reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;
reserve D for non empty set;
reserve p, q for FinSequence,
  X, Y, x, y for set,
  D for non empty set,
  i, j, k, l, m, n, r for Nat;
reserve a, a1, a2 for TwoValued Alternating FinSequence;
reserve fs, fs1, fs2 for FinSequence of X,
  fss, fss2 for Subset of fs;

theorem
  for f1 being FinSequence of D, f2 being non trivial FinSequence of D
  holds (f1^'f2)/.len(f1^'f2) = f2/.len f2
proof
  let f1 be FinSequence of D, f2 be non trivial FinSequence of D;
A1: len (f1^'f2) + 1 = len f1 + len f2 by Th13;
  2 <= len f2 by NAT_D:60;
  then
A2: 1 < len f2 by XXREAL_0:2;
  then 1+0 < len f1 + len f2 by XREAL_1:8;
  then 1 <= len(f1^'f2) by A1,NAT_1:13;
  hence (f1^'f2)/.len(f1^'f2) = (f1^'f2).len(f1^'f2) by FINSEQ_4:15
    .= f2.len f2 by A2,Th16
    .= f2/.len f2 by A2,FINSEQ_4:15;
end;
