proposition: Lemma add_inj_r p x y : gen_phiPOS1 rI radd rmul p + x == gen_phiPOS1 rI radd rmul p + y -> x==y.
proof: Proof. elim p using Pos.peano_ind; simpl; [intros H|intros ? H ?]. - apply S_inj; trivial. - apply H. apply S_inj. rewrite !(ARadd_assoc ARth). rewrite <- (ARgen_phiPOS_Psucc Rsth Reqe ARth); trivial. Qed.
imports: ZArith_base