proposition: Lemma recip_apart (x : F) (Px : x ≶ 0) : // (x;Px) ≶ 0.
proof: Proof. apply (strong_extensionality (x*.) (// (x; Px)) 0). rewrite (recip_inverse (x;Px)). rewrite mult_0_r. solve_propholds. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.theory.apartness HoTT.Classes.theory.rings