proposition: Lemma one_eighth_lt_one_quarter: (1/(1+1+1+1))*(1/(1+1+1+1))<(1/(1+1))*(1/(1+1)):> R.
proof: Proof. apply ltr_pmul. rewrite mul1r ltW // ?invr_gt0 ?addr_gt0 ?ltr01 //. rewrite mul1r ltW // ?invr_gt0 ?addr_gt0 ?ltr01 //. rewrite -quarter. exact: one_quarter_lt_one_half. rewrite -quarter. exact: one_quarter_lt_one_half. 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