theorem
  not X is finite & (X,Y are_equipotent or Y,X are_equipotent) implies
  X \/ Y,X are_equipotent & card (X \/ Y) = card X
proof
  assume that
A1: not X is finite and
A2: X,Y are_equipotent or Y,X are_equipotent;
A3: card X = card Y by A2,CARD_1:5;
A4: card X c= card (X \/ Y) by CARD_1:11,XBOOLE_1:7;
A5: card (X \/ Y) c= card X +` card Y by Th33;
  card X +` card Y = card X by A1,A3,Th74;
  then card X = card (X \/ Y) by A4,A5;
  hence thesis by CARD_1:5;
end;
