Theorems · Theorem · order theory

directed_of_isDirected_le

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

A monotone function on an upwards-directed type is directed.

Defined in

Mathlib.Order.Directed

Cited by

8 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

LEIsDirectedOrder