proposition: Lemma skipP' x y : y \in a -> fconnect f (f x) y -> skip_spec' x (skip x).
proof: Proof. move => y_a c_xy; rewrite /skip. case: {-}_ / idP => [p|]; last by rewrite (skip_exists' y_a c_xy). case: ex_minnP => n N1 N2; constructor; auto. case/existsP : p => -[m Hm] /N2/= ?. exact: leq_trans Hm. Qed.
imports: mathcomp(all_ssreflect) GraphTheory(edone preliminaries bij) fourcolor(hypermap geometry cfmap jordan color coloring combinatorial4ct) fourcolor(walkup)