End Fprop_plus_error.
Section Fprop_plus_zero.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable fexp : Z -> Z.
Context { valid_exp : Valid_exp fexp }.
Context { exp_not_FTZ : Exp_not_FTZ fexp }.
Notation format := (generic_format beta fexp).
Section round_plus_eq_zero_aux.
Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.

(* Specifications: *)
Lemma round_plus_eq_zero_aux :
forall x y,
(canonic_exp beta fexp x <= canonic_exp beta fexp y)%Z ->
format x -> format y ->
(0 <= x + y)%R ->
round beta fexp rnd (x + y) = 0%R ->
(x + y = 0)%R.
Lemma round_plus_eq_zero_aux :
forall x y,
(canonic_exp beta fexp x <= canonic_exp beta fexp y)%Z ->
format x -> format y ->
(0 <= x + y)%R ->
round beta fexp rnd (x + y) = 0%R ->
(x + y = 0)%R.