proposition: Lemma dec_recip_nonzero@{} : forall q (E : ' q <> 0), / (' q) = ' (frac (den q) (num q) (dec_recip_nonzero_aux q E)).
proof: 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.
imports: HoTT.HIT.quotient HoTT.Basics.Trunc HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.theory.dec_fields