Theorems · Theorem · order theory

GaloisConnection.l_sSup

∀ {α : Type u} {β : Type v} [inst : CompleteLattice α] [inst_1 : CompleteLattice β] {l : α → β} {u : β → α},
  GaloisConnection l u → ∀ {s : Set α}, l (sSup s) = ⨆ a ∈ s, l a

Defined in

Mathlib.Order.GaloisConnection.Basic

Cited by

19 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CompleteLatticeCompleteLattice