reserve x for Int_position,
  n,p0 for Nat;

theorem
  for s being State of SCMPDS,n,m be Nat holds ex f be
  FinSequence of INT st len f=n & f is_FinSequence_on s,m
proof
  let s be State of SCMPDS,n,m be Nat;
  consider f be FinSequence of INT such that
A1: len f=n and
A2: for i be Nat st 1<=i & i <= len f holds f.i=s.intpos(m+i)
  by Th1;
  take f;
  thus len f=n by A1;
  thus thesis by A2;
end;
