equiv@{} := fun x y => num x * den y = num y * den x. Global Instance equiv_equiv_rel@{} : EquivRel equiv. Proof. split. - intros x. hnf. reflexivity. - intros x y. unfold equiv. apply symmetry. - intros x y z. unfold equiv. intros E1 E2. apply (mult_left_cancel (den y)). + solve_propholds. + rewrite !mult_assoc, !(mult_comm (den y)). rewrite E1, <-E2. rewrite <-!mult_assoc. rewrite (mult_comm (den x)). reflexivity. Qed.
Require Import HoTT.HIT.quotient. Require Import Import Frac.