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 Th22:
  2*`K = K+`K
proof
  thus 2*`K = card([:{{}},K:] \/ [:{1},K:]) by CARD_1:50,ZFMISC_1:109
    .= card([:K,{{}}:] \/ [:K,{1}:]) by Th15
    .= card K +` card K by Th16
    .= K +` card K
    .= K +` K;
end;
