reserve x for Int_position,
  n,p0 for Nat;

theorem Th1:
  for s being State of SCMPDS,n,m be Nat holds ex f be
  FinSequence of INT st len f=n & for i be Nat st 1<=i & i <= len f
  holds f.i=s.intpos(m+i)
proof
  let s be State of SCMPDS,n,m be Nat;
  deffunc U(Nat) = s.intpos (m+$1);
  consider f being FinSequence such that
A1: len f = n & for i be Nat st i in dom f holds f.i=U(i) from FINSEQ_1:
  sch 2;
  now
    let i be Nat;
    reconsider a = i as Nat;
    assume
    i in dom f;
    then f.i = s.intpos (m+a) by A1;
    hence f.i in INT by INT_1:def 2;
  end;
  then reconsider f as FinSequence of INT by FINSEQ_2:12;
  take f;
  thus len f=n by A1;
  thus for i being Nat st 1<=i <= len f holds f.i = s.intpos (m+i)
     by A1,FINSEQ_3:25;
end;
