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).