proposition: Lemma nontrivial0P r : reflect ((exists x, x \in diskF r) /\ (exists x, x \in diskFC r)) (nontrivial_ring 0 r).
proof: Proof. rewrite /nontrivial_ring. have [nzFr|] := fcard0P (diskF_face r); last by right; case. by apply: (iffP (fcard0P (diskFC_face r))) => [|[]]. 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)