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
  exp(K+`M,2) = K*`K +` 2*`K*`M +` M*`M
proof
  thus exp(K+`M,2) = (K+`M)*`(K+`M) by CARD_1:50,FUNCT_5:66
    .= K*`(K+`M) +` M*`(K+`M) by Th23
    .= K*`K +` K*`M +` M*`(K+`M) by Th23
    .= K*`K +` K*`M +` (M*`K +` M*`M) by Th23
    .= K*`K +` K*`M +` K*`M +` M*`M by Th18
    .= K*`K +` (K*`M +` K*`M) +` M*`M by Th18
    .= K*`K +` 2*`(K*`M) +` M*`M by Th22
    .= K*`K +` 2*`K*`M +` M*`M by Th21;
end;
