Theorems · Theorem · order theory
Set.surjOn_iff_surjective
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {f : α → β}, Set.SurjOn f s Set.univ ↔ Function.Surjective (s.domRestrict f)- Defined in
- Mathlib.Data.Set.Restrict
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- Set.univstatement and proof · cited by 3,945
- Set.domRestrictstatement and proof · cited by 383
- Set.SurjOnstatement and proof · cited by 186
Cited by5
Results whose statement or proof uses this declaration.
- ContinuousOn.surjOn_of_tendstoproof · cited by 2
- AddSubgroup.index_le_of_leftCoset_cover_constproof · cited by 1
- Subgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eqproof · cited by 1
- AddSubgroup.pairwiseDisjoint_leftCoset_cover_const_of_index_eqproof · cited by 1
- Subgroup.index_le_of_leftCoset_cover_constproof · cited by 1