reserve i, j, n for Element of NAT,
  f, g, h, k for FinSequence of REAL,
  M, N for non empty MetrSpace;

theorem Th6:
  len f = len g or dom f = dom g implies len (f+g) = len f & dom (f +g) = dom f
proof
  reconsider f1 = f as Element of (len f)-tuples_on REAL by FINSEQ_2:92;
  assume len f = len g or dom f = dom g;
  then len f = len g by FINSEQ_3:29;
  then reconsider g1 = g as Element of (len f)-tuples_on REAL by FINSEQ_2:92;
  f1+g1 is Element of (len f)-tuples_on REAL;
  hence len (f+g) = len f by CARD_1:def 7;
  hence thesis by FINSEQ_3:29;
end;
