proposition: Lemma betR_bca : betR b' c' a' = 1.
proof: Proof. rewrite /betR /ratio a_eq0 sub0r; case: pickP => /= [x|/all_v_neq0 H]. rewrite /b' /c' !mxE /=; case: x => [] [|[|[|//]]] //= p; rewrite oppr_eq0 ?eqxx // sub0r divff // oppr_eq0 oner_eq0 //. exfalso; apply H; rewrite oppr_eq0 -a_eq0 /a' /b' row3_eq oner_eq0 eqxx //. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype choice seq) mathcomp(fintype finset finfun bigop order) mathcomp(ssralg ssrnum path generic_quotient matrix mxalgebra) mathcomp(zmodp) GeoCoq.Meta_theory.Models.POF_to_Tarski GeoCoq.Meta_theory.Counter_models.Planar.independence