proposition: Lemma nonpos_dec_recip_compat x : x ≤ 0 -> /x ≤ 0.
proof: Proof. intros. apply flip_nonpos_negate. rewrite dec_recip_negate. apply nonneg_dec_recip_compat. apply flip_nonpos_negate;trivial. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.dec_fields HoTT.Classes.orders.rings