Section Double_round_mult_FLX.
Variable prec : Z.
Variable prec' : Z.
Context { prec_gt_0_ : Prec_gt_0 prec }.
Context { prec_gt_0_' : Prec_gt_0 prec' }.

(* Specifications: *)
Theorem double_round_mult_FLX :
(2 * prec <= prec')%Z ->
forall x y,
FLX_format beta prec x -> FLX_format beta prec y ->
round beta (FLX_exp prec) rnd (round beta (FLX_exp prec') rnd (x * y))
= round beta (FLX_exp prec) rnd (x * y).
Theorem double_round_mult_FLX :
(2 * prec <= prec')%Z ->
forall x y,
FLX_format beta prec x -> FLX_format beta prec y ->
round beta (FLX_exp prec) rnd (round beta (FLX_exp prec') rnd (x * y))
= round beta (FLX_exp prec) rnd (x * y).