theorem
  not X is finite & Y is finite implies
  X \/ Y,X are_equipotent & card (X \/ Y) = card X
proof
  assume that
A1: not X is finite and
A2: Y is finite;
  card Y in card X by A1,A2,CARD_3:86;
  then
A3: card X +` card Y = card X by A1,Th75;
A4: card (X \/ Y) c= card X +` card Y by Th33;
  card X c= card (X \/ Y) by CARD_1:11,XBOOLE_1:7;
  then card X = card (X \/ Y) by A3,A4;
  hence thesis by CARD_1:5;
end;
