proposition: Lemma all_v_neq0 v : v != 0 -> ~ (fun k : 'I_n => v 0 k != 0) =1 xpred0.
proof: Proof. move=> /eqP v_neq0 all_v_neq0; apply: v_neq0. by apply/rowP => k; rewrite !mxE; have/negPn/eqP := all_v_neq0 k. 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