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(** * Formalization of alternated series *)
Definition tg_alt (Un:nat -> R) (i:nat) : R := (-1) ^ i * Un i.Definition positivity_seq (Un:nat -> R) : Prop := forall n:nat, 0 <= Un n.

Lemma CV_ALT_step3 : forall (Un:nat -> R) (N:nat), Un_decreasing Un -> positivity_seq Un -> sum_f_R0 (fun i:nat => tg_alt Un (S i)) N <= 0.