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 Initialized s,P
  holds IC IExec(I ";"
Goto  (card J + 1) ";" J ";" Stop SCM+FSA,P,s) =  (card I + card J + 1)
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 s2 = Initialized s;
  set P2 = P +* (I ";" Goto  (card J + 1) ";" J ";" Stop SCM+FSA);
  assume
A1: I is_halting_on Initialized s,P;
  then P2 halts_on s2 & LifeSpan(P2,s2)
   = LifeSpan(P+*I,s2) + 2 by Lm6;
  then
  IC Result(P2,s2) =
   IC Comput(P2, s2,LifeSpan(P+*I,s2) +2) by EXTPRO_1:23
    .= card I + card J + 1 by A1,Lm6;
  hence thesis by SCMFSA6B:def 1;
end;
