Theorems · Theorem · logic and foundations
Set.eq_univ_of_forall
∀ {α : Type u} {s : Set α}, (∀ (x : α), x ∈ s) → s = Set.univ- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 80 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.
Cites3
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.univstatement · cited by 3,945
- Set.eq_univ_iff_forallproof · cited by 93
Cited by80
Results whose statement or proof uses this declaration.
- Set.preimage_rangeproof · cited by 38
- EquivLike.range_eq_univproof · cited by 27
- IsAddQuotientCoveringMap.isCoveringMapproof · cited by 16
- IsQuotientCoveringMap.isCoveringMapproof · cited by 15
- Set.pi_univproof · cited by 14
- Set.preimage_const_of_memproof · cited by 14
- Set.image_univ_of_surjectiveproof · cited by 13
- Metric.eball_topproof · cited by 7
- Subgroup.IsComplement.mul_eqproof · cited by 5
- Subsingleton.eq_univ_of_nonemptyproof · cited by 5
- AddSubgroup.IsComplement.add_eqproof · cited by 5
- Set.powerset_univproof · cited by 4