Section Fprop_plus_ge_ulp.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.
Variable emin prec : Z.
Context { prec_gt_0_ : Prec_gt_0 prec }.

Theorem round_FLT_plus_ge :
forall x y e,
generic_format beta (FLT_exp emin prec) x -> generic_format beta (FLT_exp emin prec) y ->
(bpow (e + prec) <= Rabs x)%R ->
round beta (FLT_exp emin prec) rnd (x + y) <> 0%R ->
(bpow e <= Rabs (round beta (FLT_exp emin prec) rnd (x + y)))%R.