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Theorems · Theorem · order theory

iInf_exists

∀ {α : Type u_1} {ι : Sort u_4} [inst : CompleteLattice α] {p : ι → Prop} {f : Exists p → α},
  ⨅ (x : Exists p), f x = ⨅ i, ⨅ (h : p i), f ⋯
Defined in
Mathlib.Order.CompleteLattice.Basic
Cited by
6 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
CompleteLattice
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.iInter_exists · cited by 44Set.iInter_existsnhds_eq_order · cited by 9nhds_eq_orderTopCat.Presheaf.EtaleSpace.eventually_nhds · cited by 2EtaleSpace.eventually_nhdsFinset.iInf_biUnion · cited by 1Finset.iInf_biUnionFinset.iInf_finset_image · cited by 1Finset.iInf_finset_imageiInf_extend_top · cited by 0iInf_extend_topiInf · cited by 1690iInfCompleteLattice · cited by 1048CompleteLatticeiInf_le · cited by 104iInf_lele_iInf · cited by 102le_iInfle_iInf₂ · cited by 67le_iInf₂ge_antisymm · cited by 51ge_antisymmiInf₂_le · cited by 45iInf₂_leiInf_existsCITED BYCITES

Cites7

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

Cited by6

Results whose statement or proof uses this declaration.