Theorems · Theorem · order theory

partialSups_le

∀ {α : Type u_1} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : Preorder ι] [inst_2 : LocallyFiniteOrderBot ι]
  (f : ι → α) (i : ι) (a : α), (∀ j ≤ i, f j ≤ a) → (partialSups f) i ≤ a

Defined in

Mathlib.Order.PartialSups

Cited by

3 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupPreorderLocallyFiniteOrderBot