proposition: Lemma dec_recip_ne_0_iff x : / x <> 0 <-> x <> 0.
proof: Proof. split; intros E1 E2; destruct E1; apply dec_recip_zero;trivial. do 2 apply (snd (dec_recip_zero _)). trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.theory.fields HoTT.Classes.theory.apartness HoTT.Classes.theory.rings