proposition: Lemma snip_patch : patch snipd snipr snipd_ring snipr_ring.
proof: Proof. split. - exact inj_snipd. - exact inj_snipr. - exact scycle_snipd_ring. - exact ucycle_snipr_ring. - by rewrite map_snipd_ring; apply map_snipr_ring. - move=> x; rewrite /= map_snipd_ring !inE codom_snipd codom_snipr. by rewrite !inE negb_and negbK orbC. - case=> x dNx; rewrite !inE -(mem_map inj_snipd) map_snipd_ring /= => r'x. by rewrite /snipd_edge (negPf r'x). - by case. - by case. move=> u; rewrite inE /= -(mem_map inj_snipr) map_snipr_ring mem_rev /= => r'u. by rewrite /snipr_node (negPf r'u). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) fourcolor(hypermap jordan color geometry patch)