intros p q r H' H'0; unfold mZlist in |- *; CaseEq (q - p)%Z;
auto with zarith.
intros H'1; rewrite (Zle_antisym r p); auto with datatypes.
auto with zarith.
intros p0 H'1; apply mZlist_aux_correct; auto.
rewrite inject_nat_convert with (1 := H'1); auto with zarith.
intros p0 H'1; absurd (p <= q)%Z; auto.
apply Zlt_not_le; auto.
apply Zlt_O_minus_lt; auto.
replace (p - q)%Z with (- (q - p))%Z; auto with zarith.
rewrite H'1; simpl in |- *; auto with zarith.
unfold Zlt in |- *; simpl in |- *; auto.
apply Zle_trans with (m := r); auto.
Qed.

Theorem mZlist_correct_rev1 :
forall p q r : Z, In r (mZlist p q) -> (p <= r)%Z.