proposition: Lemma contraction_betR a b k1 : b != a -> 0 < k1 -> k1 < 1 -> betR a (contraction a b k1) b = k1.
proof: Proof. move=> ? ? ?; rewrite /betR /contraction -addrA subrr addr0. by apply ratio_eq; rewrite ?subr_eq0 ?eqxx. 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