Theorems · Theorem · order theory
Set.surjOn_iff_exists_bijOn_subset
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : Set β} {f : α → β}, Set.SurjOn f s t ↔ ∃ s' ⊆ s, Set.BijOn f s' t- Defined in
- Mathlib.Data.Set.Function
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.imageproof · cited by 5,609
- Set.Nonemptyproof · cited by 2,627
- Set.eq_empty_or_nonemptyproof · cited by 248
- Set.SurjOnstatement and proof · cited by 186
- Set.BijOnstatement and proof · cited by 168
- Set.empty_subsetproof · cited by 70
- Set.Subset.reflproof · cited by 66
- Set.MapsTo.image_subsetproof · cited by 49
- Function.invFunOnproof · cited by 35
- Set.BijOn.surjOnproof · cited by 31
- Set.SurjOn.monoproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- Set.exists_subset_bijOnproof · cited by 3
- Set.SurjOn.exists_bijOn_subsetproof · cited by 1