proposition: Lemma col_2D_aux_3 a b c : ((b 0 1 - a 0 1) * (c 0 0 - a 0 0) == (b 0 0 - a 0 0) * (c 0 1 - a 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 -opprB mulNr -mulrN opprB eq_sym -opprB mulNr -mulrN opprB. rewrite -[X in _ * X](addrBDB _ (b 0 1)) -[X in _ == _ * X](addrBDB _ (b 0 0)). by rewrite mulrDr [X in _ == X]mulrDr mulrC add2r_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