Theorems · Theorem · order theory

OmegaCompletePartialOrder.ContinuousHom.continuous

∀ {α : Type u_2} {β : Type u_3} [inst : OmegaCompletePartialOrder α] [inst_1 : OmegaCompletePartialOrder β] (F : α →𝒄 β)
  (C : OmegaCompletePartialOrder.Chain α),
  F (OmegaCompletePartialOrder.ωSup C) = OmegaCompletePartialOrder.ωSup (C.map ↑F)

Defined in: Mathlib.Order.OmegaCompletePartialOrder
Cited by: 2 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: OmegaCompletePartialOrder OmegaCompletePartialOrder

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Cites9

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

DFunLike.coestatement · cited by 62,936
OmegaCompletePartialOrderstatement and proof · cited by 104
OmegaCompletePartialOrder.Chainstatement and proof · cited by 85
OmegaCompletePartialOrder.ωSupstatement · cited by 48
OrderHomClass.toOrderHomstatement · cited by 44
OmegaCompletePartialOrder.Chain.mapstatement · cited by 41
OmegaCompletePartialOrder.ContinuousHomstatement and proof · cited by 41
OmegaCompletePartialOrder.ωScottContinuous.map_ωSupproof · cited by 11
OmegaCompletePartialOrder.ContinuousHom.ωScottContinuousproof · cited by 1

Cited by2

Results whose statement or proof uses this declaration.

OmegaCompletePartialOrder.fixedPoints.ωSup_iterate_mem_fixedPointproof · cited by 1
OmegaCompletePartialOrder.ContinuousHom.ωScottContinuous_applyproof · cited by 0