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Theorems · Theorem · order theory

Set.iUnion_and

∀ {α : Type u_1} {p q : Prop} (s : p ∧ q → Set α), ⋃ (h : p ∧ q), s h = ⋃ (hp : p), ⋃ (hq : q), s ⋯
Defined in
Mathlib.Data.Set.Lattice
Cited by
4 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.biUnion_and' · cited by 14Set.biUnion_and'AddSubgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3AddSubgroup.leftCoset_cov…Subgroup.leftCoset_cover_filter_FiniteIndex_aux · cited by 3Subgroup.leftCoset_cover_…Set.biUnion_and · cited by 0Set.biUnion_andSet · cited by 53352SetSet.iUnion · cited by 2483Set.iUnioniSup_and · cited by 13iSup_andSet.iUnion_andCITED BYCITES

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_andproof · cited by 13

Cited by4

Results whose statement or proof uses this declaration.