proposition: Lemma genus_WalkupE_eq : glink z z \/ ~~ cross_edge -> genus G' = genus G.
proof: Proof. rewrite /(genus G) -subSS -Euler_lhs_WalkupE -Euler_rhs_WalkupE /n_comp_z. by case=> [-> | not_zEnz]; rewrite ?(not_zEnz, not_cross_connected) ?subnDl. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) fourcolor(hypermap)