proposition: Lemma bet_lt1 (k1 k2 k3 : R) : 0 < k1 -> 0 < k2 -> k1 < 1 -> 0 < k3 -> k3 < k1 + k2 - k1 * k2 -> ((k1 + k2 - k1 * k2) / k3)^-1 < 1.
proof: Proof. by move=> *; rewrite invf_lt1 ?stuff_gt0// ltr_pdivl_mulr ?mul1r. 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