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
  x1 <> x2 implies A+^B,[:A,{x1}:] \/ [:B,{x2}:] are_equipotent & card(A
  +^B) = card([:A,{x1}:] \/ [:B,{x2}:]) by Lm1;
