proposition: Lemma exercise4_4a g x: graph_morph (direct_image^~x) unionb g.
proof: Proof. set_extens y. move => /dirim_P [a ax /setUb_P [u ud Jv]]. apply: (@setUb_i _ u); aw; trivial;rewrite LgV //; apply /dirim_P; ex_tac. move /setUb_P => [z]; rewrite Lgd => zd; rewrite LgV//. move /dirim_P => [u ux Jv]; apply /dirim_P; ex_tac; union_tac. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)