Theorems · Theorem · general topology
Filter.union_mem_sup
∀ {α : Type u} {f g : Filter α} {s t : Set α}, s ∈ f → t ∈ g → s ∪ t ∈ f ⊔ 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.
Cites5
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
- Filterstatement and proof · cited by 8,121
- Filter.mem_of_supersetproof · cited by 308
- Set.subset_union_leftproof · cited by 142
- Set.subset_union_rightproof · cited by 123
Cited by9
Results whose statement or proof uses this declaration.
- preimage_extChartAt_eventuallyEq_compl_singletonproof · cited by 3
- exists_Icc_mem_subset_of_mem_nhdsproof · cited by 2
- extChartAt_target_union_compl_range_mem_nhds_of_memproof · cited by 1
- MeasureTheory.IntegrableAtFilter.sup_iffproof · cited by 1
- union_mem_nhdsSetproof · cited by 1
- MeasureTheory.Measure.FiniteAtFilter.filterSupproof · cited by 0
- isUniformEmbedding_inlproof · cited by 0
- isUniformEmbedding_inrproof · cited by 0
- union_mem_uniformity_sumproof · cited by 0