isSuccLimit_add_iff_of_isSuccLimit

English

If a is a succ-limit ordinal, then IsSuccLimit(a + b) is equivalent to IsSuccPrelimit(b).

Русский

Если a — упорядоченно предельно-супер порядок, то IsSuccLimit(a + b) эквивалентно IsSuccPrelimit(b).

LaTeX

$$$\\text{IsSuccLimit}(a + b) \\\\Leftrightarrow \\text{IsSuccPrelimit}(b)$, при условии, что $a$ — IsSuccLimit.$$

Lean4

theorem isSuccLimit_add_iff_of_isSuccLimit {a b : Ordinal} (h : IsSuccLimit a) :
    IsSuccLimit (a + b) ↔ IsSuccPrelimit b := by
  rw [isSuccLimit_add_iff]
  obtain rfl | hb := eq_or_ne b 0
  · simpa
  · simp [hb, isSuccLimit_iff]

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