proposition: Lemma finite_sum_finite_aux x: sub x (domain f) -> natp (csum (restr f x)).
proof: Proof. move: fif => [alN fsd] sxd. have fsx:= (sub_finite_set sxd fsd). move: x fsx sxd; apply: finite_set_induction0. move=> _;rewrite csum_trivial;aww. move=> a b ap nba st;rewrite (induction_sum0 _ nba). apply: NS_sum; [apply: ap; apply: sub_trans st | ];fprops. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(binomial div)