dec_recip_nonzero@{} : forall q (E : ' q <> 0), / (' q) = ' (frac (den q) (num q) (dec_recip_nonzero_aux q E)). Proof. intros. apply path. red;simpl. unfold Frac.dec_rec. apply classes_neq_related, Frac.nonzero_num in E. destruct (decide_rel paths (num q) 0) as [E'|?];[destruct E;apply E'|]. simpl. reflexivity. Qed.
Require Import HoTT.HIT.quotient. Require Import Import Frac.