Theorems · Theorem · order theory

GaloisConnection.l_iSup

∀ {α : Type u} {β : Type v} {ι : Sort x} [inst : CompleteLattice α] [inst_1 : CompleteLattice β] {l : α → β}
  {u : β → α}, GaloisConnection l u → ∀ {f : ι → α}, l (iSup f) = ⨆ i, l (f i)

Defined in

Mathlib.Order.GaloisConnection.Basic

Cited by

78 results in Mathlib

Foundations

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

Assumes

CompleteLatticeCompleteLattice