proposition: Lemma xt_neq (x': @Vector R 1): bet a' b' x' -> x' != b' -> x'!= t'.
proof: Proof. move=> ? ?. rewrite -subr_eq0 vector2_neq0 !mxE /= bet_abx_x00_eq0 //. by rewrite add0r oppr_eq0 one_half_neq0 orTb. 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