reserve x, x1, x2, y, X, D for set,
  i, j, k, l, m, n, N for Nat,
  p, q for XFinSequence of NAT,
  q9 for XFinSequence,
  pd, qd for XFinSequence of D;
reserve pN, qN for Element of NAT^omega;
reserve seq1,seq2,seq3,seq4 for Real_Sequence,
  r,s,e for Real,
  Fr,Fr1, Fr2 for XFinSequence of REAL;

theorem
  for Fr1,Fr2 st dom Fr1=dom Fr2 & for n st n in len Fr1 holds Fr1.n=Fr2
  .(len Fr1-'(1+n)) holds Sum Fr1 = Sum Fr2 by Lm4;
