reserve i,j,x,y for object,
  f,g for Function;
reserve T,T1 for finite Tree,
  t,p for Element of T,
  t1 for Element of T1;

theorem
  for f, g being finite Function st dom f misses dom g holds
  card (f +* g) = card f + card g
proof
  let f, g be finite Function such that
A1: dom f misses dom g;
  thus card (f +* g) = card dom (f +* g) by CARD_1:62
    .= card (dom f \/ dom g) by FUNCT_4:def 1
    .= card dom f + card dom g by A1,CARD_2:40
    .= card dom f + card g by CARD_1:62
    .= card f + card g by CARD_1:62;
end;
