proposition: Lemma plain_neq : plain -> forall x, (edge x == x) = false.
proof: Proof. by move/plainP=> plainG x; apply/idPn; case: (plainG x). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) fourcolor(hypermap jordan)