proposition: Lemma range_gP y: (inc y (range f) <-> (exists2 x, inc x (domain f) & y = Vg f x)).
proof: Proof. move: (fgf) => [sg _]; split. case/(rangeP sg)=> x Px; exists x; first by ex_tac. by move:(in_graph_V Px); aw; apply: pr2_def. by move => [x xdf ->]; apply/(rangeP sg); exists x; apply: fdomain_pr1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)