theorem
  for p,q being FinSequence st p^q = <*x*> holds
  p = <*x*> & q = {} or p = {} & q = <*x*>
proof
  let p,q be FinSequence;
  assume
A1: p^q = <*x*>;
then A2: 1 = len(p^q) by Th40
    .= len p + len q by Th22;
A3: now
    assume len p = 0;
    thus
then  p = {};
    hence q = <*x*> by A1,Th34;
  end;
 now
    assume len p <> 0;
then A4: 0+1 <= len p by NAT_1:13;
 len p <= 1 by A2,NAT_1:11;
then  len p = 1 by A4,XXREAL_0:1;
    thus
then  q = {} by A2;
    hence p = <*x*> by A1,Th34;
  end;
  hence thesis by A3;
end;
