set_theory.surreal.dyadic ⟷ Mathlib.SetTheory.Surreal.Dyadic

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

@@ -251,7 +251,7 @@ theorem nsmul_pow_two_powHalf (n : ℕ) : 2 ^ n • powHalf n = 1 :=
   · simp only [nsmul_one, pow_half_zero, Nat.cast_one, pow_zero]
   ·
     rw [← hn, ← double_pow_half_succ_eq_pow_half n, smul_smul (2 ^ n) 2 (pow_half n.succ), mul_comm,
-      pow_succ]
+      pow_succ']
 #align surreal.nsmul_pow_two_pow_half Surreal.nsmul_pow_two_powHalf
 -/
 

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

@@ -264,7 +264,7 @@ theorem nsmul_pow_two_powHalf' (n k : ℕ) : 2 ^ n • powHalf (n + k) = powHalf
     simp only [add_zero, Surreal.nsmul_pow_two_powHalf, Nat.zero_eq, eq_self_iff_true,
       Surreal.powHalf_zero]
   · rw [← double_pow_half_succ_eq_pow_half (n + k), ← double_pow_half_succ_eq_pow_half k,
-      smul_algebra_smul_comm] at hk 
+      smul_algebra_smul_comm] at hk
     rwa [← zsmul_eq_zsmul_iff' two_ne_zero]
 #align surreal.nsmul_pow_two_pow_half' Surreal.nsmul_pow_two_powHalf'
 -/
@@ -287,11 +287,11 @@ theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ =
   · intro m₁ m₂ aux; exact (this (le_of_not_le h) aux.symm).symm
   intro m₁ m₂ h₂
   obtain ⟨c, rfl⟩ := le_iff_exists_add.mp h
-  rw [add_comm, pow_add, ← mul_assoc, mul_eq_mul_right_iff] at h₂ 
+  rw [add_comm, pow_add, ← mul_assoc, mul_eq_mul_right_iff] at h₂
   cases h₂
   · rw [h₂, add_comm, zsmul_pow_two_pow_half m₂ c y₁]
   · have := Nat.one_le_pow y₁ 2 Nat.succ_pos'
-    norm_cast at h₂ ; linarith
+    norm_cast at h₂; linarith
 #align surreal.dyadic_aux Surreal.dyadic_aux
 -/
 
@@ -304,7 +304,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
       by
       intro m₁ m₂ n₁ n₂ h₁
       obtain ⟨⟨n₃, y₃, hn₃⟩, h₂⟩ := localization.r_iff_exists.mp h₁
-      simp only [Subtype.coe_mk, mul_eq_mul_left_iff] at h₂ 
+      simp only [Subtype.coe_mk, mul_eq_mul_left_iff] at h₂
       cases h₂
       · simp only
         obtain ⟨a₁, ha₁⟩ := n₁.prop
@@ -324,7 +324,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
       rintro ⟨a, ⟨b, ⟨b', rfl⟩⟩⟩ ⟨c, ⟨d, ⟨d', rfl⟩⟩⟩
       have h₂ : 1 < (2 : ℤ).natAbs := one_lt_two
       have hpow₂ := Submonoid.log_pow_int_eq_self h₂
-      simp_rw [Submonoid.pow_apply] at hpow₂ 
+      simp_rw [Submonoid.pow_apply] at hpow₂
       simp_rw [Localization.add_mk, Localization.liftOn_mk, Subtype.coe_mk,
         Submonoid.log_mul (Int.pow_right_injective h₂), hpow₂]
       calc

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Apurva Nakade. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Apurva Nakade
 -/
-import Mathbin.Algebra.Algebra.Basic
-import Mathbin.SetTheory.Game.Birthday
-import Mathbin.SetTheory.Surreal.Basic
-import Mathbin.RingTheory.Localization.Basic
+import Algebra.Algebra.Basic
+import SetTheory.Game.Birthday
+import SetTheory.Surreal.Basic
+import RingTheory.Localization.Basic
 
 #align_import set_theory.surreal.dyadic from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
 

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

@@ -32,136 +32,145 @@ rational numbers to construct an ordered field embedding of ℝ into `surreal`.
 
 universe u
 
-local infixl:0 " ≈ " => PGame.Equiv
+local infixl:0 " ≈ " => SetTheory.PGame.Equiv
 
-namespace PGame
+namespace SetTheory.PGame
 
-#print PGame.powHalf /-
+#print SetTheory.PGame.powHalf /-
 /-- For a natural number `n`, the pre-game `pow_half (n + 1)` is recursively defined as
 `{0 | pow_half n}`. These are the explicit expressions of powers of `1 / 2`. By definition, we have
 `pow_half 0 = 1` and `pow_half 1 ≈ 1 / 2` and we prove later on that
 `pow_half (n + 1) + pow_half (n + 1) ≈ pow_half n`. -/
-def powHalf : ℕ → PGame
+def SetTheory.PGame.powHalf : ℕ → SetTheory.PGame
   | 0 => 1
   | n + 1 => ⟨PUnit, PUnit, 0, fun _ => pow_half n⟩
-#align pgame.pow_half PGame.powHalf
+#align pgame.pow_half SetTheory.PGame.powHalf
 -/
 
-#print PGame.powHalf_zero /-
+#print SetTheory.PGame.powHalf_zero /-
 @[simp]
-theorem powHalf_zero : powHalf 0 = 1 :=
+theorem SetTheory.PGame.powHalf_zero : SetTheory.PGame.powHalf 0 = 1 :=
   rfl
-#align pgame.pow_half_zero PGame.powHalf_zero
+#align pgame.pow_half_zero SetTheory.PGame.powHalf_zero
 -/
 
-#print PGame.powHalf_leftMoves /-
-theorem powHalf_leftMoves (n) : (powHalf n).LeftMoves = PUnit := by cases n <;> rfl
-#align pgame.pow_half_left_moves PGame.powHalf_leftMoves
+#print SetTheory.PGame.powHalf_leftMoves /-
+theorem SetTheory.PGame.powHalf_leftMoves (n) : (SetTheory.PGame.powHalf n).LeftMoves = PUnit := by
+  cases n <;> rfl
+#align pgame.pow_half_left_moves SetTheory.PGame.powHalf_leftMoves
 -/
 
-#print PGame.powHalf_zero_rightMoves /-
-theorem powHalf_zero_rightMoves : (powHalf 0).RightMoves = PEmpty :=
+#print SetTheory.PGame.powHalf_zero_rightMoves /-
+theorem SetTheory.PGame.powHalf_zero_rightMoves : (SetTheory.PGame.powHalf 0).RightMoves = PEmpty :=
   rfl
-#align pgame.pow_half_zero_right_moves PGame.powHalf_zero_rightMoves
+#align pgame.pow_half_zero_right_moves SetTheory.PGame.powHalf_zero_rightMoves
 -/
 
-#print PGame.powHalf_succ_rightMoves /-
-theorem powHalf_succ_rightMoves (n) : (powHalf (n + 1)).RightMoves = PUnit :=
+#print SetTheory.PGame.powHalf_succ_rightMoves /-
+theorem SetTheory.PGame.powHalf_succ_rightMoves (n) :
+    (SetTheory.PGame.powHalf (n + 1)).RightMoves = PUnit :=
   rfl
-#align pgame.pow_half_succ_right_moves PGame.powHalf_succ_rightMoves
+#align pgame.pow_half_succ_right_moves SetTheory.PGame.powHalf_succ_rightMoves
 -/
 
-#print PGame.powHalf_moveLeft /-
+#print SetTheory.PGame.powHalf_moveLeft /-
 @[simp]
-theorem powHalf_moveLeft (n i) : (powHalf n).moveLeft i = 0 := by cases n <;> cases i <;> rfl
-#align pgame.pow_half_move_left PGame.powHalf_moveLeft
+theorem SetTheory.PGame.powHalf_moveLeft (n i) : (SetTheory.PGame.powHalf n).moveLeft i = 0 := by
+  cases n <;> cases i <;> rfl
+#align pgame.pow_half_move_left SetTheory.PGame.powHalf_moveLeft
 -/
 
-#print PGame.powHalf_succ_moveRight /-
+#print SetTheory.PGame.powHalf_succ_moveRight /-
 @[simp]
-theorem powHalf_succ_moveRight (n i) : (powHalf (n + 1)).moveRight i = powHalf n :=
+theorem SetTheory.PGame.powHalf_succ_moveRight (n i) :
+    (SetTheory.PGame.powHalf (n + 1)).moveRight i = SetTheory.PGame.powHalf n :=
   rfl
-#align pgame.pow_half_succ_move_right PGame.powHalf_succ_moveRight
+#align pgame.pow_half_succ_move_right SetTheory.PGame.powHalf_succ_moveRight
 -/
 
-#print PGame.uniquePowHalfLeftMoves /-
-instance uniquePowHalfLeftMoves (n) : Unique (powHalf n).LeftMoves := by
-  cases n <;> exact PUnit.unique
-#align pgame.unique_pow_half_left_moves PGame.uniquePowHalfLeftMoves
+#print SetTheory.PGame.uniquePowHalfLeftMoves /-
+instance SetTheory.PGame.uniquePowHalfLeftMoves (n) :
+    Unique (SetTheory.PGame.powHalf n).LeftMoves := by cases n <;> exact PUnit.unique
+#align pgame.unique_pow_half_left_moves SetTheory.PGame.uniquePowHalfLeftMoves
 -/
 
-#print PGame.isEmpty_powHalf_zero_rightMoves /-
-instance isEmpty_powHalf_zero_rightMoves : IsEmpty (powHalf 0).RightMoves :=
+#print SetTheory.PGame.isEmpty_powHalf_zero_rightMoves /-
+instance SetTheory.PGame.isEmpty_powHalf_zero_rightMoves :
+    IsEmpty (SetTheory.PGame.powHalf 0).RightMoves :=
   PEmpty.isEmpty
-#align pgame.is_empty_pow_half_zero_right_moves PGame.isEmpty_powHalf_zero_rightMoves
+#align pgame.is_empty_pow_half_zero_right_moves SetTheory.PGame.isEmpty_powHalf_zero_rightMoves
 -/
 
-#print PGame.uniquePowHalfSuccRightMoves /-
-instance uniquePowHalfSuccRightMoves (n) : Unique (powHalf (n + 1)).RightMoves :=
+#print SetTheory.PGame.uniquePowHalfSuccRightMoves /-
+instance SetTheory.PGame.uniquePowHalfSuccRightMoves (n) :
+    Unique (SetTheory.PGame.powHalf (n + 1)).RightMoves :=
   PUnit.unique
-#align pgame.unique_pow_half_succ_right_moves PGame.uniquePowHalfSuccRightMoves
+#align pgame.unique_pow_half_succ_right_moves SetTheory.PGame.uniquePowHalfSuccRightMoves
 -/
 
-#print PGame.birthday_half /-
+#print SetTheory.PGame.birthday_half /-
 @[simp]
-theorem birthday_half : birthday (powHalf 1) = 2 := by rw [birthday_def]; dsimp;
-  simpa using Order.le_succ (1 : Ordinal)
-#align pgame.birthday_half PGame.birthday_half
+theorem SetTheory.PGame.birthday_half : SetTheory.PGame.birthday (SetTheory.PGame.powHalf 1) = 2 :=
+  by rw [birthday_def]; dsimp; simpa using Order.le_succ (1 : Ordinal)
+#align pgame.birthday_half SetTheory.PGame.birthday_half
 -/
 
-#print PGame.numeric_powHalf /-
+#print SetTheory.PGame.numeric_powHalf /-
 /-- For all natural numbers `n`, the pre-games `pow_half n` are numeric. -/
-theorem numeric_powHalf (n) : (powHalf n).Numeric :=
+theorem SetTheory.PGame.numeric_powHalf (n) : (SetTheory.PGame.powHalf n).Numeric :=
   by
   induction' n with n hn
   · exact numeric_one
   · constructor
     · simpa using hn.move_left_lt default
     · exact ⟨fun _ => numeric_zero, fun _ => hn⟩
-#align pgame.numeric_pow_half PGame.numeric_powHalf
+#align pgame.numeric_pow_half SetTheory.PGame.numeric_powHalf
 -/
 
-#print PGame.powHalf_succ_lt_powHalf /-
-theorem powHalf_succ_lt_powHalf (n : ℕ) : powHalf (n + 1) < powHalf n :=
-  (numeric_powHalf (n + 1)).lt_moveRight default
-#align pgame.pow_half_succ_lt_pow_half PGame.powHalf_succ_lt_powHalf
+#print SetTheory.PGame.powHalf_succ_lt_powHalf /-
+theorem SetTheory.PGame.powHalf_succ_lt_powHalf (n : ℕ) :
+    SetTheory.PGame.powHalf (n + 1) < SetTheory.PGame.powHalf n :=
+  (SetTheory.PGame.numeric_powHalf (n + 1)).lt_moveRight default
+#align pgame.pow_half_succ_lt_pow_half SetTheory.PGame.powHalf_succ_lt_powHalf
 -/
 
-#print PGame.powHalf_succ_le_powHalf /-
-theorem powHalf_succ_le_powHalf (n : ℕ) : powHalf (n + 1) ≤ powHalf n :=
-  (powHalf_succ_lt_powHalf n).le
-#align pgame.pow_half_succ_le_pow_half PGame.powHalf_succ_le_powHalf
+#print SetTheory.PGame.powHalf_succ_le_powHalf /-
+theorem SetTheory.PGame.powHalf_succ_le_powHalf (n : ℕ) :
+    SetTheory.PGame.powHalf (n + 1) ≤ SetTheory.PGame.powHalf n :=
+  (SetTheory.PGame.powHalf_succ_lt_powHalf n).le
+#align pgame.pow_half_succ_le_pow_half SetTheory.PGame.powHalf_succ_le_powHalf
 -/
 
-#print PGame.powHalf_le_one /-
-theorem powHalf_le_one (n : ℕ) : powHalf n ≤ 1 :=
+#print SetTheory.PGame.powHalf_le_one /-
+theorem SetTheory.PGame.powHalf_le_one (n : ℕ) : SetTheory.PGame.powHalf n ≤ 1 :=
   by
   induction' n with n hn
   · exact le_rfl
   · exact (pow_half_succ_le_pow_half n).trans hn
-#align pgame.pow_half_le_one PGame.powHalf_le_one
+#align pgame.pow_half_le_one SetTheory.PGame.powHalf_le_one
 -/
 
-#print PGame.powHalf_succ_lt_one /-
-theorem powHalf_succ_lt_one (n : ℕ) : powHalf (n + 1) < 1 :=
-  (powHalf_succ_lt_powHalf n).trans_le <| powHalf_le_one n
-#align pgame.pow_half_succ_lt_one PGame.powHalf_succ_lt_one
+#print SetTheory.PGame.powHalf_succ_lt_one /-
+theorem SetTheory.PGame.powHalf_succ_lt_one (n : ℕ) : SetTheory.PGame.powHalf (n + 1) < 1 :=
+  (SetTheory.PGame.powHalf_succ_lt_powHalf n).trans_le <| SetTheory.PGame.powHalf_le_one n
+#align pgame.pow_half_succ_lt_one SetTheory.PGame.powHalf_succ_lt_one
 -/
 
-#print PGame.powHalf_pos /-
-theorem powHalf_pos (n : ℕ) : 0 < powHalf n := by
+#print SetTheory.PGame.powHalf_pos /-
+theorem SetTheory.PGame.powHalf_pos (n : ℕ) : 0 < SetTheory.PGame.powHalf n := by
   rw [← lf_iff_lt numeric_zero (numeric_pow_half n), zero_lf_le]; simp
-#align pgame.pow_half_pos PGame.powHalf_pos
+#align pgame.pow_half_pos SetTheory.PGame.powHalf_pos
 -/
 
-#print PGame.zero_le_powHalf /-
-theorem zero_le_powHalf (n : ℕ) : 0 ≤ powHalf n :=
-  (powHalf_pos n).le
-#align pgame.zero_le_pow_half PGame.zero_le_powHalf
+#print SetTheory.PGame.zero_le_powHalf /-
+theorem SetTheory.PGame.zero_le_powHalf (n : ℕ) : 0 ≤ SetTheory.PGame.powHalf n :=
+  (SetTheory.PGame.powHalf_pos n).le
+#align pgame.zero_le_pow_half SetTheory.PGame.zero_le_powHalf
 -/
 
-#print PGame.add_powHalf_succ_self_eq_powHalf /-
-theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1) ≈ powHalf n :=
+#print SetTheory.PGame.add_powHalf_succ_self_eq_powHalf /-
+theorem SetTheory.PGame.add_powHalf_succ_self_eq_powHalf (n) :
+    SetTheory.PGame.powHalf (n + 1) + SetTheory.PGame.powHalf (n + 1) ≈ SetTheory.PGame.powHalf n :=
   by
   induction' n using Nat.strong_induction_on with n hn
   · constructor <;> rw [le_iff_forall_lf] <;> constructor
@@ -197,25 +206,26 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
         calc
           pow_half n ≈ 0 + pow_half n := (zero_add_equiv _).symm
           _ < pow_half n.succ + pow_half n := add_lt_add_right (pow_half_pos _) _
-#align pgame.add_pow_half_succ_self_eq_pow_half PGame.add_powHalf_succ_self_eq_powHalf
+#align pgame.add_pow_half_succ_self_eq_pow_half SetTheory.PGame.add_powHalf_succ_self_eq_powHalf
 -/
 
-#print PGame.half_add_half_equiv_one /-
-theorem half_add_half_equiv_one : powHalf 1 + powHalf 1 ≈ 1 :=
-  add_powHalf_succ_self_eq_powHalf 0
-#align pgame.half_add_half_equiv_one PGame.half_add_half_equiv_one
+#print SetTheory.PGame.half_add_half_equiv_one /-
+theorem SetTheory.PGame.half_add_half_equiv_one :
+    SetTheory.PGame.powHalf 1 + SetTheory.PGame.powHalf 1 ≈ 1 :=
+  SetTheory.PGame.add_powHalf_succ_self_eq_powHalf 0
+#align pgame.half_add_half_equiv_one SetTheory.PGame.half_add_half_equiv_one
 -/
 
-end PGame
+end SetTheory.PGame
 
 namespace Surreal
 
-open PGame
+open SetTheory.PGame
 
 #print Surreal.powHalf /-
 /-- Powers of the surreal number `half`. -/
 def powHalf (n : ℕ) : Surreal :=
-  ⟦⟨PGame.powHalf n, PGame.numeric_powHalf n⟩⟧
+  ⟦⟨SetTheory.PGame.powHalf n, SetTheory.PGame.numeric_powHalf n⟩⟧
 #align surreal.pow_half Surreal.powHalf
 -/
 
@@ -229,7 +239,7 @@ theorem powHalf_zero : powHalf 0 = 1 :=
 #print Surreal.double_powHalf_succ_eq_powHalf /-
 @[simp]
 theorem double_powHalf_succ_eq_powHalf (n : ℕ) : 2 • powHalf n.succ = powHalf n := by
-  rw [two_nsmul]; exact Quotient.sound (PGame.add_powHalf_succ_self_eq_powHalf n)
+  rw [two_nsmul]; exact Quotient.sound (SetTheory.PGame.add_powHalf_succ_self_eq_powHalf n)
 #align surreal.double_pow_half_succ_eq_pow_half Surreal.double_powHalf_succ_eq_powHalf
 -/
 

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Apurva Nakade. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Apurva Nakade
-
-! This file was ported from Lean 3 source module set_theory.surreal.dyadic
-! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Algebra.Basic
 import Mathbin.SetTheory.Game.Birthday
 import Mathbin.SetTheory.Surreal.Basic
 import Mathbin.RingTheory.Localization.Basic
 
+#align_import set_theory.surreal.dyadic from "leanprover-community/mathlib"@"d0b1936853671209a866fa35b9e54949c81116e2"
+
 /-!
 # Dyadic numbers
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/728ef9dbb281241906f25cbeb30f90d83e0bb451

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Apurva Nakade
 
 ! This file was ported from Lean 3 source module set_theory.surreal.dyadic
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit d0b1936853671209a866fa35b9e54949c81116e2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Localization.Basic
 
 /-!
 # Dyadic numbers
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 Dyadic numbers are obtained by localizing ℤ away from 2. They are the initial object in the category
 of rings with no 2-torsion.
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b981918a93bc45a8600de608cde7944a80d92b9

@@ -36,6 +36,7 @@ local infixl:0 " ≈ " => PGame.Equiv
 
 namespace PGame
 
+#print PGame.powHalf /-
 /-- For a natural number `n`, the pre-game `pow_half (n + 1)` is recursively defined as
 `{0 | pow_half n}`. These are the explicit expressions of powers of `1 / 2`. By definition, we have
 `pow_half 0 = 1` and `pow_half 1 ≈ 1 / 2` and we prove later on that
@@ -44,49 +45,71 @@ def powHalf : ℕ → PGame
   | 0 => 1
   | n + 1 => ⟨PUnit, PUnit, 0, fun _ => pow_half n⟩
 #align pgame.pow_half PGame.powHalf
+-/
 
+#print PGame.powHalf_zero /-
 @[simp]
 theorem powHalf_zero : powHalf 0 = 1 :=
   rfl
 #align pgame.pow_half_zero PGame.powHalf_zero
+-/
 
+#print PGame.powHalf_leftMoves /-
 theorem powHalf_leftMoves (n) : (powHalf n).LeftMoves = PUnit := by cases n <;> rfl
 #align pgame.pow_half_left_moves PGame.powHalf_leftMoves
+-/
 
+#print PGame.powHalf_zero_rightMoves /-
 theorem powHalf_zero_rightMoves : (powHalf 0).RightMoves = PEmpty :=
   rfl
 #align pgame.pow_half_zero_right_moves PGame.powHalf_zero_rightMoves
+-/
 
+#print PGame.powHalf_succ_rightMoves /-
 theorem powHalf_succ_rightMoves (n) : (powHalf (n + 1)).RightMoves = PUnit :=
   rfl
 #align pgame.pow_half_succ_right_moves PGame.powHalf_succ_rightMoves
+-/
 
+#print PGame.powHalf_moveLeft /-
 @[simp]
 theorem powHalf_moveLeft (n i) : (powHalf n).moveLeft i = 0 := by cases n <;> cases i <;> rfl
 #align pgame.pow_half_move_left PGame.powHalf_moveLeft
+-/
 
+#print PGame.powHalf_succ_moveRight /-
 @[simp]
 theorem powHalf_succ_moveRight (n i) : (powHalf (n + 1)).moveRight i = powHalf n :=
   rfl
 #align pgame.pow_half_succ_move_right PGame.powHalf_succ_moveRight
+-/
 
+#print PGame.uniquePowHalfLeftMoves /-
 instance uniquePowHalfLeftMoves (n) : Unique (powHalf n).LeftMoves := by
   cases n <;> exact PUnit.unique
 #align pgame.unique_pow_half_left_moves PGame.uniquePowHalfLeftMoves
+-/
 
+#print PGame.isEmpty_powHalf_zero_rightMoves /-
 instance isEmpty_powHalf_zero_rightMoves : IsEmpty (powHalf 0).RightMoves :=
   PEmpty.isEmpty
 #align pgame.is_empty_pow_half_zero_right_moves PGame.isEmpty_powHalf_zero_rightMoves
+-/
 
+#print PGame.uniquePowHalfSuccRightMoves /-
 instance uniquePowHalfSuccRightMoves (n) : Unique (powHalf (n + 1)).RightMoves :=
   PUnit.unique
 #align pgame.unique_pow_half_succ_right_moves PGame.uniquePowHalfSuccRightMoves
+-/
 
+#print PGame.birthday_half /-
 @[simp]
 theorem birthday_half : birthday (powHalf 1) = 2 := by rw [birthday_def]; dsimp;
   simpa using Order.le_succ (1 : Ordinal)
 #align pgame.birthday_half PGame.birthday_half
+-/
 
+#print PGame.numeric_powHalf /-
 /-- For all natural numbers `n`, the pre-games `pow_half n` are numeric. -/
 theorem numeric_powHalf (n) : (powHalf n).Numeric :=
   by
@@ -96,34 +119,48 @@ theorem numeric_powHalf (n) : (powHalf n).Numeric :=
     · simpa using hn.move_left_lt default
     · exact ⟨fun _ => numeric_zero, fun _ => hn⟩
 #align pgame.numeric_pow_half PGame.numeric_powHalf
+-/
 
+#print PGame.powHalf_succ_lt_powHalf /-
 theorem powHalf_succ_lt_powHalf (n : ℕ) : powHalf (n + 1) < powHalf n :=
   (numeric_powHalf (n + 1)).lt_moveRight default
 #align pgame.pow_half_succ_lt_pow_half PGame.powHalf_succ_lt_powHalf
+-/
 
+#print PGame.powHalf_succ_le_powHalf /-
 theorem powHalf_succ_le_powHalf (n : ℕ) : powHalf (n + 1) ≤ powHalf n :=
   (powHalf_succ_lt_powHalf n).le
 #align pgame.pow_half_succ_le_pow_half PGame.powHalf_succ_le_powHalf
+-/
 
+#print PGame.powHalf_le_one /-
 theorem powHalf_le_one (n : ℕ) : powHalf n ≤ 1 :=
   by
   induction' n with n hn
   · exact le_rfl
   · exact (pow_half_succ_le_pow_half n).trans hn
 #align pgame.pow_half_le_one PGame.powHalf_le_one
+-/
 
+#print PGame.powHalf_succ_lt_one /-
 theorem powHalf_succ_lt_one (n : ℕ) : powHalf (n + 1) < 1 :=
   (powHalf_succ_lt_powHalf n).trans_le <| powHalf_le_one n
 #align pgame.pow_half_succ_lt_one PGame.powHalf_succ_lt_one
+-/
 
+#print PGame.powHalf_pos /-
 theorem powHalf_pos (n : ℕ) : 0 < powHalf n := by
   rw [← lf_iff_lt numeric_zero (numeric_pow_half n), zero_lf_le]; simp
 #align pgame.pow_half_pos PGame.powHalf_pos
+-/
 
+#print PGame.zero_le_powHalf /-
 theorem zero_le_powHalf (n : ℕ) : 0 ≤ powHalf n :=
   (powHalf_pos n).le
 #align pgame.zero_le_pow_half PGame.zero_le_powHalf
+-/
 
+#print PGame.add_powHalf_succ_self_eq_powHalf /-
 theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1) ≈ powHalf n :=
   by
   induction' n using Nat.strong_induction_on with n hn
@@ -161,10 +198,13 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
           pow_half n ≈ 0 + pow_half n := (zero_add_equiv _).symm
           _ < pow_half n.succ + pow_half n := add_lt_add_right (pow_half_pos _) _
 #align pgame.add_pow_half_succ_self_eq_pow_half PGame.add_powHalf_succ_self_eq_powHalf
+-/
 
+#print PGame.half_add_half_equiv_one /-
 theorem half_add_half_equiv_one : powHalf 1 + powHalf 1 ≈ 1 :=
   add_powHalf_succ_self_eq_powHalf 0
 #align pgame.half_add_half_equiv_one PGame.half_add_half_equiv_one
+-/
 
 end PGame
 
@@ -172,21 +212,28 @@ namespace Surreal
 
 open PGame
 
+#print Surreal.powHalf /-
 /-- Powers of the surreal number `half`. -/
 def powHalf (n : ℕ) : Surreal :=
   ⟦⟨PGame.powHalf n, PGame.numeric_powHalf n⟩⟧
 #align surreal.pow_half Surreal.powHalf
+-/
 
+#print Surreal.powHalf_zero /-
 @[simp]
 theorem powHalf_zero : powHalf 0 = 1 :=
   rfl
 #align surreal.pow_half_zero Surreal.powHalf_zero
+-/
 
+#print Surreal.double_powHalf_succ_eq_powHalf /-
 @[simp]
 theorem double_powHalf_succ_eq_powHalf (n : ℕ) : 2 • powHalf n.succ = powHalf n := by
   rw [two_nsmul]; exact Quotient.sound (PGame.add_powHalf_succ_self_eq_powHalf n)
 #align surreal.double_pow_half_succ_eq_pow_half Surreal.double_powHalf_succ_eq_powHalf
+-/
 
+#print Surreal.nsmul_pow_two_powHalf /-
 @[simp]
 theorem nsmul_pow_two_powHalf (n : ℕ) : 2 ^ n • powHalf n = 1 :=
   by
@@ -196,9 +243,11 @@ theorem nsmul_pow_two_powHalf (n : ℕ) : 2 ^ n • powHalf n = 1 :=
     rw [← hn, ← double_pow_half_succ_eq_pow_half n, smul_smul (2 ^ n) 2 (pow_half n.succ), mul_comm,
       pow_succ]
 #align surreal.nsmul_pow_two_pow_half Surreal.nsmul_pow_two_powHalf
+-/
 
+#print Surreal.nsmul_pow_two_powHalf' /-
 @[simp]
-theorem nsmul_pow_two_pow_half' (n k : ℕ) : 2 ^ n • powHalf (n + k) = powHalf k :=
+theorem nsmul_pow_two_powHalf' (n k : ℕ) : 2 ^ n • powHalf (n + k) = powHalf k :=
   by
   induction' k with k hk
   ·
@@ -207,8 +256,10 @@ theorem nsmul_pow_two_pow_half' (n k : ℕ) : 2 ^ n • powHalf (n + k) = powHal
   · rw [← double_pow_half_succ_eq_pow_half (n + k), ← double_pow_half_succ_eq_pow_half k,
       smul_algebra_smul_comm] at hk 
     rwa [← zsmul_eq_zsmul_iff' two_ne_zero]
-#align surreal.nsmul_pow_two_pow_half' Surreal.nsmul_pow_two_pow_half'
+#align surreal.nsmul_pow_two_pow_half' Surreal.nsmul_pow_two_powHalf'
+-/
 
+#print Surreal.zsmul_pow_two_powHalf /-
 theorem zsmul_pow_two_powHalf (m : ℤ) (n k : ℕ) : (m * 2 ^ n) • powHalf (n + k) = m • powHalf k :=
   by
   rw [mul_zsmul]
@@ -216,7 +267,9 @@ theorem zsmul_pow_two_powHalf (m : ℤ) (n k : ℕ) : (m * 2 ^ n) • powHalf (n
   norm_cast
   exact nsmul_pow_two_pow_half' n k
 #align surreal.zsmul_pow_two_pow_half Surreal.zsmul_pow_two_powHalf
+-/
 
+#print Surreal.dyadic_aux /-
 theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ = m₂ * 2 ^ y₂) :
     m₁ • powHalf y₂ = m₂ • powHalf y₁ := by
   revert m₁ m₂
@@ -230,7 +283,9 @@ theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ =
   · have := Nat.one_le_pow y₁ 2 Nat.succ_pos'
     norm_cast at h₂ ; linarith
 #align surreal.dyadic_aux Surreal.dyadic_aux
+-/
 
+#print Surreal.dyadicMap /-
 /-- The additive monoid morphism `dyadic_map` sends ⟦⟨m, 2^n⟩⟧ to m • half ^ n. -/
 def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
     where
@@ -269,25 +324,32 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
         _ = c • pow_half d' + a • pow_half b' := by simp only [zsmul_pow_two_pow_half]
         _ = a • pow_half b' + c • pow_half d' := add_comm _ _
 #align surreal.dyadic_map Surreal.dyadicMap
+-/
 
+#print Surreal.dyadicMap_apply /-
 @[simp]
 theorem dyadicMap_apply (m : ℤ) (p : Submonoid.powers (2 : ℤ)) :
     dyadicMap (IsLocalization.mk' (Localization (Submonoid.powers 2)) m p) =
       m • powHalf (Submonoid.log p) :=
   by rw [← Localization.mk_eq_mk']; rfl
 #align surreal.dyadic_map_apply Surreal.dyadicMap_apply
+-/
 
+#print Surreal.dyadicMap_apply_pow /-
 @[simp]
 theorem dyadicMap_apply_pow (m : ℤ) (n : ℕ) :
     dyadicMap (IsLocalization.mk' (Localization (Submonoid.powers 2)) m (Submonoid.pow 2 n)) =
       m • powHalf n :=
   by rw [dyadic_map_apply, @Submonoid.log_pow_int_eq_self 2 one_lt_two]
 #align surreal.dyadic_map_apply_pow Surreal.dyadicMap_apply_pow
+-/
 
+#print Surreal.dyadic /-
 /-- We define dyadic surreals as the range of the map `dyadic_map`. -/
 def dyadic : Set Surreal :=
   Set.range dyadicMap
 #align surreal.dyadic Surreal.dyadic
+-/
 
 -- We conclude with some ideas for further work on surreals; these would make fun projects.
 -- TODO show that the map from dyadic rationals to surreals is injective

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

@@ -32,7 +32,6 @@ rational numbers to construct an ordered field embedding of ℝ into `surreal`.
 
 universe u
 
--- mathport name: pgame.equiv
 local infixl:0 " ≈ " => PGame.Equiv
 
 namespace PGame

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

@@ -134,12 +134,10 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
         calc
           0 + pow_half n.succ ≈ pow_half n.succ := zero_add_equiv _
           _ < pow_half n := pow_half_succ_lt_pow_half n
-          
       ·
         calc
           pow_half n.succ + 0 ≈ pow_half n.succ := add_zero_equiv _
           _ < pow_half n := pow_half_succ_lt_pow_half n
-          
     · cases n; · rintro ⟨⟩
       rintro ⟨⟩
       apply lf_of_move_right_le
@@ -148,25 +146,21 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
         pow_half n.succ + pow_half (n.succ + 1) ≤ pow_half n.succ + pow_half n.succ :=
           add_le_add_left (pow_half_succ_le_pow_half _) _
         _ ≈ pow_half n := hn _ (Nat.lt_succ_self n)
-        
     · simp only [pow_half_move_left, forall_const]
       apply lf_of_lt
       calc
         0 ≈ 0 + 0 := (add_zero_equiv 0).symm
         _ ≤ pow_half n.succ + 0 := (add_le_add_right (zero_le_pow_half _) _)
         _ < pow_half n.succ + pow_half n.succ := add_lt_add_left (pow_half_pos _) _
-        
     · rintro (⟨⟨⟩⟩ | ⟨⟨⟩⟩) <;> apply lf_of_lt
       ·
         calc
           pow_half n ≈ pow_half n + 0 := (add_zero_equiv _).symm
           _ < pow_half n + pow_half n.succ := add_lt_add_left (pow_half_pos _) _
-          
       ·
         calc
           pow_half n ≈ 0 + pow_half n := (zero_add_equiv _).symm
           _ < pow_half n.succ + pow_half n := add_lt_add_right (pow_half_pos _) _
-          
 #align pgame.add_pow_half_succ_self_eq_pow_half PGame.add_powHalf_succ_self_eq_powHalf
 
 theorem half_add_half_equiv_one : powHalf 1 + powHalf 1 ≈ 1 :=
@@ -275,7 +269,6 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
           by simp only [add_smul, mul_comm, add_comm]
         _ = c • pow_half d' + a • pow_half b' := by simp only [zsmul_pow_two_pow_half]
         _ = a • pow_half b' + c • pow_half d' := add_comm _ _
-        
 #align surreal.dyadic_map Surreal.dyadicMap
 
 @[simp]

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

@@ -235,7 +235,7 @@ theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ =
   cases h₂
   · rw [h₂, add_comm, zsmul_pow_two_pow_half m₂ c y₁]
   · have := Nat.one_le_pow y₁ 2 Nat.succ_pos'
-    norm_cast  at h₂ ; linarith
+    norm_cast at h₂ ; linarith
 #align surreal.dyadic_aux Surreal.dyadic_aux
 
 /-- The additive monoid morphism `dyadic_map` sends ⟦⟨m, 2^n⟩⟧ to m • half ^ n. -/

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

@@ -212,7 +212,7 @@ theorem nsmul_pow_two_pow_half' (n k : ℕ) : 2 ^ n • powHalf (n + k) = powHal
     simp only [add_zero, Surreal.nsmul_pow_two_powHalf, Nat.zero_eq, eq_self_iff_true,
       Surreal.powHalf_zero]
   · rw [← double_pow_half_succ_eq_pow_half (n + k), ← double_pow_half_succ_eq_pow_half k,
-      smul_algebra_smul_comm] at hk
+      smul_algebra_smul_comm] at hk 
     rwa [← zsmul_eq_zsmul_iff' two_ne_zero]
 #align surreal.nsmul_pow_two_pow_half' Surreal.nsmul_pow_two_pow_half'
 
@@ -231,11 +231,11 @@ theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ =
   · intro m₁ m₂ aux; exact (this (le_of_not_le h) aux.symm).symm
   intro m₁ m₂ h₂
   obtain ⟨c, rfl⟩ := le_iff_exists_add.mp h
-  rw [add_comm, pow_add, ← mul_assoc, mul_eq_mul_right_iff] at h₂
+  rw [add_comm, pow_add, ← mul_assoc, mul_eq_mul_right_iff] at h₂ 
   cases h₂
   · rw [h₂, add_comm, zsmul_pow_two_pow_half m₂ c y₁]
   · have := Nat.one_le_pow y₁ 2 Nat.succ_pos'
-    norm_cast  at h₂; linarith
+    norm_cast  at h₂ ; linarith
 #align surreal.dyadic_aux Surreal.dyadic_aux
 
 /-- The additive monoid morphism `dyadic_map` sends ⟦⟨m, 2^n⟩⟧ to m • half ^ n. -/
@@ -246,7 +246,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
       by
       intro m₁ m₂ n₁ n₂ h₁
       obtain ⟨⟨n₃, y₃, hn₃⟩, h₂⟩ := localization.r_iff_exists.mp h₁
-      simp only [Subtype.coe_mk, mul_eq_mul_left_iff] at h₂
+      simp only [Subtype.coe_mk, mul_eq_mul_left_iff] at h₂ 
       cases h₂
       · simp only
         obtain ⟨a₁, ha₁⟩ := n₁.prop
@@ -266,7 +266,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
       rintro ⟨a, ⟨b, ⟨b', rfl⟩⟩⟩ ⟨c, ⟨d, ⟨d', rfl⟩⟩⟩
       have h₂ : 1 < (2 : ℤ).natAbs := one_lt_two
       have hpow₂ := Submonoid.log_pow_int_eq_self h₂
-      simp_rw [Submonoid.pow_apply] at hpow₂
+      simp_rw [Submonoid.pow_apply] at hpow₂ 
       simp_rw [Localization.add_mk, Localization.liftOn_mk, Subtype.coe_mk,
         Submonoid.log_mul (Int.pow_right_injective h₂), hpow₂]
       calc

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

@@ -84,10 +84,7 @@ instance uniquePowHalfSuccRightMoves (n) : Unique (powHalf (n + 1)).RightMoves :
 #align pgame.unique_pow_half_succ_right_moves PGame.uniquePowHalfSuccRightMoves
 
 @[simp]
-theorem birthday_half : birthday (powHalf 1) = 2 :=
-  by
-  rw [birthday_def]
-  dsimp
+theorem birthday_half : birthday (powHalf 1) = 2 := by rw [birthday_def]; dsimp;
   simpa using Order.le_succ (1 : Ordinal)
 #align pgame.birthday_half PGame.birthday_half
 
@@ -120,10 +117,8 @@ theorem powHalf_succ_lt_one (n : ℕ) : powHalf (n + 1) < 1 :=
   (powHalf_succ_lt_powHalf n).trans_le <| powHalf_le_one n
 #align pgame.pow_half_succ_lt_one PGame.powHalf_succ_lt_one
 
-theorem powHalf_pos (n : ℕ) : 0 < powHalf n :=
-  by
-  rw [← lf_iff_lt numeric_zero (numeric_pow_half n), zero_lf_le]
-  simp
+theorem powHalf_pos (n : ℕ) : 0 < powHalf n := by
+  rw [← lf_iff_lt numeric_zero (numeric_pow_half n), zero_lf_le]; simp
 #align pgame.pow_half_pos PGame.powHalf_pos
 
 theorem zero_le_powHalf (n : ℕ) : 0 ≤ powHalf n :=
@@ -145,12 +140,10 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
           pow_half n.succ + 0 ≈ pow_half n.succ := add_zero_equiv _
           _ < pow_half n := pow_half_succ_lt_pow_half n
           
-    · cases n
-      · rintro ⟨⟩
+    · cases n; · rintro ⟨⟩
       rintro ⟨⟩
       apply lf_of_move_right_le
-      swap
-      exact Sum.inl default
+      swap; exact Sum.inl default
       calc
         pow_half n.succ + pow_half (n.succ + 1) ≤ pow_half n.succ + pow_half n.succ :=
           add_le_add_left (pow_half_succ_le_pow_half _) _
@@ -197,10 +190,8 @@ theorem powHalf_zero : powHalf 0 = 1 :=
 #align surreal.pow_half_zero Surreal.powHalf_zero
 
 @[simp]
-theorem double_powHalf_succ_eq_powHalf (n : ℕ) : 2 • powHalf n.succ = powHalf n :=
-  by
-  rw [two_nsmul]
-  exact Quotient.sound (PGame.add_powHalf_succ_self_eq_powHalf n)
+theorem double_powHalf_succ_eq_powHalf (n : ℕ) : 2 • powHalf n.succ = powHalf n := by
+  rw [two_nsmul]; exact Quotient.sound (PGame.add_powHalf_succ_self_eq_powHalf n)
 #align surreal.double_pow_half_succ_eq_pow_half Surreal.double_powHalf_succ_eq_powHalf
 
 @[simp]
@@ -237,16 +228,14 @@ theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ =
     m₁ • powHalf y₂ = m₂ • powHalf y₁ := by
   revert m₁ m₂
   wlog h : y₁ ≤ y₂
-  · intro m₁ m₂ aux
-    exact (this (le_of_not_le h) aux.symm).symm
+  · intro m₁ m₂ aux; exact (this (le_of_not_le h) aux.symm).symm
   intro m₁ m₂ h₂
   obtain ⟨c, rfl⟩ := le_iff_exists_add.mp h
   rw [add_comm, pow_add, ← mul_assoc, mul_eq_mul_right_iff] at h₂
   cases h₂
   · rw [h₂, add_comm, zsmul_pow_two_pow_half m₂ c y₁]
   · have := Nat.one_le_pow y₁ 2 Nat.succ_pos'
-    norm_cast  at h₂
-    linarith
+    norm_cast  at h₂; linarith
 #align surreal.dyadic_aux Surreal.dyadic_aux
 
 /-- The additive monoid morphism `dyadic_map` sends ⟦⟨m, 2^n⟩⟧ to m • half ^ n. -/
@@ -293,9 +282,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal
 theorem dyadicMap_apply (m : ℤ) (p : Submonoid.powers (2 : ℤ)) :
     dyadicMap (IsLocalization.mk' (Localization (Submonoid.powers 2)) m p) =
       m • powHalf (Submonoid.log p) :=
-  by
-  rw [← Localization.mk_eq_mk']
-  rfl
+  by rw [← Localization.mk_eq_mk']; rfl
 #align surreal.dyadic_map_apply Surreal.dyadicMap_apply
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -33,55 +33,55 @@ rational numbers to construct an ordered field embedding of ℝ into `surreal`.
 universe u
 
 -- mathport name: pgame.equiv
-local infixl:0 " ≈ " => Pgame.Equiv
+local infixl:0 " ≈ " => PGame.Equiv
 
-namespace Pgame
+namespace PGame
 
 /-- For a natural number `n`, the pre-game `pow_half (n + 1)` is recursively defined as
 `{0 | pow_half n}`. These are the explicit expressions of powers of `1 / 2`. By definition, we have
 `pow_half 0 = 1` and `pow_half 1 ≈ 1 / 2` and we prove later on that
 `pow_half (n + 1) + pow_half (n + 1) ≈ pow_half n`. -/
-def powHalf : ℕ → Pgame
+def powHalf : ℕ → PGame
   | 0 => 1
   | n + 1 => ⟨PUnit, PUnit, 0, fun _ => pow_half n⟩
-#align pgame.pow_half Pgame.powHalf
+#align pgame.pow_half PGame.powHalf
 
 @[simp]
 theorem powHalf_zero : powHalf 0 = 1 :=
   rfl
-#align pgame.pow_half_zero Pgame.powHalf_zero
+#align pgame.pow_half_zero PGame.powHalf_zero
 
 theorem powHalf_leftMoves (n) : (powHalf n).LeftMoves = PUnit := by cases n <;> rfl
-#align pgame.pow_half_left_moves Pgame.powHalf_leftMoves
+#align pgame.pow_half_left_moves PGame.powHalf_leftMoves
 
 theorem powHalf_zero_rightMoves : (powHalf 0).RightMoves = PEmpty :=
   rfl
-#align pgame.pow_half_zero_right_moves Pgame.powHalf_zero_rightMoves
+#align pgame.pow_half_zero_right_moves PGame.powHalf_zero_rightMoves
 
 theorem powHalf_succ_rightMoves (n) : (powHalf (n + 1)).RightMoves = PUnit :=
   rfl
-#align pgame.pow_half_succ_right_moves Pgame.powHalf_succ_rightMoves
+#align pgame.pow_half_succ_right_moves PGame.powHalf_succ_rightMoves
 
 @[simp]
 theorem powHalf_moveLeft (n i) : (powHalf n).moveLeft i = 0 := by cases n <;> cases i <;> rfl
-#align pgame.pow_half_move_left Pgame.powHalf_moveLeft
+#align pgame.pow_half_move_left PGame.powHalf_moveLeft
 
 @[simp]
 theorem powHalf_succ_moveRight (n i) : (powHalf (n + 1)).moveRight i = powHalf n :=
   rfl
-#align pgame.pow_half_succ_move_right Pgame.powHalf_succ_moveRight
+#align pgame.pow_half_succ_move_right PGame.powHalf_succ_moveRight
 
 instance uniquePowHalfLeftMoves (n) : Unique (powHalf n).LeftMoves := by
   cases n <;> exact PUnit.unique
-#align pgame.unique_pow_half_left_moves Pgame.uniquePowHalfLeftMoves
+#align pgame.unique_pow_half_left_moves PGame.uniquePowHalfLeftMoves
 
 instance isEmpty_powHalf_zero_rightMoves : IsEmpty (powHalf 0).RightMoves :=
   PEmpty.isEmpty
-#align pgame.is_empty_pow_half_zero_right_moves Pgame.isEmpty_powHalf_zero_rightMoves
+#align pgame.is_empty_pow_half_zero_right_moves PGame.isEmpty_powHalf_zero_rightMoves
 
 instance uniquePowHalfSuccRightMoves (n) : Unique (powHalf (n + 1)).RightMoves :=
   PUnit.unique
-#align pgame.unique_pow_half_succ_right_moves Pgame.uniquePowHalfSuccRightMoves
+#align pgame.unique_pow_half_succ_right_moves PGame.uniquePowHalfSuccRightMoves
 
 @[simp]
 theorem birthday_half : birthday (powHalf 1) = 2 :=
@@ -89,7 +89,7 @@ theorem birthday_half : birthday (powHalf 1) = 2 :=
   rw [birthday_def]
   dsimp
   simpa using Order.le_succ (1 : Ordinal)
-#align pgame.birthday_half Pgame.birthday_half
+#align pgame.birthday_half PGame.birthday_half
 
 /-- For all natural numbers `n`, the pre-games `pow_half n` are numeric. -/
 theorem numeric_powHalf (n) : (powHalf n).Numeric :=
@@ -99,36 +99,36 @@ theorem numeric_powHalf (n) : (powHalf n).Numeric :=
   · constructor
     · simpa using hn.move_left_lt default
     · exact ⟨fun _ => numeric_zero, fun _ => hn⟩
-#align pgame.numeric_pow_half Pgame.numeric_powHalf
+#align pgame.numeric_pow_half PGame.numeric_powHalf
 
 theorem powHalf_succ_lt_powHalf (n : ℕ) : powHalf (n + 1) < powHalf n :=
   (numeric_powHalf (n + 1)).lt_moveRight default
-#align pgame.pow_half_succ_lt_pow_half Pgame.powHalf_succ_lt_powHalf
+#align pgame.pow_half_succ_lt_pow_half PGame.powHalf_succ_lt_powHalf
 
 theorem powHalf_succ_le_powHalf (n : ℕ) : powHalf (n + 1) ≤ powHalf n :=
   (powHalf_succ_lt_powHalf n).le
-#align pgame.pow_half_succ_le_pow_half Pgame.powHalf_succ_le_powHalf
+#align pgame.pow_half_succ_le_pow_half PGame.powHalf_succ_le_powHalf
 
 theorem powHalf_le_one (n : ℕ) : powHalf n ≤ 1 :=
   by
   induction' n with n hn
   · exact le_rfl
   · exact (pow_half_succ_le_pow_half n).trans hn
-#align pgame.pow_half_le_one Pgame.powHalf_le_one
+#align pgame.pow_half_le_one PGame.powHalf_le_one
 
 theorem powHalf_succ_lt_one (n : ℕ) : powHalf (n + 1) < 1 :=
   (powHalf_succ_lt_powHalf n).trans_le <| powHalf_le_one n
-#align pgame.pow_half_succ_lt_one Pgame.powHalf_succ_lt_one
+#align pgame.pow_half_succ_lt_one PGame.powHalf_succ_lt_one
 
 theorem powHalf_pos (n : ℕ) : 0 < powHalf n :=
   by
   rw [← lf_iff_lt numeric_zero (numeric_pow_half n), zero_lf_le]
   simp
-#align pgame.pow_half_pos Pgame.powHalf_pos
+#align pgame.pow_half_pos PGame.powHalf_pos
 
 theorem zero_le_powHalf (n : ℕ) : 0 ≤ powHalf n :=
   (powHalf_pos n).le
-#align pgame.zero_le_pow_half Pgame.zero_le_powHalf
+#align pgame.zero_le_pow_half PGame.zero_le_powHalf
 
 theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1) ≈ powHalf n :=
   by
@@ -174,21 +174,21 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
           pow_half n ≈ 0 + pow_half n := (zero_add_equiv _).symm
           _ < pow_half n.succ + pow_half n := add_lt_add_right (pow_half_pos _) _
           
-#align pgame.add_pow_half_succ_self_eq_pow_half Pgame.add_powHalf_succ_self_eq_powHalf
+#align pgame.add_pow_half_succ_self_eq_pow_half PGame.add_powHalf_succ_self_eq_powHalf
 
 theorem half_add_half_equiv_one : powHalf 1 + powHalf 1 ≈ 1 :=
   add_powHalf_succ_self_eq_powHalf 0
-#align pgame.half_add_half_equiv_one Pgame.half_add_half_equiv_one
+#align pgame.half_add_half_equiv_one PGame.half_add_half_equiv_one
 
-end Pgame
+end PGame
 
 namespace Surreal
 
-open Pgame
+open PGame
 
 /-- Powers of the surreal number `half`. -/
 def powHalf (n : ℕ) : Surreal :=
-  ⟦⟨Pgame.powHalf n, Pgame.numeric_powHalf n⟩⟧
+  ⟦⟨PGame.powHalf n, PGame.numeric_powHalf n⟩⟧
 #align surreal.pow_half Surreal.powHalf
 
 @[simp]
@@ -200,7 +200,7 @@ theorem powHalf_zero : powHalf 0 = 1 :=
 theorem double_powHalf_succ_eq_powHalf (n : ℕ) : 2 • powHalf n.succ = powHalf n :=
   by
   rw [two_nsmul]
-  exact Quotient.sound (Pgame.add_powHalf_succ_self_eq_powHalf n)
+  exact Quotient.sound (PGame.add_powHalf_succ_self_eq_powHalf n)
 #align surreal.double_pow_half_succ_eq_pow_half Surreal.double_powHalf_succ_eq_powHalf
 
 @[simp]

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -160,7 +160,7 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
       apply lf_of_lt
       calc
         0 ≈ 0 + 0 := (add_zero_equiv 0).symm
-        _ ≤ pow_half n.succ + 0 := add_le_add_right (zero_le_pow_half _) _
+        _ ≤ pow_half n.succ + 0 := (add_le_add_right (zero_le_pow_half _) _)
         _ < pow_half n.succ + pow_half n.succ := add_lt_add_left (pow_half_pos _) _
         
     · rintro (⟨⟨⟩⟩ | ⟨⟨⟩⟩) <;> apply lf_of_lt

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -134,7 +134,8 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
       · rintro ⟨⟩
       rintro ⟨⟩
       apply lf_of_moveRight_le
-      swap; exact Sum.inl default
+      swap
+      · exact Sum.inl default
       calc
         powHalf n.succ + powHalf (n.succ + 1) ≤ powHalf n.succ + powHalf n.succ :=
           add_le_add_left (powHalf_succ_le_powHalf _) _

Splits Algebra.Algebra.Defs off Algebra.Algebra.Basic. Most imports only need the Defs file, which has significantly smaller imports. The remaining Algebra.Algebra.Basic is now a grab-bag of unrelated results, and should probably be split further or rehomed.

This is mostly motivated by the wasted effort during minimization upon encountering Algebra.Algebra.Basic.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -3,7 +3,7 @@ Copyright (c) 2021 Apurva Nakade. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Apurva Nakade
 -/
-import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.Algebra.Defs
 import Mathlib.Algebra.GroupPower.Order
 import Mathlib.RingTheory.Localization.Basic
 import Mathlib.SetTheory.Game.Birthday

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

@@ -142,15 +142,15 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
     · simp only [powHalf_moveLeft, forall_const]
       apply lf_of_lt
       calc
-        0 ≈ 0 + 0 := (Equiv.symm (add_zero_equiv 0))
-        _ ≤ powHalf n.succ + 0 := (add_le_add_right (zero_le_powHalf _) _)
+        0 ≈ 0 + 0 := Equiv.symm (add_zero_equiv 0)
+        _ ≤ powHalf n.succ + 0 := add_le_add_right (zero_le_powHalf _) _
         _ < powHalf n.succ + powHalf n.succ := add_lt_add_left (powHalf_pos _) _
     · rintro (⟨⟨⟩⟩ | ⟨⟨⟩⟩) <;> apply lf_of_lt
       · calc
-          powHalf n ≈ powHalf n + 0 := (Equiv.symm (add_zero_equiv _))
+          powHalf n ≈ powHalf n + 0 := Equiv.symm (add_zero_equiv _)
           _ < powHalf n + powHalf n.succ := add_lt_add_left (powHalf_pos _) _
       · calc
-          powHalf n ≈ 0 + powHalf n := (Equiv.symm (zero_add_equiv _))
+          powHalf n ≈ 0 + powHalf n := Equiv.symm (zero_add_equiv _)
           _ < powHalf n.succ + powHalf n := add_lt_add_right (powHalf_pos _) _
 #align pgame.add_pow_half_succ_self_eq_pow_half SetTheory.PGame.add_powHalf_succ_self_eq_powHalf
 

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.

@@ -186,7 +186,7 @@ theorem nsmul_pow_two_powHalf (n : ℕ) : 2 ^ n • powHalf n = 1 := by
   induction' n with n hn
   · simp only [Nat.zero_eq, pow_zero, powHalf_zero, one_smul]
   · rw [← hn, ← double_powHalf_succ_eq_powHalf n, smul_smul (2 ^ n) 2 (powHalf n.succ), mul_comm,
-      pow_succ]
+      pow_succ']
 #align surreal.nsmul_pow_two_pow_half Surreal.nsmul_pow_two_powHalf
 
 @[simp]

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>

@@ -239,7 +239,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal where
         apply dyadic_aux
         rwa [ha₁, ha₂, mul_comm, mul_comm m₂]
       · have : (1 : ℤ) ≤ 2 ^ y₃ := mod_cast Nat.one_le_pow y₃ 2 Nat.succ_pos'
-        omega
+        linarith
   map_zero' := Localization.liftOn_zero _ _
   map_add' x y :=
     Localization.induction_on₂ x y <| by

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

@@ -218,7 +218,7 @@ theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ =
   cases' h₂ with h₂ h₂
   · rw [h₂, add_comm, zsmul_pow_two_powHalf m₂ c y₁]
   · have := Nat.one_le_pow y₁ 2 Nat.succ_pos'
-    norm_cast at h₂; linarith
+    norm_cast at h₂; omega
 #align surreal.dyadic_aux Surreal.dyadic_aux
 
 /-- The additive monoid morphism `dyadicMap` sends ⟦⟨m, 2^n⟩⟧ to m • half ^ n. -/
@@ -239,7 +239,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal where
         apply dyadic_aux
         rwa [ha₁, ha₂, mul_comm, mul_comm m₂]
       · have : (1 : ℤ) ≤ 2 ^ y₃ := mod_cast Nat.one_le_pow y₃ 2 Nat.succ_pos'
-        linarith
+        omega
   map_zero' := Localization.liftOn_zero _ _
   map_add' x y :=
     Localization.induction_on₂ x y <| by

I loogled for every occurrence of "cast", Nat and "natCast" and where the casted nat was n, and made sure there were corresponding @[simp] lemmas for 0, 1, and OfNat.ofNat n. This is necessary in general for simp confluence. Example:

import Mathlib

variable {α : Type*} [LinearOrderedRing α] (m n : ℕ) [m.AtLeastTwo] [n.AtLeastTwo]

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp only [Nat.cast_le] -- this `@[simp]` lemma can apply

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) := by
  simp only [Nat.cast_ofNat] -- and so can this one

example : (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp -- fails! `simp` doesn't have a lemma to bridge their results. confluence issue.

As far as I know, the only file this PR leaves with ofNat gaps is PartENat.lean. #8002 is addressing that file in parallel.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -82,7 +82,7 @@ instance uniquePowHalfSuccRightMoves (n) : Unique (powHalf (n + 1)).RightMoves :
 
 @[simp]
 theorem birthday_half : birthday (powHalf 1) = 2 := by
-  rw [birthday_def]; dsimp; simpa using Order.le_succ (1 : Ordinal)
+  rw [birthday_def]; simp
 #align pgame.birthday_half SetTheory.PGame.birthday_half
 
 /-- For all natural numbers `n`, the pre-games `powHalf n` are numeric. -/

The goal here is to have access to positivity earlier in the import hierarchy

@@ -4,9 +4,10 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Apurva Nakade
 -/
 import Mathlib.Algebra.Algebra.Basic
+import Mathlib.Algebra.GroupPower.Order
+import Mathlib.RingTheory.Localization.Basic
 import Mathlib.SetTheory.Game.Birthday
 import Mathlib.SetTheory.Surreal.Basic
-import Mathlib.RingTheory.Localization.Basic
 
 #align_import set_theory.surreal.dyadic from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
 

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

@@ -237,7 +237,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal where
         rw [hn₁, hn₂, Submonoid.log_pow_int_eq_self h₂, Submonoid.log_pow_int_eq_self h₂]
         apply dyadic_aux
         rwa [ha₁, ha₂, mul_comm, mul_comm m₂]
-      · have : (1 : ℤ) ≤ 2 ^ y₃ := by exact_mod_cast Nat.one_le_pow y₃ 2 Nat.succ_pos'
+      · have : (1 : ℤ) ≤ 2 ^ y₃ := mod_cast Nat.one_le_pow y₃ 2 Nat.succ_pos'
         linarith
   map_zero' := Localization.liftOn_zero _ _
   map_add' x y :=

move Game and PGame into namespace SetTheory as _root_.Game might collide with other definitions (e.g. in projects depending on mathlib)

@@ -29,6 +29,8 @@ rational numbers to construct an ordered field embedding of ℝ into `Surreal`.
 
 universe u
 
+namespace SetTheory
+
 namespace PGame
 
 /-- For a natural number `n`, the pre-game `powHalf (n + 1)` is recursively defined as
@@ -38,49 +40,49 @@ namespace PGame
 def powHalf : ℕ → PGame
   | 0 => 1
   | n + 1 => ⟨PUnit, PUnit, 0, fun _ => powHalf n⟩
-#align pgame.pow_half PGame.powHalf
+#align pgame.pow_half SetTheory.PGame.powHalf
 
 @[simp]
 theorem powHalf_zero : powHalf 0 = 1 :=
   rfl
-#align pgame.pow_half_zero PGame.powHalf_zero
+#align pgame.pow_half_zero SetTheory.PGame.powHalf_zero
 
 theorem powHalf_leftMoves (n) : (powHalf n).LeftMoves = PUnit := by cases n <;> rfl
-#align pgame.pow_half_left_moves PGame.powHalf_leftMoves
+#align pgame.pow_half_left_moves SetTheory.PGame.powHalf_leftMoves
 
 theorem powHalf_zero_rightMoves : (powHalf 0).RightMoves = PEmpty :=
   rfl
-#align pgame.pow_half_zero_right_moves PGame.powHalf_zero_rightMoves
+#align pgame.pow_half_zero_right_moves SetTheory.PGame.powHalf_zero_rightMoves
 
 theorem powHalf_succ_rightMoves (n) : (powHalf (n + 1)).RightMoves = PUnit :=
   rfl
-#align pgame.pow_half_succ_right_moves PGame.powHalf_succ_rightMoves
+#align pgame.pow_half_succ_right_moves SetTheory.PGame.powHalf_succ_rightMoves
 
 @[simp]
 theorem powHalf_moveLeft (n i) : (powHalf n).moveLeft i = 0 := by cases n <;> cases i <;> rfl
-#align pgame.pow_half_move_left PGame.powHalf_moveLeft
+#align pgame.pow_half_move_left SetTheory.PGame.powHalf_moveLeft
 
 @[simp]
 theorem powHalf_succ_moveRight (n i) : (powHalf (n + 1)).moveRight i = powHalf n :=
   rfl
-#align pgame.pow_half_succ_move_right PGame.powHalf_succ_moveRight
+#align pgame.pow_half_succ_move_right SetTheory.PGame.powHalf_succ_moveRight
 
 instance uniquePowHalfLeftMoves (n) : Unique (powHalf n).LeftMoves := by
   cases n <;> exact PUnit.unique
-#align pgame.unique_pow_half_left_moves PGame.uniquePowHalfLeftMoves
+#align pgame.unique_pow_half_left_moves SetTheory.PGame.uniquePowHalfLeftMoves
 
 instance isEmpty_powHalf_zero_rightMoves : IsEmpty (powHalf 0).RightMoves :=
   inferInstanceAs (IsEmpty PEmpty)
-#align pgame.is_empty_pow_half_zero_right_moves PGame.isEmpty_powHalf_zero_rightMoves
+#align pgame.is_empty_pow_half_zero_right_moves SetTheory.PGame.isEmpty_powHalf_zero_rightMoves
 
 instance uniquePowHalfSuccRightMoves (n) : Unique (powHalf (n + 1)).RightMoves :=
   PUnit.unique
-#align pgame.unique_pow_half_succ_right_moves PGame.uniquePowHalfSuccRightMoves
+#align pgame.unique_pow_half_succ_right_moves SetTheory.PGame.uniquePowHalfSuccRightMoves
 
 @[simp]
 theorem birthday_half : birthday (powHalf 1) = 2 := by
   rw [birthday_def]; dsimp; simpa using Order.le_succ (1 : Ordinal)
-#align pgame.birthday_half PGame.birthday_half
+#align pgame.birthday_half SetTheory.PGame.birthday_half
 
 /-- For all natural numbers `n`, the pre-games `powHalf n` are numeric. -/
 theorem numeric_powHalf (n) : (powHalf n).Numeric := by
@@ -89,33 +91,33 @@ theorem numeric_powHalf (n) : (powHalf n).Numeric := by
   · constructor
     · simpa using hn.moveLeft_lt default
     · exact ⟨fun _ => numeric_zero, fun _ => hn⟩
-#align pgame.numeric_pow_half PGame.numeric_powHalf
+#align pgame.numeric_pow_half SetTheory.PGame.numeric_powHalf
 
 theorem powHalf_succ_lt_powHalf (n : ℕ) : powHalf (n + 1) < powHalf n :=
   (numeric_powHalf (n + 1)).lt_moveRight default
-#align pgame.pow_half_succ_lt_pow_half PGame.powHalf_succ_lt_powHalf
+#align pgame.pow_half_succ_lt_pow_half SetTheory.PGame.powHalf_succ_lt_powHalf
 
 theorem powHalf_succ_le_powHalf (n : ℕ) : powHalf (n + 1) ≤ powHalf n :=
   (powHalf_succ_lt_powHalf n).le
-#align pgame.pow_half_succ_le_pow_half PGame.powHalf_succ_le_powHalf
+#align pgame.pow_half_succ_le_pow_half SetTheory.PGame.powHalf_succ_le_powHalf
 
 theorem powHalf_le_one (n : ℕ) : powHalf n ≤ 1 := by
   induction' n with n hn
   · exact le_rfl
   · exact (powHalf_succ_le_powHalf n).trans hn
-#align pgame.pow_half_le_one PGame.powHalf_le_one
+#align pgame.pow_half_le_one SetTheory.PGame.powHalf_le_one
 
 theorem powHalf_succ_lt_one (n : ℕ) : powHalf (n + 1) < 1 :=
   (powHalf_succ_lt_powHalf n).trans_le <| powHalf_le_one n
-#align pgame.pow_half_succ_lt_one PGame.powHalf_succ_lt_one
+#align pgame.pow_half_succ_lt_one SetTheory.PGame.powHalf_succ_lt_one
 
 theorem powHalf_pos (n : ℕ) : 0 < powHalf n := by
   rw [← lf_iff_lt numeric_zero (numeric_powHalf n), zero_lf_le]; simp
-#align pgame.pow_half_pos PGame.powHalf_pos
+#align pgame.pow_half_pos SetTheory.PGame.powHalf_pos
 
 theorem zero_le_powHalf (n : ℕ) : 0 ≤ powHalf n :=
   (powHalf_pos n).le
-#align pgame.zero_le_pow_half PGame.zero_le_powHalf
+#align pgame.zero_le_pow_half SetTheory.PGame.zero_le_powHalf
 
 theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1) ≈ powHalf n := by
   induction' n using Nat.strong_induction_on with n hn
@@ -149,17 +151,19 @@ theorem add_powHalf_succ_self_eq_powHalf (n) : powHalf (n + 1) + powHalf (n + 1)
       · calc
           powHalf n ≈ 0 + powHalf n := (Equiv.symm (zero_add_equiv _))
           _ < powHalf n.succ + powHalf n := add_lt_add_right (powHalf_pos _) _
-#align pgame.add_pow_half_succ_self_eq_pow_half PGame.add_powHalf_succ_self_eq_powHalf
+#align pgame.add_pow_half_succ_self_eq_pow_half SetTheory.PGame.add_powHalf_succ_self_eq_powHalf
 
 theorem half_add_half_equiv_one : powHalf 1 + powHalf 1 ≈ 1 :=
   add_powHalf_succ_self_eq_powHalf 0
-#align pgame.half_add_half_equiv_one PGame.half_add_half_equiv_one
+#align pgame.half_add_half_equiv_one SetTheory.PGame.half_add_half_equiv_one
 
 end PGame
 
+end SetTheory
+
 namespace Surreal
 
-open PGame
+open SetTheory PGame
 
 /-- Powers of the surreal number `half`. -/
 def powHalf (n : ℕ) : Surreal :=

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -242,7 +242,7 @@ def dyadicMap : Localization.Away (2 : ℤ) →+ Surreal where
       have h₂ : 1 < (2 : ℤ).natAbs := one_lt_two
       have hpow₂ := Submonoid.log_pow_int_eq_self h₂
       simp_rw [Submonoid.pow_apply] at hpow₂
-      simp_rw [Localization.add_mk, Localization.liftOn_mk, Subtype.coe_mk,
+      simp_rw [Localization.add_mk, Localization.liftOn_mk,
         Submonoid.log_mul (Int.pow_right_injective h₂), hpow₂]
       calc
         (2 ^ b' * c + 2 ^ d' * a) • powHalf (b' + d') =

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Apurva Nakade. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Apurva Nakade
-
-! This file was ported from Lean 3 source module set_theory.surreal.dyadic
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Algebra.Basic
 import Mathlib.SetTheory.Game.Birthday
 import Mathlib.SetTheory.Surreal.Basic
 import Mathlib.RingTheory.Localization.Basic
 
+#align_import set_theory.surreal.dyadic from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
+
 /-!
 # Dyadic numbers
 Dyadic numbers are obtained by localizing ℤ away from 2. They are the initial object in the category

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -216,7 +216,7 @@ theorem dyadic_aux {m₁ m₂ : ℤ} {y₁ y₂ : ℕ} (h₂ : m₁ * 2 ^ y₁ =
   cases' h₂ with h₂ h₂
   · rw [h₂, add_comm, zsmul_pow_two_powHalf m₂ c y₁]
   · have := Nat.one_le_pow y₁ 2 Nat.succ_pos'
-    norm_cast at h₂ ; linarith
+    norm_cast at h₂; linarith
 #align surreal.dyadic_aux Surreal.dyadic_aux
 
 /-- The additive monoid morphism `dyadicMap` sends ⟦⟨m, 2^n⟩⟧ to m • half ^ n. -/

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