Theorems · Theorem · order theory

OrderIso.map_ciInf_of_directed

∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderInf α]
  [inst_1 : ConditionallyCompletePartialOrderInf β] [Nonempty ι] (e : α ≃o β) {f : ι → α},
  Directed (fun x1 x2 => x2 ≤ x1) f → BddBelow (Set.range f) → e (⨅ i, f i) = ⨅ i, e (f i)

Defined in: Mathlib.Order.ConditionallyCompletePartialOrder.Indexed
Cited by: 0 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ConditionallyCompletePartialOrderInf ConditionallyCompletePartialOrderInf Nonempty

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DFunLike.coestatement · cited by 62,936
Set.rangestatement and proof · cited by 4,705
iInfstatement · cited by 1,690
OrderIsostatement and proof · cited by 874
BddBelowstatement and proof · cited by 401
Directedstatement and proof · cited by 213
ConditionallyCompletePartialOrderInfstatement and proof · cited by 51
GaloisConnection.u_ciInf_of_directedproof · cited by 2

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