proposition: Lemma Rseq_equiv_continuity : forall Un Vn l f, continuity_pt f l -> f l <> 0 -> Rseq_cv Un l -> Rseq_cv Vn l -> (fun n : nat => f (Un n)) ~ (fun n : nat => f (Vn n)).
proof: Proof. intros Un Vn l f Hcont H0 Hun Hvn. apply Rseq_equiv_trans with (f l). apply Rseq_cv_equiv_constant. assumption. apply Rseq_cv_continuity_compat ; [assumption | reg]. apply Rseq_equiv_sym. apply Rseq_cv_equiv_constant. assumption. apply Rseq_cv_continuity_compat ; [assumption | reg]. Qed.
imports: PeanoNat Reals Rintegral Rintegral_usual Rintegral_tactic Lia Lra Rsequence_facts Rsequence_subsequence Rpser RTaylor MyRfunctions Rsequence_tactics