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[Merged by Bors] - chore: rename isSuccLimit_iff → isSuccLimit_iff_of_orderBot #37410

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[Merged by Bors] - chore: rename isSuccLimit_iff → isSuccLimit_iff_of_orderBot #37410

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5 changes: 4 additions & 1 deletion Mathlib/Order/SuccPred/Limit.lean
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Expand Up @@ -252,9 +252,12 @@ section PartialOrder
variable [PartialOrder α]

@[to_dual]
theorem isSuccLimit_iff [OrderBot α] : IsSuccLimit a ↔ a ≠ ⊥ ∧ IsSuccPrelimit a := by
theorem isSuccLimit_iff_of_orderBot [OrderBot α] : IsSuccLimit a ↔ a ≠ ⊥ ∧ IsSuccPrelimit a := by
rw [IsSuccLimit, isMin_iff_eq_bot]

@[deprecated (since := "2026-03-31")] alias isSuccLimit_iff := isSuccLimit_iff_of_orderBot
@[deprecated (since := "2026-03-31")] alias isPredLimit_iff := isPredLimit_iff_of_orderTop

@[to_dual lt_top]
theorem IsSuccLimit.bot_lt [OrderBot α] (h : IsSuccLimit a) : ⊥ < a :=
h.ne_bot.bot_lt
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2 changes: 1 addition & 1 deletion Mathlib/SetTheory/Cardinal/Order.lean
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Expand Up @@ -426,7 +426,7 @@ theorem isSuccPrelimit_zero : IsSuccPrelimit (0 : Cardinal) :=
isSuccPrelimit_bot

protected theorem isSuccLimit_iff {c : Cardinal} : IsSuccLimit c ↔ c ≠ 0 ∧ IsSuccPrelimit c :=
isSuccLimit_iff
isSuccLimit_iff_of_orderBot

@[simp]
protected theorem not_isSuccLimit_zero : ¬ IsSuccLimit (0 : Cardinal) :=
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4 changes: 2 additions & 2 deletions Mathlib/SetTheory/Ordinal/Arithmetic.lean
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Expand Up @@ -124,8 +124,8 @@ theorem right_eq_zero_of_add_eq_zero {a b : Ordinal} (h : a + b = 0) : b = 0 :=

/-! ### Limit ordinals -/

theorem isSuccLimit_iff {o : Ordinal} : IsSuccLimit o ↔ o ≠ 0 ∧ IsSuccPrelimit o := by
simp [IsSuccLimit]
theorem isSuccLimit_iff {o : Ordinal} : IsSuccLimit o ↔ o ≠ 0 ∧ IsSuccPrelimit o :=
isSuccLimit_iff_of_orderBot

@[simp]
theorem isSuccPrelimit_zero : IsSuccPrelimit (0 : Ordinal) := isSuccPrelimit_bot
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