testable — Mathlib

English

Let α and β be preordered sets and f: α → β. A function is monotone if x ≤ y implies f(x) ≤ f(y).

Русский

Пусть α и β — предваозрастания, f: α → β. Функция монотонна, если x ≤ y тогда f(x) ≤ f(y).

LaTeX

$$$\forall x,y:\alpha,\; x\le y \Rightarrow f(x)\le f(y)$$$

Lean4

instance testable [Preorder α] [Preorder β] (f : α → β)
    [I : Testable (NamedBinder "x" <| ∀ x : α, NamedBinder "y" <| ∀ y : α, NamedBinder "H" <| x ≤ y → f x ≤ f y)] :
    Testable (Monotone f) :=
  I

Похожие утверждения