Countable strict weak orders embed in the rationals #
[UPSTREAM] candidate for Mathlib/Order/CountableDenseLinearOrder.lean. A countable strict
weak order is the pullback of < on ℚ along some map. Its quotient by incomparability is a
countable linear order, which embeds in ℚ by Cantor's theorem
Order.embedding_from_countable_to_dense.
theorem
Order.exists_rat_rel_iff_lt
{β : Type u_1}
[Countable β]
(r : β → β → Prop)
[IsStrictWeakOrder β r]
:
∃ (f : β → ℚ), ∀ (x y : β), r x y ↔ f x < f y
A countable strict weak order is the pullback of < on ℚ along some map.