chore: Move pow_lt_pow_succ to Algebra.Order.WithZero (#11507)

These lemmas can be defined earlier, ridding us of an import in `Algebra.GroupPower.Order`

Mathlib/Algebra/GroupPower/Order.lean

@@ -5,7 +5,6 @@ Authors: Jeremy Avigad, Robert Y. Lewis
 -/
 import Mathlib.Algebra.GroupPower.CovariantClass
 import Mathlib.Algebra.GroupPower.Ring
-import Mathlib.Algebra.Order.WithZero
 
 #align_import algebra.group_power.order from "leanprover-community/mathlib"@"00f91228655eecdcd3ac97a7fd8dbcb139fe990a"
 
@@ -508,31 +507,6 @@ lemma pow_four_le_pow_two_of_pow_two_le (h : a ^ 2 ≤ b) : a ^ 4 ≤ b ^ 2 :=
 
 end LinearOrderedRing
 
-section LinearOrderedCommMonoidWithZero
-
-variable [LinearOrderedCommMonoidWithZero M] [NoZeroDivisors M] {a : M} {n : ℕ}
-
-theorem pow_pos_iff (hn : n ≠ 0) : 0 < a ^ n ↔ 0 < a := by simp_rw [zero_lt_iff, pow_ne_zero_iff hn]
-#align pow_pos_iff pow_pos_iff
-
-end LinearOrderedCommMonoidWithZero
-
-section LinearOrderedCommGroupWithZero
-
-variable [LinearOrderedCommGroupWithZero M] {a : M} {m n : ℕ}
-
-theorem pow_lt_pow_succ (ha : 1 < a) : a ^ n < a ^ n.succ := by
-  rw [← one_mul (a ^ n), pow_succ]
-  exact mul_lt_right₀ _ ha (pow_ne_zero _ (zero_lt_one.trans ha).ne')
-#align pow_lt_pow_succ pow_lt_pow_succ
-
-theorem pow_lt_pow_right₀ (ha : 1 < a) (hmn : m < n) : a ^ m < a ^ n := by
-  induction' hmn with n _ ih
-  exacts [pow_lt_pow_succ ha, lt_trans ih (pow_lt_pow_succ ha)]
-#align pow_lt_pow₀ pow_lt_pow_right₀
-
-end LinearOrderedCommGroupWithZero
-
 namespace MonoidHom
 
 variable [Ring R] [Monoid M] [LinearOrder M] [CovariantClass M M (· * ·) (· ≤ ·)] (f : R →* M)
@@ -571,5 +545,4 @@ Those lemmas have been deprecated on 2023-12-23.
 @[deprecated] alias pow_lt_pow_of_lt_one := pow_lt_pow_right_of_lt_one
 @[deprecated] alias lt_of_pow_lt_pow := lt_of_pow_lt_pow_left
 @[deprecated] alias le_of_pow_le_pow := le_of_pow_le_pow_left
-@[deprecated] alias pow_lt_pow₀ := pow_lt_pow_right₀
 @[deprecated] alias self_le_pow := le_self_pow

Mathlib/Algebra/Order/Field/Basic.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
 -/
 import Mathlib.Algebra.Field.Basic
+import Mathlib.Algebra.GroupWithZero.Units.Equiv
 import Mathlib.Algebra.Order.Field.Defs
 import Mathlib.Algebra.Order.Ring.Abs
 import Mathlib.Order.Bounds.OrderIso

Mathlib/Algebra/Order/Floor.lean

@@ -334,7 +334,7 @@ theorem ceil_one : ⌈(1 : α)⌉₊ = 1 := by rw [← Nat.cast_one, ceil_natCas
 #align nat.ceil_one Nat.ceil_one
 
 @[simp]
-theorem ceil_eq_zero : ⌈a⌉₊ = 0 ↔ a ≤ 0 := by rw [← le_zero_iff, ceil_le, Nat.cast_zero]
+theorem ceil_eq_zero : ⌈a⌉₊ = 0 ↔ a ≤ 0 := by rw [← Nat.le_zero, ceil_le, Nat.cast_zero]
 #align nat.ceil_eq_zero Nat.ceil_eq_zero
 
 @[simp]

Mathlib/Algebra/Order/WithZero.lean

@@ -36,8 +36,7 @@ class LinearOrderedCommGroupWithZero (α : Type*) extends LinearOrderedCommMonoi
   CommGroupWithZero α
 #align linear_ordered_comm_group_with_zero LinearOrderedCommGroupWithZero
 
-variable {α : Type*}
-variable {a b c d x y z : α}
+variable {α : Type*} {a b c d x y z : α}
 
 instance instLinearOrderedCommMonoidWithZeroMultiplicativeOrderDual
     [LinearOrderedAddCommMonoidWithTop α] :
@@ -67,9 +66,8 @@ instance instLinearOrderedCommMonoidWithZeroWithZero [LinearOrderedCommMonoid α
 instance [LinearOrderedCommGroup α] : LinearOrderedCommGroupWithZero (WithZero α) :=
   { instLinearOrderedCommMonoidWithZeroWithZero, WithZero.commGroupWithZero with }
 
-section LinearOrderedCommMonoid
-
-variable [LinearOrderedCommMonoidWithZero α]
+section LinearOrderedCommMonoidWithZero
+variable [LinearOrderedCommMonoidWithZero α] {n : ℕ}
 
 /-
 The following facts are true more generally in a (linearly) ordered commutative monoid.
@@ -117,9 +115,14 @@ instance instLinearOrderedAddCommMonoidWithTopAdditiveOrderDual :
     le_top := fun _ ↦ zero_le' }
 #align additive.linear_ordered_add_comm_monoid_with_top instLinearOrderedAddCommMonoidWithTopAdditiveOrderDual
 
-end LinearOrderedCommMonoid
+variable [NoZeroDivisors α]
+
+lemma pow_pos_iff (hn : n ≠ 0) : 0 < a ^ n ↔ 0 < a := by simp_rw [zero_lt_iff, pow_ne_zero_iff hn]
+#align pow_pos_iff pow_pos_iff
+
+end LinearOrderedCommMonoidWithZero
 
-variable [LinearOrderedCommGroupWithZero α]
+variable [LinearOrderedCommGroupWithZero α] {m n : ℕ}
 
 -- TODO: Do we really need the following two?
 /-- Alias of `mul_le_one'` for unification. -/
@@ -285,3 +288,15 @@ instance : LinearOrderedAddCommGroupWithTop (Additive αᵒᵈ) :=
     Additive.instNontrivial with
     neg_top := @inv_zero _ (_)
     add_neg_cancel := fun a ha ↦ mul_inv_cancel (G₀ := α) (id ha : Additive.toMul a ≠ 0) }
+
+lemma pow_lt_pow_succ (ha : 1 < a) : a ^ n < a ^ n.succ := by
+  rw [← one_mul (a ^ n), pow_succ];
+  exact mul_lt_right₀ _ ha (pow_ne_zero _ (zero_lt_one.trans ha).ne')
+#align pow_lt_pow_succ pow_lt_pow_succ
+
+lemma pow_lt_pow_right₀ (ha : 1 < a) (hmn : m < n) : a ^ m < a ^ n := by
+  induction' hmn with n _ ih; exacts [pow_lt_pow_succ ha, lt_trans ih (pow_lt_pow_succ ha)]
+#align pow_lt_pow₀ pow_lt_pow_right₀
+
+-- 2023-12-23
+@[deprecated] alias pow_lt_pow₀ := pow_lt_pow_right₀

Mathlib/Data/Ordmap/Ordset.lean

@@ -681,15 +681,15 @@ theorem balance_eq_balance' {l x r} (hl : Balanced l) (hr : Balanced r) (sl : Si
       · rfl
       · have : size rrl = 0 ∧ size rrr = 0 := by
           have := balancedSz_zero.1 hr.1.symm
-          rwa [size, sr.2.2.1, Nat.succ_le_succ_iff, le_zero_iff, add_eq_zero_iff] at this
+          rwa [size, sr.2.2.1, Nat.succ_le_succ_iff, Nat.le_zero, add_eq_zero_iff] at this
         cases sr.2.2.2.1.size_eq_zero.1 this.1
         cases sr.2.2.2.2.size_eq_zero.1 this.2
         obtain rfl : rrs = 1 := sr.2.2.1
         rw [if_neg, if_pos, rotateL, if_pos]; · rfl
         all_goals dsimp only [size]; decide
       · have : size rll = 0 ∧ size rlr = 0 := by
           have := balancedSz_zero.1 hr.1
-          rwa [size, sr.2.1.1, Nat.succ_le_succ_iff, le_zero_iff, add_eq_zero_iff] at this
+          rwa [size, sr.2.1.1, Nat.succ_le_succ_iff, Nat.le_zero, add_eq_zero_iff] at this
         cases sr.2.1.2.1.size_eq_zero.1 this.1
         cases sr.2.1.2.2.size_eq_zero.1 this.2
         obtain rfl : rls = 1 := sr.2.1.1
@@ -708,15 +708,15 @@ theorem balance_eq_balance' {l x r} (hl : Balanced l) (hr : Balanced r) (sl : Si
       · rfl
       · have : size lrl = 0 ∧ size lrr = 0 := by
           have := balancedSz_zero.1 hl.1.symm
-          rwa [size, sl.2.2.1, Nat.succ_le_succ_iff, le_zero_iff, add_eq_zero_iff] at this
+          rwa [size, sl.2.2.1, Nat.succ_le_succ_iff, Nat.le_zero, add_eq_zero_iff] at this
         cases sl.2.2.2.1.size_eq_zero.1 this.1
         cases sl.2.2.2.2.size_eq_zero.1 this.2
         obtain rfl : lrs = 1 := sl.2.2.1
         rw [if_neg, if_neg, if_pos, rotateR, if_neg]; · rfl
         all_goals dsimp only [size]; decide
       · have : size lll = 0 ∧ size llr = 0 := by
           have := balancedSz_zero.1 hl.1
-          rwa [size, sl.2.1.1, Nat.succ_le_succ_iff, le_zero_iff, add_eq_zero_iff] at this
+          rwa [size, sl.2.1.1, Nat.succ_le_succ_iff, Nat.le_zero, add_eq_zero_iff] at this
         cases sl.2.1.2.1.size_eq_zero.1 this.1
         cases sl.2.1.2.2.size_eq_zero.1 this.2
         obtain rfl : lls = 1 := sl.2.1.1
@@ -766,7 +766,7 @@ theorem balanceL_eq_balance {l x r} (sl : Sized l) (sr : Sized r) (H1 : size l =
   · cases' l with ls ll lx lr
     · have : size rl = 0 ∧ size rr = 0 := by
         have := H1 rfl
-        rwa [size, sr.1, Nat.succ_le_succ_iff, le_zero_iff, add_eq_zero_iff] at this
+        rwa [size, sr.1, Nat.succ_le_succ_iff, Nat.le_zero, add_eq_zero_iff] at this
       cases sr.2.1.size_eq_zero.1 this.1
       cases sr.2.2.size_eq_zero.1 this.2
       rw [sr.eq_node']; rfl
@@ -1196,7 +1196,7 @@ theorem Valid'.node4L {l} {x : α} {m} {y : α} {r o₁ o₂} (hl : Valid' o₁
       · rw [Nat.succ_add] at mm; rcases mm with (_ | ⟨⟨⟩⟩)
     rcases hm.3.1.resolve_left mm with ⟨mm₁, mm₂⟩
     rcases Nat.eq_zero_or_pos (size ml) with ml0 | ml0
-    · rw [ml0, mul_zero, le_zero_iff] at mm₂
+    · rw [ml0, mul_zero, Nat.le_zero] at mm₂
       rw [ml0, mm₂] at mm; cases mm (by decide)
     have : 2 * size l ≤ size ml + size mr + 1 := by
       have := Nat.mul_le_mul_left ratio lr₁
@@ -1275,9 +1275,9 @@ theorem Valid'.rotateL {l} {x : α} {r o₁ o₂} (hl : Valid' o₁ l x) (hr : V
         le_trans hb₂
           (Nat.mul_le_mul_left _ <| le_trans (Nat.le_add_left _ _) (Nat.le_add_right _ _))
   · rcases Nat.eq_zero_or_pos (size rl) with rl0 | rl0
-    · rw [rl0, not_lt, le_zero_iff, Nat.mul_eq_zero] at h
+    · rw [rl0, not_lt, Nat.le_zero, Nat.mul_eq_zero] at h
       replace h := h.resolve_left (by decide)
-      erw [rl0, h, le_zero_iff, Nat.mul_eq_zero] at H2
+      erw [rl0, h, Nat.le_zero, Nat.mul_eq_zero] at H2
       rw [hr.2.size_eq, rl0, h, H2.resolve_left (by decide)] at H1
       cases H1 (by decide)
     refine' hl.node4L hr.left hr.right rl0 _

Mathlib/Order/RelSeries.lean

@@ -453,11 +453,9 @@ lemma smash_succ_castAdd {p q : RelSeries r} (h : p.last = q.head)
 
 lemma smash_natAdd {p q : RelSeries r} (h : p.last = q.head) (i : Fin q.length) :
     smash p q h (Fin.castSucc <| i.natAdd p.length) = q (Fin.castSucc i) := by
-  rw [smash_toFun]
-  split_ifs with H
-  · simp only [Fin.coe_castSucc, Fin.coe_natAdd, add_lt_iff_neg_left, not_lt_zero'] at H
-  · congr
-    exact Nat.add_sub_self_left _ _
+  rw [smash_toFun, dif_neg (by simp)]
+  congr
+  exact Nat.add_sub_self_left _ _
 
 lemma smash_succ_natAdd {p q : RelSeries r} (h : p.last = q.head) (i : Fin q.length) :
     smash p q h (i.natAdd p.length).succ = q i.succ := by