Theorems · Theorem · order theory
Set.iUnion_subtype
∀ {α : Type u_1} {β : Type u_2} (p : α → Prop) (s : { x // p x } → Set β), ⋃ x, s x = ⋃ x, ⋃ (hx : p x), s ⟨x, hx⟩- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, 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
- iSup_subtypeproof · cited by 26
Cited by14
Results whose statement or proof uses this declaration.
- Set.iUnion_coe_setproof · cited by 53
- QuotientAddGroup.preimage_image_mk_eq_addproof · cited by 3
- MeasureTheory.measure_limsup_cofinite_eq_zeroproof · cited by 3
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- QuotientGroup.preimage_image_mk_eq_mulproof · cited by 3
- TopologicalSpace.isOpen_biUnion_countableproof · cited by 2
- AlgebraicGeometry.Scheme.exists_isOpenCover_and_isAffineproof · cited by 1
- TopologicalSpace.Opens.IsBasis.exists_iSup_eq_of_isCompactproof · cited by 0
- TopologicalSpace.IsOpenCover.exists_finite_of_compactSpaceproof · cited by 0