proposition: Lemma sub_1_ratio v1 v2 : v2 != 0 -> 1 - ratio v1 v2 = ratio (v2 - v1) v2.
proof: Proof. move=> v_neq0; apply /eqP; rewrite subr_eq add_ratio //. by rewrite addrAC -addrA subrr addr0 ratiovv. 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