proposition: Lemma col_2D_aux_2 a b c : ((c 0 1 - b 0 1) * (a 0 0 - b 0 0) == (c 0 0 - b 0 0) * (a 0 1 - b 0 1)) = ((a 0 0 - b 0 0) * (b 0 1 - c 0 1) == (a 0 1 - b 0 1) * (b 0 0 - c 0 0)).
proof: Proof. rewrite mulrC [X in _ == X]mulrC -[X in _ * X]opprB. by rewrite mulrN eqr_oppLR -mulrN opprB. 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