reserve m,n for Element of NAT,
  i,j for Instruction of SCMPDS,
  I for Program
  of SCMPDS,
  a for Int_position;
reserve Q,U,P for Instruction-Sequence of SCMPDS;

theorem
  for s being 0-started State of SCMPDS,
  n be Element of NAT
  holds IExec(Fib-macro(n),P,s).intpos 1=Fib n &
IExec(Fib-macro(n),P,s).intpos 2=Fib (n+1) & Fib-macro(n)
  is parahalting
proof
  let s be 0-started State of SCMPDS,n be Element of NAT;
  thus IExec(Fib-macro(n),P,s).a1=Fib n &
  IExec(Fib-macro(n),P,s).a2=Fib (n+1) by Lm6;
  for t be State of SCMPDS,Q holds Fib-macro(n) is_halting_on t,Q
   proof let t be State of SCMPDS, Q;
     Fib-macro(n) is_halting_on Initialize t,Q by Lm6;
    hence thesis by SCMPDS_6:126;
   end;
  hence thesis by SCMPDS_6:21;
end;
