map_le_iff — Mathlib

English

For f and a monotone-iff equivalence mono_iff, x.map f ≤ y.map f iff x ≤ y.

Русский

Для f и эквивалентности монотонности mono_iff, x.map f ≤ y.map f эквивалентно x ≤ y.

LaTeX

$$$ (f : \alpha \to \beta) (mono\_iff : \forall {a b}, f a \le f b \iff a \le b) \Rightarrow ( x.map f \le y.map f \iff x \le y ) $$$

Lean4

theorem map_le_iff (f : α → β) (mono_iff : ∀ {a b}, f a ≤ f b ↔ a ≤ b) : x.map f ≤ y.map f ↔ x ≤ y := by
  cases x <;> cases y <;> simp [mono_iff]

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