Definition INR {R : ConstructiveReals} (n : nat) : CRcarrier R
:= CR_of_Q R (Z.of_nat n # 1).

Lemma decomp_sum :
forall {R : ConstructiveReals} (An:nat -> CRcarrier R) (N:nat),
(0 < N)%nat ->
CRsum An N == An 0%nat + CRsum (fun i:nat => An (S i)) (pred N).