reserve SBT for Permutation of (8-tuples_on BOOLEAN);
reserve MCFunc for Permutation of
4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN));
reserve MixColumns for
Permutation of 4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN));

theorem INV01:
  for input be Element of 4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN))
  holds (MCFunc").(MCFunc.input) = input
proof
  let input be Element of 4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN));
  thus (MCFunc").(MCFunc.(input)) = ((MCFunc")*MCFunc).input by FUNCT_2:15
    .= (id (4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN)))).input
    by FUNCT_2:61
    .= input;
end;
