proposition: Lemma pos_minus_lt_compat_l x z : 0 < z <-> - z + x < x.
proof: Proof. split; intros ltz. - rewrite (commutativity (-z) x); apply pos_minus_lt_compat_r; assumption. - rewrite (commutativity (-z) x) in ltz. apply (snd (pos_minus_lt_compat_r x z)); assumption. Qed.
imports: HoTT.Classes.interfaces.abstract_algebra HoTT.Classes.interfaces.orders HoTT.Classes.theory.groups HoTT.Classes.theory.rings HoTT.Classes.orders.semirings