Theorems · Theorem · order theory

Set.SurjOn.exists_subset_injOn_image_eq

∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β} {f : α → β},
  Set.SurjOn f s t → ∃ u ⊆ s, Set.InjOn f u ∧ f '' u = t

If t ⊆ f '' s, there exists a preimage of t under f contained in s such that f restricted to u is injective.

Defined in

Mathlib.Data.Set.Function

Cited by

2 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound