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Theorems · Theorem · order theory

iInf_iUnion

∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_5} [inst : CompleteLattice β] (s : ι → Set α) (f : α → β),
  ⨅ a ∈ ⋃ i, s i, f a = ⨅ i, ⨅ a ∈ s i, f a
Defined in
Mathlib.Data.Set.Lattice
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Quot.sound
Assumes
CompleteLattice
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Around this declaration

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

Metric.infEDist_iUnion · cited by 4Metric.infEDist_iUnioniInf_sUnion · cited by 3iInf_sUnionSet · cited by 53352SetSet.iUnion · cited by 2483Set.iUnioniInf · cited by 1690iInfCompleteLattice · cited by 1048CompleteLatticeiSup_iUnion · cited by 5iSup_iUnioniInf_iUnionCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.