theorem Th12:
  card(A+^B) = card A +` card B
proof
A1: A+^B,plus(A,B) are_equipotent by Lm1;
  A,card A are_equipotent & B,card B are_equipotent by CARD_1:def 2;
  then
A2: plus(A,B),plus( card A, card B) are_equipotent by Th11;
  plus( card A, card B),card A +^ card B are_equipotent by Lm1;
  then plus(A,B),card A +^ card B are_equipotent by A2,WELLORD2:15;
  then A+^B,card A +^ card B are_equipotent by A1,WELLORD2:15;
  hence thesis by CARD_1:5;
end;
