toWithTop_ofENat — Mathlib

English

The map toWithTop is order-preserving: x ≤ y iff toWithTop x ≤ toWithTop y.

Русский

Отображение toWithTop сохраняет порядок: x ≤ y эквивалентно toWithTop x ≤ toWithTop y.

LaTeX

$$$\\\\operatorname{toWithTop} x \\\\le \\\\operatorname{toWithTop} y \\\\iff x \\\\le y$$$

Lean4

@[simp, norm_cast]
theorem toWithTop_ofENat (n : ℕ∞) {_ : Decidable (n : PartENat).Dom} : toWithTop (↑n) = n := by
  cases n with
  | top => simp
  | coe n => simp

Похожие утверждения