proposition: Lemma ratio_cp (a b c : R) : a - b != 0 -> b - c != 0 -> c - a != 0 -> 0 < (b - a) / (c - a) < 1 \/ 0 < (c - b) / (a - b) < 1 \/ 0 < (a - c) / (b - c) < 1.
proof: Proof. by rewrite subr_eq add0r eq_sym -[X in _ != X]add0r -subr_eq=> H1 H3 H2; move: (ratio_cp' H1 H2 H3)=> /or3P HE; elim HE=> H; [left|right; left|right; right]. 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