proposition: Lemma Nat_induction_alt (r:property): (r \0c) -> (forall n, natp n -> r n -> r (csucc n)) -> (forall n, natp n -> r n).
proof: Proof. move=> r0 ri. apply:(omega_rec r0) => i iN. by rewrite - (succ_of_nat iN); apply: ri. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)