proposition: Lemma quad_eq0 v : (v *m v^T == 0) = (v == 0).
proof: Proof. apply/eqP/eqP => [/matrixP /(_ 0 0) /eqP|->]; last by rewrite mul0mx. by rewrite [X in _ == X]mxE quad_eq0' => /eqP. 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