proposition: Lemma contraction_rec_succ'' a n m: natp n -> natp m -> Vf (contraction_rec a) (n +c m) = Vf (contraction_rec (Vf (contraction_rec a) n)) m.
proof: Proof. move => nN mN; move: m mN n nN. apply: Nat_induction. move => n nN; rewrite contraction_rec0 csum0r; fprops. move => m mN Hrec n nN. rewrite (csum_nS _ mN) (contraction_rec_succ _ (NS_sum nN mN)). rewrite (Hrec _ nN) contraction_rec_succ //. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)