Theorems · Theorem · order theory
Set.mem_biUnion
∀ {α : Type u_1} {β : Type u_2} {s : Set α} {t : α → Set β} {x : α} {y : β}, x ∈ s → y ∈ t x → y ∈ ⋃ x ∈ s, t xA specialization of mem_iUnion₂.
- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 37 results in Mathlib
- Foundations
- Depth 11 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.iUnionstatement · cited by 2,483
- Set.mem_iUnion₂_of_memproof · cited by 13
Cited by37
Results whose statement or proof uses this declaration.
- IsLindelof.elim_countable_subcoverproof · cited by 10
- Algebra.IsInvariant.exists_smul_of_under_eqproof · cited by 5
- Set.Countable.isLindelof_biUnionproof · cited by 4
- LocallyFinite.finite_nonempty_inter_compactproof · cited by 4
- Set.Finite.totallyBoundedproof · cited by 3
- IsGLB.biUnion_Ioi_eqproof · cited by 3
- IsPreconnected.biUnion_of_reflTransGenproof · cited by 3
- Set.subset_accumulateproof · cited by 3
- exists_covby_infinite_Ici_of_infinite_Iciproof · cited by 2
- ShrinkingLemma.PartialRefinement.le_chainSupproof · cited by 2
- Set.Finite.iUnionproof · cited by 2
- IsCompact.cthickening_eq_biUnion_closedBallproof · cited by 2