proposition: Lemma bet_lt (k1 k2 : R) : 0 < k2 -> k1 - k1 * k2 < k1 + k2 - k1 * k2.
proof: Proof. by move=> ?; rewrite -addrA ltr_add2l -{1}[-(k1 * k2)]add0r ltr_add2r. 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