ZMod (2 * n)) : orderOf (a i) = 2 * n / Nat.gcd (2 * n) i.val :=
@@ -278,7 +305,9 @@ theorem orderOf_a [NeZero n] (i : ZMod (2 * n)) : orderOf (a i) = 2 * n / Nat.gc
   conv_lhs => rw [← ZMod.nat_cast_zmod_val i]
   rw [← a_one_pow, orderOf_pow, order_of_a_one]
 #align quaternion_group.order_of_a QuaternionGroup.orderOf_a
+-/
 
+#print QuaternionGroup.exponent /-
 theorem exponent : Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2 :=
   by
   rw [← normalize_eq 2, ← lcm_mul_left, normalize_eq]
@@ -301,6 +330,7 @@ theorem exponent : Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2 :=
     · convert Monoid.order_dvd_exponent (xa 0)
       exact (order_of_xa 0).symm
 #align quaternion_group.exponent QuaternionGroup.exponent
+-/
 
 end QuaternionGroup

c2092722

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -101,7 +101,6 @@ instance : Group (QuaternionGroup n) where
       -(n : ZMod (2 * n)) = 0 - n := by rw [zero_sub]
       _ = 2 * n - n := by norm_cast; simp
       _ = n := by ring
-      
   one := one
   one_mul := by
     rintro (i | i)

c2092722

bump to nightly-2023-06-08-03

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

8f04dc2b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
 
 ! This file was ported from Lean 3 source module group_theory.specific_groups.quaternion
-! leanprover-community/mathlib commit 879155bff5af618b9062cbb2915347dafd749ad6
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.GroupTheory.SpecificGroups.Cyclic
 /-!
 # Quaternion Groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define the (generalised) quaternion groups `quaternion_group n` of order `4n`, also known as
 dicyclic groups, with elements `a i` and `xa i` for `i : zmod n`. The (generalised) quaternion
 groups can be defined by the presentation

879155bf

bump to nightly-2023-06-06-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

7fcd2dd2

Diff

@@ -49,6 +49,7 @@ Show that `quaternion_group 2 ≃* (quaternion ℤ)ˣ`.
 -/
 
 
+#print QuaternionGroup /-
 /-- The (generalised) quaternion group `quaternion_group n` of order `4n`. It can be defined by the
 presentation $\langle a, x | a^{2n} = 1, x^2 = a^n, x^{-1}ax=a^{-1}\rangle$. We write `a i` for
 $a^i$ and `xa i` for $x * a^i$.
@@ -58,6 +59,7 @@ inductive QuaternionGroup (n : ℕ) : Type
   | xa : ZMod (2 * n) → QuaternionGroup
   deriving DecidableEq
 #align quaternion_group QuaternionGroup
+-/
 
 namespace QuaternionGroup
 
@@ -173,6 +175,7 @@ instance [NeZero n] : Fintype (QuaternionGroup n) :=
 instance : Nontrivial (QuaternionGroup n) :=
   ⟨⟨a 0, xa 0, by decide⟩⟩
 
+#print QuaternionGroup.card /-
 /-- If `0 < n`, then `quaternion_group n` has `4n` elements.
 -/
 theorem card [NeZero n] : Fintype.card (QuaternionGroup n) = 4 * n :=
@@ -180,6 +183,7 @@ theorem card [NeZero n] : Fintype.card (QuaternionGroup n) = 4 * n :=
   rw [← fintype.card_eq.mpr ⟨fintype_helper⟩, Fintype.card_sum, ZMod.card, two_mul]
   ring
 #align quaternion_group.card QuaternionGroup.card
+-/
 
 @[simp]
 theorem a_one_pow (k : ℕ) : (a 1 : QuaternionGroup n) ^ k = a k :=

879155bf

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -225,8 +225,8 @@ theorem orderOf_xa [NeZero n] (i : ZMod (2 * n)) : orderOf (xa i) = 4 :=
   · intro h
     simp only [pow_one, xa_sq] at h 
     injection h with h'
-    apply_fun ZMod.val  at h' 
-    apply_fun (· / n)  at h' 
+    apply_fun ZMod.val at h' 
+    apply_fun (· / n) at h' 
     simp only [ZMod.val_nat_cast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
       Nat.div_self (NeZero.pos n)] at h' 
     norm_num at h'

879155bf

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -223,13 +223,13 @@ theorem orderOf_xa [NeZero n] (i : ZMod (2 * n)) : orderOf (xa i) = 4 :=
   haveI : Fact (Nat.Prime 2) := Fact.mk Nat.prime_two
   apply orderOf_eq_prime_pow
   · intro h
-    simp only [pow_one, xa_sq] at h
+    simp only [pow_one, xa_sq] at h 
     injection h with h'
-    apply_fun ZMod.val  at h'
-    apply_fun (· / n)  at h'
+    apply_fun ZMod.val  at h' 
+    apply_fun (· / n)  at h' 
     simp only [ZMod.val_nat_cast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
-      Nat.div_self (NeZero.pos n)] at h'
-    norm_num at h'
+      Nat.div_self (NeZero.pos n)] at h' 
+    norm_num at h' 
   · norm_num
 #align quaternion_group.order_of_xa QuaternionGroup.orderOf_xa
 
@@ -259,9 +259,9 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n :=
           (orderOf_dvd_of_pow_eq_one (@a_one_pow_n n))).lt_or_eq.resolve_left
   intro h
   have h1 : (a 1 : QuaternionGroup n) ^ orderOf (a 1) = 1 := pow_orderOf_eq_one _
-  rw [a_one_pow] at h1
+  rw [a_one_pow] at h1 
   injection h1 with h2
-  rw [← ZMod.val_eq_zero, ZMod.val_nat_cast, Nat.mod_eq_of_lt h] at h2
+  rw [← ZMod.val_eq_zero, ZMod.val_nat_cast, Nat.mod_eq_of_lt h] at h2 
   exact absurd h2.symm (orderOf_pos _).Ne
 #align quaternion_group.order_of_a_one QuaternionGroup.orderOf_a_one

879155bf

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -94,9 +94,7 @@ instance : Group (QuaternionGroup n) where
     simp only [neg_mul, one_mul, Int.cast_one, zsmul_eq_mul, Int.cast_neg, add_right_inj]
     calc
       -(n : ZMod (2 * n)) = 0 - n := by rw [zero_sub]
-      _ = 2 * n - n := by
-        norm_cast
-        simp
+      _ = 2 * n - n := by norm_cast; simp
       _ = n := by ring
       
   one := one
@@ -164,10 +162,7 @@ def quaternionGroupZeroEquivDihedralGroupZero : QuaternionGroup 0 ≃* DihedralG
     | DihedralGroup.sr j => xa j
   left_inv := by rintro (k | k) <;> rfl
   right_inv := by rintro (k | k) <;> rfl
-  map_mul' := by
-    rintro (k | k) (l | l) <;>
-      · dsimp
-        simp
+  map_mul' := by rintro (k | k) (l | l) <;> · dsimp; simp
 #align quaternion_group.quaternion_group_zero_equiv_dihedral_group_zero QuaternionGroup.quaternionGroupZeroEquivDihedralGroupZero
 
 /-- If `0 < n`, then `quaternion_group n` is a finite group.
@@ -190,8 +185,7 @@ theorem card [NeZero n] : Fintype.card (QuaternionGroup n) = 4 * n :=
 theorem a_one_pow (k : ℕ) : (a 1 : QuaternionGroup n) ^ k = a k :=
   by
   induction' k with k IH
-  · rw [Nat.cast_zero]
-    rfl
+  · rw [Nat.cast_zero]; rfl
   · rw [pow_succ, IH, a_mul_a]
     congr 1
     norm_cast

879155bf

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -70,13 +70,11 @@ private def mul : QuaternionGroup n → QuaternionGroup n → QuaternionGroup n
   | a i, xa j => xa (j - i)
   | xa i, a j => xa (i + j)
   | xa i, xa j => a (n + j - i)
-#align quaternion_group.mul quaternion_group.mul
 
 /-- The identity `1` is given by `aⁱ`.
 -/
 private def one : QuaternionGroup n :=
   a 0
-#align quaternion_group.one quaternion_group.one
 
 instance : Inhabited (QuaternionGroup n) :=
   ⟨one⟩
@@ -86,7 +84,6 @@ instance : Inhabited (QuaternionGroup n) :=
 private def inv : QuaternionGroup n → QuaternionGroup n
   | a i => a (-i)
   | xa i => xa (n + i)
-#align quaternion_group.inv quaternion_group.inv
 
 /-- The group structure on `quaternion_group n`.
 -/
@@ -155,7 +152,6 @@ private def fintype_helper : Sum (ZMod (2 * n)) (ZMod (2 * n)) ≃ QuaternionGro
     | Sum.inr j => xa j
   left_inv := by rintro (x | x) <;> rfl
   right_inv := by rintro (x | x) <;> rfl
-#align quaternion_group.fintype_helper quaternion_group.fintype_helper
 
 /-- The special case that more or less by definition `quaternion_group 0` is isomorphic to the
 infinite dihedral group. -/

879155bf

bump to nightly-2023-03-18-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/02ba8949f486ebecf93fe7460f1ed0564b5e442c

1c3193ff

Diff

@@ -279,7 +279,7 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n :=
 -/
 theorem orderOf_a [NeZero n] (i : ZMod (2 * n)) : orderOf (a i) = 2 * n / Nat.gcd (2 * n) i.val :=
   by
-  conv_lhs => rw [← ZMod.nat_cast_zMod_val i]
+  conv_lhs => rw [← ZMod.nat_cast_zmod_val i]
   rw [← a_one_pow, orderOf_pow, order_of_a_one]
 #align quaternion_group.order_of_a QuaternionGroup.orderOf_a

879155bf

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -258,7 +258,7 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n :=
   by
   cases' eq_zero_or_neZero n with hn hn
   · subst hn
-    simp_rw [mul_zero, orderOf_eq_zero_iff']
+    simp_rw [MulZeroClass.mul_zero, orderOf_eq_zero_iff']
     intro n h
     rw [one_def, a_one_pow]
     apply mt a.inj
@@ -289,7 +289,7 @@ theorem exponent : Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2 :=
   norm_num
   cases' eq_zero_or_neZero n with hn hn
   · subst hn
-    simp only [lcm_zero_left, mul_zero]
+    simp only [lcm_zero_left, MulZeroClass.mul_zero]
     exact Monoid.exponent_eq_zero_of_order_zero order_of_a_one
   apply Nat.dvd_antisymm
   · apply Monoid.exponent_dvd_of_forall_pow_eq_one

879155bf

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

879155bf

chore: refactor to avoid importing Ring for Group topics (#11913)

This is a far from a complete success at the PR title, but it makes a fair bit of progress, and then guards this with appropriate assert_not_exists Ring statements.

It also breaks apart the Mathlib.GroupTheory.Subsemigroup.[Center|Centralizer] files, to pull the Set.center and Set.centralizer declarations into their own files not depending on Subsemigroup.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

8e052acc

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
 -/
 import Mathlib.Data.ZMod.Basic
-import Mathlib.Algebra.Ring.Nat
+import Mathlib.Algebra.Group.Nat
 import Mathlib.Tactic.IntervalCases
 import Mathlib.GroupTheory.SpecificGroups.Dihedral
 import Mathlib.GroupTheory.SpecificGroups.Cyclic

879155bf

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -189,7 +189,7 @@ theorem a_one_pow (k : ℕ) : (a 1 : QuaternionGroup n) ^ k = a k := by
 theorem a_one_pow_n : (a 1 : QuaternionGroup n) ^ (2 * n) = 1 := by
   rw [a_one_pow, one_def]
   congr 1
-  exact ZMod.nat_cast_self _
+  exact ZMod.natCast_self _
 #align quaternion_group.a_one_pow_n QuaternionGroup.a_one_pow_n
 
 @[simp]
@@ -217,7 +217,7 @@ theorem orderOf_xa [NeZero n] (i : ZMod (2 * n)) : orderOf (xa i) = 4 := by
     injection h with h'
     apply_fun ZMod.val at h'
     apply_fun (· / n) at h'
-    simp only [ZMod.val_nat_cast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
+    simp only [ZMod.val_natCast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
       Nat.div_self (NeZero.pos n)] at h'
   · norm_num
 #align quaternion_group.order_of_xa QuaternionGroup.orderOf_xa
@@ -247,7 +247,7 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n := by
   have h1 : (a 1 : QuaternionGroup n) ^ orderOf (a 1) = 1 := pow_orderOf_eq_one _
   rw [a_one_pow] at h1
   injection h1 with h2
-  rw [← ZMod.val_eq_zero, ZMod.val_nat_cast, Nat.mod_eq_of_lt h] at h2
+  rw [← ZMod.val_eq_zero, ZMod.val_natCast, Nat.mod_eq_of_lt h] at h2
   exact absurd h2.symm (orderOf_pos _).ne
 #align quaternion_group.order_of_a_one QuaternionGroup.orderOf_a_one
 
@@ -255,7 +255,7 @@ theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n := by
 -/
 theorem orderOf_a [NeZero n] (i : ZMod (2 * n)) :
     orderOf (a i) = 2 * n / Nat.gcd (2 * n) i.val := by
-  conv_lhs => rw [← ZMod.nat_cast_zmod_val i]
+  conv_lhs => rw [← ZMod.natCast_zmod_val i]
   rw [← a_one_pow, orderOf_pow, orderOf_a_one]
 #align quaternion_group.order_of_a QuaternionGroup.orderOf_a

879155bf

chore: Split Data.{Nat,Int}{.Order}.Basic in group vs ring instances (#11924)

Scatter the content of Data.Nat.Basic across:

Data.Nat.Defs for the lemmas having no dependencies
Algebra.Group.Nat for the monoid instances and the few miscellaneous lemmas needing them.
Algebra.Ring.Nat for the semiring instance and the few miscellaneous lemmas following it.

Similarly, scatter

Data.Int.Basic across Data.Int.Defs, Algebra.Group.Int, Algebra.Ring.Int
Data.Nat.Order.Basic across Data.Nat.Defs, Algebra.Order.Group.Nat, Algebra.Order.Ring.Nat
Data.Int.Order.Basic across Data.Int.Defs, Algebra.Order.Group.Int, Algebra.Order.Ring.Int

Also move a few lemmas from Data.Nat.Order.Lemmas to Data.Nat.Defs.

Before pre_11924

After post_11924

47062a71

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
 -/
 import Mathlib.Data.ZMod.Basic
-import Mathlib.Data.Nat.Basic
+import Mathlib.Algebra.Ring.Nat
 import Mathlib.Tactic.IntervalCases
 import Mathlib.GroupTheory.SpecificGroups.Dihedral
 import Mathlib.GroupTheory.SpecificGroups.Cyclic

879155bf

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -183,7 +183,6 @@ theorem a_one_pow (k : ℕ) : (a 1 : QuaternionGroup n) ^ k = a k := by
   · rw [pow_succ, IH, a_mul_a]
     congr 1
     norm_cast
-    rw [Nat.one_add]
 #align quaternion_group.a_one_pow QuaternionGroup.a_one_pow
 
 -- @[simp] -- Porting note: simp changes this to `a 0 = 1`, so this is no longer a good simp lemma.
@@ -199,8 +198,8 @@ theorem xa_sq (i : ZMod (2 * n)) : xa i ^ 2 = a n := by simp [sq]
 
 @[simp]
 theorem xa_pow_four (i : ZMod (2 * n)) : xa i ^ 4 = 1 := by
-  rw [pow_succ, pow_succ, sq, xa_mul_xa, xa_mul_a, xa_mul_xa, add_sub_cancel_right, add_sub_assoc,
-    add_sub_cancel_left]
+  rw [pow_succ, pow_succ, sq, xa_mul_xa, a_mul_xa, xa_mul_xa,
+    add_sub_cancel_right, add_sub_assoc, sub_sub_cancel]
   norm_cast
   rw [← two_mul]
   simp [one_def]

879155bf

chore: Rename mul-div cancellation lemmas (#11530)

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

4ea4a86a

Diff

@@ -199,8 +199,8 @@ theorem xa_sq (i : ZMod (2 * n)) : xa i ^ 2 = a n := by simp [sq]
 
 @[simp]
 theorem xa_pow_four (i : ZMod (2 * n)) : xa i ^ 4 = 1 := by
-  rw [pow_succ, pow_succ, sq, xa_mul_xa, xa_mul_a, xa_mul_xa, add_sub_cancel, add_sub_assoc,
-    add_sub_cancel']
+  rw [pow_succ, pow_succ, sq, xa_mul_xa, xa_mul_a, xa_mul_xa, add_sub_cancel_right, add_sub_assoc,
+    add_sub_cancel_left]
   norm_cast
   rw [← two_mul]
   simp [one_def]

879155bf

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -262,6 +262,7 @@ theorem orderOf_a [NeZero n] (i : ZMod (2 * n)) :
 
 theorem exponent : Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2 := by
   rw [← normalize_eq 2, ← lcm_mul_left, normalize_eq]
+  set_option tactic.skipAssignedInstances false in
   norm_num
   cases' eq_zero_or_neZero n with hn hn
   · subst hn

879155bf

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -236,7 +236,7 @@ theorem quaternionGroup_one_isCyclic : IsCyclic (QuaternionGroup 1) := by
 theorem orderOf_a_one : orderOf (a 1 : QuaternionGroup n) = 2 * n := by
   cases' eq_zero_or_neZero n with hn hn
   · subst hn
-    simp_rw [MulZeroClass.mul_zero, orderOf_eq_zero_iff']
+    simp_rw [mul_zero, orderOf_eq_zero_iff']
     intro n h
     rw [one_def, a_one_pow]
     apply mt a.inj
@@ -265,7 +265,7 @@ theorem exponent : Monoid.exponent (QuaternionGroup n) = 2 * lcm n 2 := by
   norm_num
   cases' eq_zero_or_neZero n with hn hn
   · subst hn
-    simp only [lcm_zero_left, MulZeroClass.mul_zero]
+    simp only [lcm_zero_left, mul_zero]
     exact Monoid.exponent_eq_zero_of_order_zero orderOf_a_one
   apply Nat.dvd_antisymm
   · apply Monoid.exponent_dvd_of_forall_pow_eq_one

879155bf

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Julian Kuelshammer. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Julian Kuelshammer
-
-! This file was ported from Lean 3 source module group_theory.specific_groups.quaternion
-! leanprover-community/mathlib commit 879155bff5af618b9062cbb2915347dafd749ad6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.ZMod.Basic
 import Mathlib.Data.Nat.Basic
@@ -14,6 +9,8 @@ import Mathlib.Tactic.IntervalCases
 import Mathlib.GroupTheory.SpecificGroups.Dihedral
 import Mathlib.GroupTheory.SpecificGroups.Cyclic
 
+#align_import group_theory.specific_groups.quaternion from "leanprover-community/mathlib"@"879155bff5af618b9062cbb2915347dafd749ad6"
+
 /-!
 # Quaternion Groups

879155bf

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -219,8 +219,8 @@ theorem orderOf_xa [NeZero n] (i : ZMod (2 * n)) : orderOf (xa i) = 4 := by
   · intro h
     simp only [pow_one, xa_sq] at h
     injection h with h'
-    apply_fun ZMod.val  at h'
-    apply_fun (· / n)  at h'
+    apply_fun ZMod.val at h'
+    apply_fun (· / n) at h'
     simp only [ZMod.val_nat_cast, ZMod.val_zero, Nat.zero_div, Nat.mod_mul_left_div_self,
       Nat.div_self (NeZero.pos n)] at h'
   · norm_num

879155bf

feat: port GroupTheory.SpecificGroups.Quaternion (#4448)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

cdb1b898

`group_theory.specific_groups.quaternion` ⟷ `Mathlib.GroupTheory.SpecificGroups.Quaternion`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 524

group_theory.specific_groups.quaternion ⟷ Mathlib.GroupTheory.SpecificGroups.Quaternion

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 524

`group_theory.specific_groups.quaternion` ⟷ `Mathlib.GroupTheory.SpecificGroups.Quaternion`