Theorems · Theorem · order theory

GaloisCoinsertion.isAtom_iff

∀ {α : Type u_2} {β : Type u_3} [inst : PartialOrder α] [inst_1 : PartialOrder β] [inst_2 : OrderBot α]
  [inst_3 : OrderBot β] [IsAtomic β] {l : α → β} {u : β → α} (gi : GaloisCoinsertion l u),
  (∀ (b : β), IsAtom b → l (u b) = b) → ∀ (a : α), IsAtom (l a) ↔ IsAtom a

Defined in

Mathlib.Order.Atoms

Cited by

0 results in Mathlib

Foundations

Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderOrderBotOrderBotIsAtomic