proposition: Lemma extension_f: function (extension f x y).
proof: Proof. rewrite /extension; apply: function_pr. - by apply: fgraph_setU1; fprops; rewrite domain_fg. - rewrite range_setU1 => t /setU1_P [] tr; apply/setU1_P;[left | by right]. by apply:f_range_graph. - by rewrite domain_setU1 - (proj33 ff). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)