reserve S for 1-sorted,
  i for Element of NAT,
  p for FinSequence,
  X for set;

theorem Th20:
  for a,b being Element of Z_2, c being Subset of X holds a \*\ (b
  \*\ c) = (a*b) \*\ c
proof
  let a,b be Element of Z_2, c be Subset of X;
  per cases by Th5,Th6,CARD_1:50,TARSKI:def 2;
  suppose
A1: a = 0.Z_2;
    then a \*\ (b \*\ c) = {}X by Def4;
    hence thesis by A1,Def4;
  end;
  suppose
A2: a = 1.Z_2;
    then a \*\ (b \*\ c) = b \*\ c by Def4;
    hence thesis by A2;
  end;
end;
