proposition: Lemma fconnect_switch_x_fx x y : ~~ fconnect f x y -> fconnect (switch x y f) x (f x).
proof: Proof. move=> n_xy; have xDy : x != y by apply: contraNneq n_xy => ->. apply: (connect_trans (y := y)); first by rewrite fconnect_switched. by apply: connect1; rewrite /= ?eqxx [_ == x]eq_sym (negbTE xDy). Qed.
imports: mathcomp(all_ssreflect) GraphTheory(edone preliminaries bij) fourcolor(hypermap geometry cfmap jordan color coloring combinatorial4ct) fourcolor(walkup)