reserve k, m for Nat,
  x, x1, x2, x3, y, y1, y2, y3, X,Y,Z for set,
  N for with_zero set;
reserve n,m for Nat;

theorem
 for S being IC-Ins-separated halting non empty with_non-empty_values
  AMI-Struct over N,
  P being Instruction-Sequence of S,
  s being State of S st  s =  Following(P,s)
  holds for n holds Comput(P,s,n) =  s
proof
  let S be IC-Ins-separated halting non empty with_non-empty_values
  AMI-Struct over N,
  P be Instruction-Sequence of S,
  s be State of S;
  defpred X[Nat] means  Comput(P,s,$1) =  s;
  assume
A1:   s =  Following(P,s);
A2: for n st X[n] holds X[n+1] by A1,EXTPRO_1:3;
A3: X[ 0];
  thus for n holds X[n] from NAT_1:sch 2(A3, A2);
end;
