Theorems · Theorem · order theory

GaloisConnection.l_csSup

∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] [inst_1 : ConditionallyCompleteLattice β]
  {l : α → β} {u : β → α}, GaloisConnection l u → ∀ {s : Set α}, s.Nonempty → BddAbove s → l (sSup s) = ⨆ x, l ↑x

Defined in

Mathlib.Order.ConditionallyCompleteLattice.Indexed

Cited by

4 results in Mathlib

Foundations

Depth 12 from the axioms · uses propext, Quot.sound

Assumes

ConditionallyCompleteLatticeConditionallyCompleteLattice