proposition: Lemma ZL4' : forall y : positive, {h : nat | nat_of_P y = S h}.
proof: Proof. simple induction y; [ intros p H; elim H; intros x H1; exists (S x + S x); unfold nat_of_P in |- *; simpl in |- *; rewrite ZL0; rewrite Pmult_nat_r_plus_morphism; unfold nat_of_P in H1; rewrite H1; auto with arith | intros p H1; elim H1; intros x H2; exists (x + S x); unfold nat_of_P in |- *; simpl in |- *; rewrite ZL0; rewrite Pmult_nat_r_plus_morphism; unfold nat_of_P in H2; rewrite H2; auto with arith | exists 0; auto with arith ]. Qed.
imports: Coq.Arith.Compare_dec CoRN.logic.CornBasics Coq.ZArith.ZArith Coq.setoid_ring.ZArithRing Coq.Arith.Wf_nat Coq(Lia)