reserve
  X,x,y,z for set,
  k,n,m for Nat ,
  f for Function,
  p,q,r for FinSequence of NAT;
reserve p1,p2,p3 for FinSequence;

theorem Th10:
  for p being FinSequence st x in ProperPrefixes p holds x is FinSequence
proof
  let p be FinSequence;
  assume x in ProperPrefixes p;
  then
  ex q being FinSequence st x = q & q is_a_proper_prefix_of p by Def2;
  hence thesis;
end;
