Theorems · Theorem · order theory

GaloisConnection.u_eq_top

∀ {α : Type u} {β : Type v} [inst : PartialOrder α] [inst_1 : Preorder β] [inst_2 : OrderTop α] {l : α → β} {u : β → α},
  GaloisConnection l u → ∀ {x : β}, u x = ⊤ ↔ l ⊤ ≤ x

Defined in

Mathlib.Order.GaloisConnection.Defs

Cited by

4 results in Mathlib

Foundations

Depth 9 from the axioms · uses no axioms

Assumes

PartialOrderPreorderOrderTop