theorem Th30:
  a c= b implies exp(a,b) = exp(2,b)
proof
A1: card bool a = exp(2,card a) by CARD_2:31;
  card a = a & card a in card bool a by CARD_1:14;
  then
A2: exp(a,b) c= exp(exp(2,a),b) by A1,CARD_2:92;
  assume a c= b;
  then
A3: exp(exp(2,a),b) = exp(2,a*`b) & a*`b = b by Th17,CARD_2:30;
  2 in a by Lm2,Th15;
  then exp(2,b) c= exp(a,b) by CARD_2:92;
  hence thesis by A2,A3;
end;
