Section Fprop_plus_FLT.
Variable beta : radix.
Notation bpow e := (bpow beta e).
Variable emin prec : Z.
Context { prec_gt_0_ : Prec_gt_0 prec }.
Proof with auto with typeclass_instances.
intros x y Fx Fy H.
apply generic_format_FLT_FIX...
rewrite Zplus_comm; assumption.
apply generic_format_FIX_FLT, FIX_format_generic in Fx.
apply generic_format_FIX_FLT, FIX_format_generic in Fy.
destruct Fx as [nx H1x H2x].
destruct Fy as [ny H1y H2y].
apply generic_format_FIX.
exists (Float beta (Fnum nx+Fnum ny)%Z emin).
rewrite H1x,H1y; unfold F2R; simpl.
rewrite H2x, H2y.
rewrite plus_IZR; ring.
easy.
Qed.
Variable choice : Z -> bool.

Lemma FLT_plus_error_N_ex : forall x y,
generic_format beta (FLT_exp emin prec) x ->
generic_format beta (FLT_exp emin prec) y ->
exists eps,
(Rabs eps <= u_ro beta prec / (1 + u_ro beta prec))%R /\
round beta (FLT_exp emin prec) (Znearest choice) (x + y)
= ((x + y) * (1 + eps))%R.