proposition: Lemma froot_face_rev_ring : map (froot face) (rev_ring r) = rev (rot 1 (map (froot face) r)).
proof: Proof. rewrite map_rev -map_rot; congr (rev _). case: r cycRr => // x0 p; rewrite rot1_cons /=; move: {1 3}x0. by elim: p => [|y p IHp] x /= /andP[xRy yRp]; rewrite (rootP cfaceC xRy) ?IHp. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype path fingraph) fourcolor(hypermap geometry patch sew snip color chromogram) fourcolor(coloring kempe)