proposition: Lemma b'_in_unit_disk : (b' *m b'^T) 0 0 < 1.
proof: Proof. rewrite /b' !mxE !big_ord_recr /= big_ord0 !mxE /= mulr0 addr0 add0r. apply mulr_ilt1 ; rewrite ?one_half_ge0 ?one_half_lt1 //. 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