proposition: Lemma skip_exists' x y : y \in a -> fconnect f (f x) y -> [exists n : 'I_(order f (f x)), iter n.+1 f x \in a].
proof: Proof. move => y_a c_xy; have:= iter_findex c_xy; rewrite -iterSr => E. set n := findex _ _ _ in E. have Hn : n < order f (f x) by apply: findex_max. apply/existsP; exists (Ordinal Hn); by rewrite E. Qed.
imports: mathcomp(all_ssreflect) GraphTheory(edone preliminaries bij) fourcolor(hypermap geometry cfmap jordan color coloring combinatorial4ct) fourcolor(walkup)