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 Th9:
  x1 <> x2 implies K+`M,[:K,{x1}:] \/ [:M,{x2}:] are_equipotent &
  K+`M = card([:K,{x1}:] \/ [:M,{x2}:])
proof
  assume x1 <> x2;
  then card([:K,{x1}:] \/ [:M,{x2}:]) = K+`M by Lm1;
  hence thesis by CARD_1:def 2;
end;
