proposition: Lemma betR_abc : betR a b c = 0.
proof: Proof. rewrite a_eq0 /b /c /betR /ratio; case: pickP => /= [x|all_v_neq0 //]. rewrite !subr0 /b /c /to_nD /row_mx !mxE; case: (split x)=> [x0|x1]; by rewrite ?mxE ?eqxx //; case: x0 => [] [|[|//]] p /=; rewrite ?divr1 ?eqxx. 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