proposition: Lemma euclid_fails_aux (a b c : 'rV[R]_(2)) : bet a b c -> bet a (c + a -b) c.
proof: Proof. move=> bet_abc. rewrite (bet_trans _ _ _(-c)) subrr. rewrite [X in bet _ X _]addrC !addrA -[-c+c]addrC subrr add0r. rewrite bet_opp !opprB (bet_trans _ _ _ a). rewrite -!addrA [-a+a]addrC subrr !addr0 addrC subr0. by rewrite bet_sym. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun ssrnat eqtype choice seq) mathcomp(fintype finset finfun bigop order) mathcomp(ssralg ssrnum path generic_quotient matrix mxalgebra algC) mathcomp(zmodp) GeoCoq.Meta_theory.Models.POF_to_Tarski GeoCoq.Axioms.gupta_inspired_variant_axioms GeoCoq.Meta_theory.Models.tarski_to_gupta_inspired GeoCoq.Tarski_dev.Ch06_out_lines GeoCoq.Tarski_dev.Ch11_angles GeoCoq.Meta_theory.Parallel_postulates.parallel_postulates GeoCoq.Meta_theory.Counter_models.Planar.independence