proposition: Lemma del_face_hom : {homo del_node_face : x / x \notin N}.
proof: Proof. move => x xN;rewrite /del_node_face; case: (boolP (face x \in N)) => //. apply: del_node_neighbor1'. apply: contraNN xN. rewrite cnode1r plain_eq' // -edgeN. exact: mem_closure. Qed.
imports: mathcomp(all_ssreflect) GraphTheory(edone preliminaries bij) fourcolor(hypermap geometry cfmap jordan color coloring combinatorial4ct) fourcolor(walkup)