proposition: Lemma d'_in_unit_disk : (d' *m d'^T) 0 0 < 1.
proof: Proof. rewrite /d' !mxE !big_ord_recr /= big_ord0 !mxE /= add0r. apply lt_trans with ((1/(1+1))*(1/(1+1))+(1/(1+1))*(1/(1+1))). apply ltr_add ; exact: one_eighth_lt_one_quarter. apply lt_le_trans with ((1/(1+1))+(1/(1+1))). apply ltr_add ; exact: one_quarter_lt_one_half. rewrite -mulrDl divff ?add11_neq0 //. 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