Theorems · Theorem · order theory

Directed.ciInf_mono

∀ {α : Type u_1} {ι : Sort u_4} [inst : ConditionallyCompletePartialOrderInf α] {f g : ι → α},
  Directed (fun x1 x2 => x2 ≤ x1) f →
    Directed (fun x1 x2 => x2 ≤ x1) g → BddBelow (Set.range g) → (∀ (x : ι), g x ≤ f x) → iInf g ≤ iInf f

The indexed infimum of two functions are comparable if the functions are pointwise comparable

Defined in

Mathlib.Order.ConditionallyCompletePartialOrder.Indexed

Cited by

0 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ConditionallyCompletePartialOrderInf