Theorems · Theorem · order theory
Set.iUnion_coe_set
∀ {α : Type u_12} {β : Type u_13} (s : Set α) (f : ↑s → Set β), ⋃ i, f i = ⋃ i, ⋃ (h : i ∈ s), f ⟨i, h⟩- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.Elemstatement and proof · cited by 7,166
- Set.iUnionstatement · cited by 2,483
- Set.iUnion_subtypeproof · cited by 14
Cited by53
Results whose statement or proof uses this declaration.
- MeasureTheory.measure_biUnion_null_iffproof · cited by 11
- SSet.horn_eq_iSupproof · cited by 9
- AlgebraicGeometry.isCompact_iff_finite_and_eq_biUnion_affineOpensproof · cited by 6
- AlgebraicGeometry.IsZariskiLocalAtTarget.of_iSup_eq_topproof · cited by 5
- TopologicalSpace.Opens.IsBasis.exists_finite_of_isCompactproof · cited by 3
- AlgebraicGeometry.iSup_basicOpen_of_span_eq_topproof · cited by 2
- AlgebraicGeometry.compact_open_induction_onproof · cited by 2
- SimpleGraph.coe_finsetWalkLength_eqproof · cited by 2
- Cardinal.lt_power_cof_ordproof · cited by 2
- SSet.horn_obj_eq_univproof · cited by 2
- PrimeSpectrum.iSup_basicOpen_eq_top_iff'proof · cited by 2