Theorems · Theorem · order theory

exists_orderEmbedding_covby_of_forall_covby_finite_of_bot

∀ {α : Type u_1} [inst : PartialOrder α] [IsStronglyAtomic α] [inst_2 : OrderBot α] [Infinite α],
  (∀ (a : α), {x | a ⋖ x}.Finite) → ∃ f, f 0 = ⊥ ∧ ∀ (i : ℕ), f i ⋖ f (i + 1)

A version of Kőnig's lemma where the sequence starts at the minimum of an infinite order.

Defined in

Mathlib.Order.KonigLemma

Cited by

1 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

PartialOrderIsStronglyAtomicOrderBotInfinite