Theorems · Theorem · order theory
Set.range_eq_univ
∀ {α : Type u_1} {ι : Sort u_4} {f : ι → α}, Set.range f = Set.univ ↔ Function.Surjective f- Defined in
- Mathlib.Data.Set.Image
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement · cited by 4,705
- Set.univstatement · cited by 3,945
- Set.eq_univ_iff_forallproof · cited by 93
Cited by50
Results whose statement or proof uses this declaration.
- LinearMap.range_eq_topproof · cited by 107
- Function.Surjective.range_eqproof · cited by 70
- Set.range_idproof · cited by 37
- MonoidHom.range_eq_topproof · cited by 29
- AddMonoidHom.range_eq_topproof · cited by 20
- AddMonoidHom.mrange_eq_topproof · cited by 9
- AlgebraicGeometry.IsAffineOpen.range_fromSpecproof · cited by 8
- Finsupp.mapRange_surjectiveproof · cited by 7
- Algebra.FiniteType.isNoetherianRingproof · cited by 6
- AlgebraicGeometry.IsOpenImmersion.range_pullbackFstproof · cited by 4
- AlgebraicGeometry.IsOpenImmersion.range_pullbackSndproof · cited by 4
- AlgebraicGeometry.Scheme.Hom.opensRange_of_isIsoproof · cited by 4