Theorems · Theorem · order theory
Set.iUnion_iUnion_eq_left
∀ {α : Type u_1} {β : Type u_2} {b : β} {s : (x : β) → x = b → Set α}, ⋃ x, ⋃ (h : x = b), s x h = s b ⋯- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 27 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_iSup_eq_leftproof · cited by 15
Cited by27
Results whose statement or proof uses this declaration.
- Set.iUnion_iUnion_eq_or_leftproof · cited by 18
- IsLindelof.elim_countable_subcoverproof · cited by 10
- IsCompactOpenCovered.iff_of_uniqueproof · cited by 5
- BoxIntegral.Prepartition.iUnion_topproof · cited by 4
- BoxIntegral.Prepartition.iUnion_singleproof · cited by 3
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Subgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- Set.accumulate_zero_natproof · cited by 3
- PrimeSpectrum.exists_constructibleSetData_iffproof · cited by 2
- BoxIntegral.Prepartition.iUnion_splitproof · cited by 1
- Topology.CWComplex.exists_cellFrontier_one_eqproof · cited by 1
- Submodule.iUnion_ssubset_of_forall_ne_top_of_card_ltproof · cited by 1