
theorem LMINV1:
  for cipher be Element of 4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN))
  holds AES-Statearray.((AES-Statearray)".(cipher)) = cipher
proof
  let cipher be Element of 4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN));
  set f = AES-Statearray;
L0: rng AES-Statearray = 4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN))
  by FUNCT_2:def 3;
  then reconsider g = f" as Function of
  4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN)),128-tuples_on BOOLEAN
  by FUNCT_2:25;
L2: (f")*f = id (128-tuples_on BOOLEAN) & f*(f") =
  id (4-tuples_on(4-tuples_on (8-tuples_on BOOLEAN))) by FUNCT_2:29,L0;
  then g is one-to-one & rng g = 128-tuples_on BOOLEAN by FUNCT_2:18;
  then f = g" by FUNCT_2:30,L2;
  hence thesis by FUNCT_2:26;
end;
