Theorems · Theorem · logic and foundations
Set.eq_univ_iff_forall
∀ {α : Type u} {s : Set α}, s = Set.univ ↔ ∀ (x : α), x ∈ s- Defined in
- Mathlib.Data.Set.Basic
- Cited by
- 93 results in Mathlib
- Foundations
- Depth 22 from the axioms, rests on 122 definitions · 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.univ_subset_iffproof · cited by 49
Cited by93
Results whose statement or proof uses this declaration.
- Set.eq_univ_of_forallproof · cited by 80
- Set.union_compl_selfproof · cited by 57
- Set.range_eq_univproof · cited by 50
- dense_iff_closure_eqproof · cited by 26
- TopologicalSpace.IsTopologicalBasis.mem_nhds_iffproof · cited by 13
- Set.compl_subset_iff_unionproof · cited by 9
- Set.ne_univ_iff_exists_notMemproof · cited by 7
- aeconst_of_dense_setOfPred_preimage_smul_aeproof · cited by 4
- aeconst_of_dense_setOfPred_preimage_vadd_aeproof · cited by 4
- uniformContinuous_of_constproof · cited by 4
- SimpleGraph.Subgraph.isSpanning_iffproof · cited by 4
- IsCoveringMap.exists_path_liftsproof · cited by 4