proposition: Lemma I__S_R__S n: I__S (R__S n) = n.
proof: Proof. unfold I__S, R__S. destruct Nat.even eqn: H1. - symmetry. now apply Nat.Even_double, Nat.even_spec. - symmetry. eapply Nat.Odd_double, Nat.odd_spec. unfold odd; rewrite H1; eauto. Qed.
imports: FinFun Undecidability.HOU(std.decidable) Arith Lia Nat Arith.Div2