#[global]
Hint Resolve Qeq_refl Qeq_trans : qarith.
(** In a word, [Qeq] is a setoid equality. *)
#[global]
Instance Q_Setoid : Equivalence Qeq.

Lemma Qeq_bool_sym x y: Qeq_bool x y = true -> Qeq_bool y x = true.