proposition: Lemma flip_lt_dec_recip_l x y : 0 < y -> /y < x -> /x < y.
proof: Proof. intros E1 E2. rewrite <-(dec_recip_involutive y). apply flip_lt_dec_recip; trivial. apply pos_dec_recip_compat. trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.dec_fields HoTT.Classes.orders.rings