proposition: Lemma ratio_cp'_aux_2 (a b c : R) : a - b != 0 -> (b - a) / (c - a) < 0 -> 0 < (c - b) / (a - b).
proof: Proof. move=> ? ?; rewrite -[X in _ < X]addr0 -{2}(subrr 1) addrCA -{2}[1]divr1 -mulNr. rewrite addf_div ?oner_neq0 // !mulr1 mulNr mul1r opprB addrBDB -[a - b]opprB. by rewrite invrN mulrN subr_gt0; apply lt_le_trans with 0; rewrite ?ler01 // -invr_lt0 invf_div. 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