proposition: Lemma gt_abs_pser_prod_le_compat : forall Un Vn x n, gt_abs_pser (Un # Vn) x n <= ((gt_abs_pser Un x) # (gt_abs_pser Vn x)) n.
proof: Proof. intros Un Vn x n ; unfold gt_abs_pser, Rseq_abs ; rewrite gt_pser_prod_compat. unfold Rseq_prod ; eapply Rle_trans ; [eapply Rseq_sum_triang |]. right ; apply Rseq_sum_ext ; intro p ; unfold gt_pser, Rseq_abs, Rseq_mult ; apply Rabs_mult. Qed.
imports: Reals Rpser_def Rpser_def_simpl Rinterval Rsequence_def Rsequence_base_facts Rsequence_subsequence Rsequence_rewrite_facts Rsequence_cv_facts Rsequence_facts Rsequence_bound_facts Rsequence_sums_facts Rpow_facts PeanoNat Lra MyRIneq MyNat MyNNR