proposition: Lemma betSP a b c (r := betR a b c) : reflect ([ /\ b - a = r *: (c - a), 0 < r & r < 1 ]) (betS a b c).
proof: Proof. rewrite /betS -/r; case: (b - a =P r*:(c - a))=> [<-|/=]; last by constructor; case. by case: (0 < r); case: (r < 1)=> /=; constructor; try (case=> //). 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