proposition: Lemma Rpser_unique_extentionality : forall An Bn (x l1 l2 : R), An == Bn -> Rpser An x l1 -> Rpser Bn x l2 -> l1 = l2.
proof: Proof. intros An Bn x l1 l2 Heq Hl1 Hl2 ; eapply Rseq_cv_unique ; [rewrite Rseq_cv_eq_compat |] ; [| eapply Rseq_pps_ext ; symmetry |] ; eassumption. 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