reserve m for Nat;
reserve P for Instruction-Sequence of SCM+FSA;

theorem
  for I being really-closed Program of SCM+FSA,
      J being Program of SCM+FSA,s being State of SCM+FSA
   st I is_halting_on s,P
   holds
     I ";" Goto  (card J + 1) ";" J ";" Stop SCM+FSA is_halting_on s,P
proof
  let I be really-closed Program of SCM+FSA;
  let J be Program of SCM+FSA;
  let s be State of SCM+FSA;
  set IJ2 = I ";" Goto  (card J + 1) ";" J ";" Stop SCM+FSA;
  set s2 = Initialize s;
  set P2 = P +* IJ2;
  assume I is_halting_on s,P;
  then P2 halts_on s2 by Lm5;
  hence thesis by SCMFSA7B:def 7;
end;
