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Theorems · Definition · order theory

OmegaCompletePartialOrder.Chain.map

{α : Type u_2} →
  {β : Type u_3} →
    [inst : Preorder α] →
      [inst_1 : Preorder β] → OmegaCompletePartialOrder.Chain α → (α →o β) → OmegaCompletePartialOrder.Chain β

map function for Chain

Defined in
Mathlib.Order.OmegaCompletePartialOrder
Cited by
41 results in Mathlib
Foundations
Depth 22 from the axioms · uses no axioms
Assumes
PreorderPreorder

Around this declaration

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

OmegaCompletePartialOrder.ωScottContinuous.map_ωSup · cited by 11ωScottContinuous.map_ωSupOmegaCompletePartialOrder.ωScottContinuous.of_monotone_map_ωSup · cited by 9ωScottContinuous.of_monot…OmegaCompletePartialOrder.ωScottContinuous.of_map_ωSup_of_orderHom · cited by 4ωScottContinuous.of_map_ω…OmegaCompletePartialOrder.ωScottContinuous_iff_monotone_map_ωSup · cited by 3OmegaCompletePartialOrder…OmegaCompletePartialOrder.Chain.map_comp · cited by 3Chain.map_compOmegaCompletePartialOrder.ContinuousHom.ωSup · cited by 3ContinuousHom.ωSupOmegaCompletePartialOrder.ωScottContinuous_iff_map_ωSup_of_orderHom · cited by 2OmegaCompletePartialOrder…OmegaCompletePartialOrder.ContinuousHom.continuous · cited by 2ContinuousHom.continuousProd.ωSupImpl · cited by 2Prod.ωSupImplOmegaCompletePartialOrder.ContinuousHom.ωScottContinuous.bind · cited by 2ωScottContinuous.bindOmegaCompletePartialOrder.ωScottContinuous.comp · cited by 2ωScottContinuous.compOmegaCompletePartialOrder.Chain.mem_map · cited by 1Chain.mem_mapOmegaCompletePartialOrder.ContinuousHom.mk.inj · cited by 1mk.injOmegaCompletePartialOrder.ContinuousHom.mk.noConfusion · cited by 1mk.noConfusionOmegaCompletePartialOrder.ContinuousHom.map_ωSup' · cited by 1ContinuousHom.map_ωSup'Preorder · cited by 7952PreorderOrderHom · cited by 934OrderHomOmegaCompletePartialOrder.Chain · cited by 85OmegaCompletePartialOrder…OrderHom.comp · cited by 61OrderHom.compOmegaCompletePartialOrder.Chain.toOrderHom · cited by 10Chain.toOrderHomChain.mapCITED BYCITES

Cites5

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

Cited by51

Results whose statement or proof uses this declaration.