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(*         *   The Coq Proof Assistant / The Coq Development Team       *)
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(*         *     GNU Lesser General Public License Version 2.1          *)
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Local Open Scope R_scope.

Lemma decomp_sum :
forall (An:nat -> R) (N:nat),
(0 < N)%nat ->
sum_f_R0 An N = An 0%nat + sum_f_R0 (fun i:nat => An (S i)) (pred N).