proposition: Theorem ratS_num : forall n, (S n) / (S O) == 1 + (n / (S O)).
proof: Proof. rattac. unfold natToPosnat in *. inversion H0; clear H0; subst. repeat rewrite Nat.mul_1_r. inversion H; clear H; subst. trivial. Qed.
imports: micromega.Lia List FCF.StdNat Arith Lia Setoid RelationClasses Coq.Classes.Morphisms