intros x y H' H'0 H'1.
case (FshiftCorrectSym radix) with (2 := H'1); auto.
intros m1 H'2; elim H'2; intros m2 E; clear H'2.
rewrite (LSB_shift x m1); auto.
rewrite E; auto.
apply sym_equal; apply LSB_shift; auto.
apply (NisFzeroComp radix) with (x := x); auto.
Qed.

Theorem maxDiv_opp :
forall (v : Z) (p : nat), maxDiv v p = maxDiv (- v) p.