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
  for f being FinSequence st i+1 = len f holds f/^i = <*f.len f*>
proof
  let f be FinSequence;
  assume
A1: i+1 = len f;
  then i <= len f by NAT_1:11;
  then
A2: len(f/^i) = len f - i by RFINSEQ:def 1
    .= 1 by A1;
  then
A3: 1 in dom(f/^i) by FINSEQ_3:25;
  thus f/^i = <*(f/^i).1*> by A2,Th14
    .= <*f.len f*> by A1,A3,Th27;
end;
