proposition: Lemma cpcolor1R'_correct f : (forall k', coloring k' -> @cp_extcol cp1 (CpR' :: cp2) f k') -> cp_extcol (CpR' :: cp1) (cpcolor1 CpR' f) k.
proof: Proof. case/(_ k col_k); rewrite cpring_ecpR -/cpmap -/G2 -subn1 -size_cpring. rewrite map_rotr -(rotK 1 (trace _)) -trace_rot rotrK. by split; rewrite /= size_trace size_map leqNgt -size_proper_cpring G2gt1. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) fourcolor(hypermap geometry color coloring cfmap ctree)