Section Double_round_div.

Lemma round_round_really_zero :
forall (fexp1 fexp2 : Z -> Z),
Valid_exp fexp1 -> Valid_exp fexp2 ->
forall (choice1 choice2 : Z -> bool),
forall x,
0 < x ->
(mag x <= fexp1 (mag x) - 2)%Z ->
round_round_eq fexp1 fexp2 choice1 choice2 x.