proposition: Lemma NleP a: natp a -> forall x, (x <=c a <-> inc x (csucc a)).
proof: Proof. move=> aN x; rewrite (succ_of_nat aN). split; first by move=> /ocle/(oleP (OS_nat aN)). case/setU1_P;first by case/(NltP aN). move => ->; apply: (cleR (CS_nat aN)). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)