Variable rnd : R -> Z.
Context { valid_rnd : Valid_rnd rnd }.

Theorem double_round_mult :
forall (fexp1 fexp2 : Z -> Z),
double_round_mult_hyp fexp1 fexp2 ->
forall x y,
generic_format beta fexp1 x -> generic_format beta fexp1 y ->
round beta fexp1 rnd (round beta fexp2 rnd (x * y))
= round beta fexp1 rnd (x * y).