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 non empty FinSequence of D, f2 being FinSequence of D
  holds (f1^'f2)/.1 = f1/.1
proof
  let f1 be non empty FinSequence of D, f2 be FinSequence of D;
A1: 1 in dom f1 by FINSEQ_5:6;
  1 in dom (f1^(2, len f2)-cut f2) by FINSEQ_5:6;
  hence (f1^'f2)/.1 = (f1^(2, len f2)-cut f2).1 by PARTFUN1:def 6
    .= f1.1 by A1,FINSEQ_1:def 7
    .= f1/.1 by A1,PARTFUN1:def 6;
end;
