Theorems · Theorem · order theory

GaloisInsertion.isCoatom_of_image

∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : OrderTop α]
  [inst_3 : OrderTop β] {l : α → β} {u : β → α} (gi : GaloisInsertion l u) {b : β}, IsCoatom (u b) → IsCoatom b

Defined in

Mathlib.Order.Atoms

Cited by

2 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderOrderTopOrderTop