map_round — Mathlib

English

If f is a strictly monotone map between linearly ordered rings, then rounding commutes with f: round(f(a)) = round(a).

Русский

Если f строго монотоно, то для любого a верно round(f(a)) = round(a).

LaTeX

$$$\\\\forall f \\\\; (hf : \\\\text{StrictMono } f) \\\\forall a, \\, \\\\\\operatorname{round}(f(a)) = \\\\\\operatorname{round}(a).$$$

Lean4

theorem map_round (f : F) (hf : StrictMono f) (a : α) : round (f a) = round a := by
  simp_rw [round_eq, ← map_floor _ hf, map_add, one_div, map_inv₀, map_ofNat]

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