proposition: Lemma contraction_bet a b k1: 0 < k1 -> k1 < 1 -> bet a (contraction a b k1) b.
proof: Proof. move=> ? ?; have: extension a (contraction a b k1) k1 == b. by rewrite extension_contraction ?lt0r_neq0. by move/eqP=> P1 ; rewrite -{2}P1 extension_bet. 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