proposition: Lemma nat_map_P x: inc x (graph nat_fun) <-> exists n, x = J (Ro n) (Ro n.+1).
proof: Proof. by rewrite /nat_fun/nat_map; aw; split; [ move/IM_P | move => Î; apply/IM_P]. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)