Theorems · Theorem · general topology

sup_eq_of_isMaxOn

∀ {α : Type u} {β : Type v} [inst : SemilatticeSup β] [inst_1 : OrderBot β] {D : α → β} {s : Finset α} {a : α},
  a ∈ s → IsMaxOn D (↑s) a → s.sup D = D a

Defined in

Mathlib.Order.Filter.Extr

Cited by

3 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupOrderBot