proposition: Lemma contraction_betS a b k : b != a -> 0 < k -> k < 1 -> betS a (contraction a b k) b.
proof: Proof. move=> ? k_gt0 k_lt1; rewrite /betS contraction_betR// /contraction -!addrA. by rewrite subrr addr0 eqxx k_gt0 k_lt1. 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