Theorems · Theorem · general topology
Filter.mem_sup
∀ {α : Type u} {f g : Filter α} {s : Set α}, s ∈ f ⊔ g ↔ s ∈ f ∧ s ∈ g- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by9
Results whose statement or proof uses this declaration.
- HasDerivWithinAt.limsup_norm_slope_leproof · cited by 2
- hasBasis_nhdsSet_Iic_Iioproof · cited by 2
- summable_jacobiTheta₂'_term_iffproof · cited by 2
- summable_jacobiTheta₂_term_fderiv_iffproof · cited by 2
- CofiniteTopology.nhds_eqproof · cited by 2
- IsOrderBornology.cobounded_le_atBot_sup_atTopproof · cited by 1
- Asymptotics.IsBigOWith.supproof · cited by 1
- Asymptotics.IsBigOWith.sup'proof · cited by 1
- Set.compl_ordConnectedSection_ordSeparatingSet_mem_nhdsproof · cited by 1