Remark eval_same_expr:
forall a1 a2 le v1 v2,
same_expr_pure a1 a2 = true ->
eval_expr ge sp e m le a1 v1 ->
eval_expr ge sp e m le a2 v2 ->
a1 = a2 /\ v1 = v2.

Lemma eval_mod_aux:
forall divop semdivop,
(forall sp x y m, eval_operation ge sp divop (x :: y :: nil) m = semdivop x y) ->
forall le a b x y z,
eval_expr ge sp e m le a x ->
eval_expr ge sp e m le b y ->
semdivop x y = Some z ->
eval_expr ge sp e m le (mod_aux divop a b) (Val.sub x (Val.mul z y)).