map_eq_natCast_iff — Mathlib

English

For a, f, and n, a.map f = n iff there exists x with a = some x and f x = n.

Русский

Для a, f и n, a.map f = n тогда и только тогда, когда существует x, such что a = some x и f x = n.

LaTeX

$$$\\\\forall {f : β \\\\to α} {n : \\\\mathbb{N}} {a : WithTop β}, a.map f = n \\\\iff \\\\exists x, a = .some x \\\\wedge f x = n$$$

Lean4

theorem map_eq_natCast_iff {f : β → α} {n : ℕ} {a : WithTop β} : a.map f = n ↔ ∃ x, a = .some x ∧ f x = n :=
  map_eq_some_iff

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