veblenWith_apply_eq_apply_iff — Mathlib

English

For any f normal, the statement veblenWith(f,o,f(a)) = f(a) is equivalent to veblenWith(f,o,a) = a.

Русский

Для любого нормального f верно: veblenWith(f,o,f(a)) = f(a) эквивалентно veblenWith(f,o,a) = a.

LaTeX

$$$\forall f:\,\operatorname{Ordinal} \to \operatorname{Ordinal},\ \operatorname{IsNormal}(f)\Rightarrow \operatorname{veblenWith}(f,o,(f\,a)) = f(a) \iff \operatorname{veblenWith}(f,o,a) = a$$$

Lean4

theorem veblenWith_apply_eq_apply_iff : veblenWith f o (f a) = f a ↔ veblenWith f o a = a := by
  simpa using veblenWith_veblenWith_eq_veblenWith_iff hf (zero_le o)

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