proposition: Lemma fitq_cat x q sa s : (flatq q ++ sa == map arity (walkq x q ++ s)) = fitq x q && (sa == map arity s).
proof: Proof. rewrite /fitq; have /eqP := size_walkq x q. elim: {q x}(walkq x q) (flatq q) => [|x s1 IHs1] [|n s1a] //= eq_sza. by rewrite !eqseq_cons -andbA IHs1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) fourcolor(hypermap geometry coloring)