Notation bpow e := (bpow beta e).

Theorem generic_format_plus_prec: forall fexp, (forall e, (fexp e <= e - prec)%Z) -> forall x y (fx fy: float beta), (x = F2R fx)%R -> (y = F2R fy)%R -> (Rabs (x+y) < bpow (prec+Fexp fx))%R -> (Rabs (x+y) < bpow (prec+Fexp fy))%R -> generic_format beta fexp (x+y)%R.