Theorems · Theorem · logic and foundations

Set.pairwiseDisjoint_image_right_iff

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {f : α → β → γ} {s : Set α} {t : Set β},
  (∀ a ∈ s, Function.Injective (f a)) →
    ((s.PairwiseDisjoint fun a => f a '' t) ↔ Set.InjOn (fun p => f p.1 p.2) (s ×ˢ t))

The partial images of a binary function f whose partial evaluations are injective are pairwise disjoint iff f is injective .

Defined in

Mathlib.Data.Set.Pairwise.Basic

Cited by

3 results in Mathlib

Foundations

Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound