proposition: Lemma add_ratio v1 v2 v3 : v3 != 0 -> ratio v1 v3 + ratio v2 v3 = ratio (v1 + v2) v3.
proof: Proof. move=> v_neq0; rewrite /ratio; case: pickP => /= [x px|/all_v_neq0 //]. by rewrite -mulrDl !mxE. 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