proposition: Lemma csum_fin_infin a b: finite_c a -> infinite_c b -> a +c b = b.
proof: Proof. move/NatP => aN ifb; move: a aN; apply:Nat_induction. by rewrite (csum0l (proj1 ifb)). move/csucc_inf: ifb => csb. by move => a aN hr; rewrite (csum_Sn _ aN) hr - csb. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)