Theorems · Theorem · order theory
RightOrdContinuous.map_ciInf
∀ {α : Type u} {β : Type v} {ι : Sort x} [inst : ConditionallyCompleteLattice α]
[inst_1 : ConditionallyCompleteLattice β] [Nonempty ι] {f : α → β},
RightOrdContinuous f → ∀ {g : ι → α}, BddBelow (Set.range g) → f (⨅ i, g i) = ⨅ i, f (g i)- Defined in
- Mathlib.Order.OrdContinuous
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.rangestatement and proof · cited by 4,705
- iInfstatement · cited by 1,690
- InfSet.sInfproof · cited by 935
- BddBelowstatement and proof · cited by 401
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Set.range_compproof · cited by 223
- Set.range_nonemptyproof · cited by 84
- RightOrdContinuousstatement and proof · cited by 24
- RightOrdContinuous.map_csInfproof · cited by 1
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