reserve A,B for Ordinal,
  K,M,N for Cardinal,
  x,x1,x2,y,y1,y2,z,u for object,X,Y,Z,X1,X2, Y1,Y2 for set,
  f,g for Function;

theorem Th16:
  x <> y implies card X +` card Y = card([:X,{x}:] \/ [:Y,{y}:])
proof
  assume
A1: x <> y;
  X,card X are_equipotent & Y,card Y are_equipotent by CARD_1:def 2;
  then card plus(X,Y,x,y) = card plus(card X,card Y,x,y) by A1,Th11;
  hence thesis by A1,Lm1;
end;
