proposition: Lemma ratio_neq0 v1 v2: v1 != 0 -> v2 != 0 -> v1 == ratio v1 v2 *: v2 -> ratio v1 v2 != 0.
proof: Proof. move=> /eqP v1P ?; rewrite /ratio; case: pickP=> /= [x px rP|/all_v_neq0 //]. by apply/eqP; move=> neq; move: rP; rewrite neq scale0r=> /eqP ?; apply v1P. 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