proposition: Lemma betR_bca : betR b c a = 1.
proof: Proof. rewrite /b /c a_eq0 /betR /ratio add0r; case: pickP => /= [x|/all_v_neq0 H]; last by exfalso; apply H; rewrite oppr_eq0 b_neq0. rewrite /to_nD /row_mx !mxE; case: (split x)=> [x0|x1]; rewrite ?mxE ?oppr_eq0; rewrite ?eqxx //; case: x0 => [] [|[|//]] p /=; rewrite ?eqxx //. by rewrite sub0r divff ?eqxx // oppr_eq0 oner_eq0. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype seq order) mathcomp(fintype bigop) mathcomp(ssralg ssrnum matrix) mathcomp(zmodp) GeoCoq.Axioms.tarski_axioms GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.gupta_inspired_to_tarski GeoCoq.Meta_theory.Counter_models.coplanarity GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Tarski_dev.Ch12_parallel_inter_dec