Theorems · Theorem · order theory

GaloisConnection.l_sup

∀ {α : Type u} {β : Type v} {a₁ a₂ : α} [inst : SemilatticeSup α] [inst_1 : SemilatticeSup β] {l : α → β} {u : β → α},
  GaloisConnection l u → l (a₁ ⊔ a₂) = l a₁ ⊔ l a₂

Defined in

Mathlib.Order.GaloisConnection.Basic

Cited by

81 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemilatticeSupSemilatticeSup