theorem
  for D being non empty set, p being Element of D,
      f being FinSequence of D st p in rng f holds
        len(f:-p) <= len f
proof
  let D be non empty set, p be Element of D, f be FinSequence of D;
  assume
A1: p in rng f;
  then 1 <= p..f by FINSEQ_4:21;
  then
A2: len f - 1 >= len f - p..f by XREAL_1:10;
  len (f:-p) = len f - p..f + 1 by A1,FINSEQ_5:50;
  then len (f:-p) - 1 = len f - p..f;
  hence thesis by A2,XREAL_1:9;
end;
