Where, on an appeal from a judgment, decree, order or sentence of a court of a State or Territory in proceedings under a law of a State, not being an appeal to the High Court, the court is satisfied that:
(a) that law was inapplicable by reason of the operation of section 52 of the Constitution in relation to Commonwealth places; and
(b) a part of the applied provisions corresponds to that law;
the court shall deal with the appeal as though the proceedings in relation to which the appeal was brought had been brought under that part of the applied provisions and the judgment, decree, order or sentence had been given or made in proceedings so brought.