theorem Th4:
  X,Y are_equipotent iff card X = card Y
proof
A1: Y,card Y are_equipotent by Def2;
A2: X,card X are_equipotent by Def2;
  hence X,Y are_equipotent implies card X = card Y by Def2,WELLORD2:15;
  assume card X = card Y;
  hence thesis by A2,A1,WELLORD2:15;
end;
