proposition: Lemma pos_le_add : forall y x, (x <= y + x)%positive.
proof: Proof. intros y x. assert ((Z.pos x) <= Z.pos (x + y))%Z as H. - rewrite <- (Z.add_0_r (Zpos x)). rewrite <- Pos2Z.add_pos_pos. apply Z.add_le_mono_l. compute. congruence. - rewrite Pos.add_comm in H. apply H. Qed.
imports: List Bool OrderedRing RingMicromega ZCoeff Refl ZArith_base ZArithRing Ztac EnvRing Coq.micromega.Tauto BinNums Zdiv Znumtheory QArith Znumtheory