Theorems · Theorem · order theory

GaloisInsertion.isAtom_of_u_bot

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

Defined in

Mathlib.Order.Atoms

Cited by

3 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderPartialOrderOrderBotOrderBot