proposition: Lemma Rseq_sum_split_compat : forall Un k n, (k < n)%nat -> (Rseq_sum Un n = Rseq_sum Un k + Rseq_sum (Rseq_shifts Un (S k)) (n - S k))%R.
proof: Proof. intros Un k n kltn ; rewrite Rseq_sum_shifts_compat ; ring_simplify. unfold Rseq_shifts ; rewrite Nat.add_comm, Nat.sub_add ; [reflexivity | lia]. Qed.
imports: Lia Rsequence_def Rsequence_base_facts Rsequence_cv_facts Rsequence_rewrite_facts Rpser_def Rpser_def_simpl MyRIneq MyNat Lra