proposition: Lemma row2_eq_nD (a b c d : R) : (row_mx (row2 a b) (@const_mx R 1 n 0) == row_mx (row2 c d) (@const_mx R 1 n 0)) = ((a == c) && (b == d)).
proof: Proof. rewrite -subr_eq0 opp_row_mx add_row_mx subrr. by rewrite row_mx_eq0 eqxx andbT subr_eq0 row2_eq. 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