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Theorems · Theorem · order theory

directed_of_isDirected_ge

∀ {α : Type u_1} {β : Type u_2} [inst : LE α] [IsCodirectedOrder α] {f : α → β} {r : β → β → Prop},
  (∀ ⦃j i : α⦄, j ≤ i → r (f i) (f j)) → Directed r f

An antitone function on a downwards-directed type is directed.

Defined in
Mathlib.Order.Directed
Cited by
3 results in Mathlib
Foundations
Depth 7 from the axioms · uses no axioms
Assumes
LEIsCodirectedOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Monotone.directed_ge · cited by 3Monotone.directed_geAntitone.directed_le · cited by 2Antitone.directed_leDiscreteQuotient.exists_of_compat · cited by 0DiscreteQuotient.exists_o…Directed · cited by 213DirectedIsCodirectedOrder · cited by 95IsCodirectedOrderDirected.mono_comp · cited by 12Directed.mono_compdirected_id · cited by 7directed_iddirected_of_isDirected_geCITED BYCITES

Cites4

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Cited by3

Results whose statement or proof uses this declaration.