reserve i,j,k,n for Nat;
reserve D for non empty set,
  p for Element of D,
  f,g for FinSequence of D;

theorem Th32:
  for f being FinSequence st len f <= i holds f/^i is empty
proof
  let f be FinSequence;
  assume
A1: len f <= i;
  per cases;
  suppose
    len f = i;
    then len(f/^i) = len f - len f by RFINSEQ:def 1
      .= 0;
    hence thesis;
  end;
  suppose
    len f <> i;
    then len f < i by A1,XXREAL_0:1;
    hence thesis by RFINSEQ:def 1;
  end;
end;
