proposition: Lemma cdiff_fin_infin a b: finite_c a -> infinite_c b -> b -c a = b.
proof: Proof. move => ha hb; move: (cdiff_pr (cle_fin_inf ha hb)) => ea. case: (finite_or_infinite (CS_diff b a)) => fd. move: ha fd => /NatP aN /NatP dN; move:(NS_sum aN dN); rewrite ea => /NatP. by case/ finite_not_infinite. by move: ea; rewrite (csum_fin_infin ha fd). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)