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