Theorems · Theorem · combinatorics

Finset.image_preimage

∀ {α : Type u} {β : Type v} [inst : DecidableEq β] (f : α → β) (s : Finset β)
  [inst_1 : (x : β) → Decidable (x ∈ Set.range f)] (hf : Set.InjOn f (f ⁻¹' ↑s)),
  Finset.image f (s.preimage f hf) = {x ∈ s | x ∈ Set.range f}

Defined in

Mathlib.Data.Finset.Preimage

Cited by

8 results in Mathlib

Foundations

Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

DecidableEqDecidable