proposition: Lemma sfunctionsP x y f: inc f (sub_functions x y) <-> [/\ function f, sub (source f) x & target f = y].
proof: Proof. split. move/setUf_P => [z /setP_P zx /functionsP [pa pb pc]];split => //; ue. by move => [pa /setP_P pb pc]; apply /setUf_P; ex_tac; apply/functionsP. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)