reserve p,P,P1,P2 for Instruction-Sequence of SCM+FSA;
reserve s, S for State of SCM+FSA,
  I, J for Program of SCM+FSA,
  Ig for good Program of SCM+FSA,
  i for good sequential Instruction of SCM+FSA,
  j for sequential Instruction of SCM+FSA,
  a, b for Int-Location,
  f for FinSeq-Location;

theorem Th13:
 for J being really-closed Program of SCM+FSA holds
  J is parahalting or J is_halting_on Exec(i, Initialized s),p
implies IExec(i ";" J,p,s).a = IExec(J,p,Exec(i,Initialized s)).a
proof let J be really-closed Program of SCM+FSA;
  set Mi = Macro i;
A1:  IExec(Mi,p,s) =  Exec(i,Initialized s) by SCMFSA6C:5;
  assume J is parahalting or J is_halting_on Exec(i, Initialized s),p;
  then
A2: J is_halting_on Exec(i, Initialized s),p
    by SCMFSA7B:19;
  J is_halting_on IExec(Mi,p,s),p by A2,A1;
  hence IExec(i ";" J,p,s).a
     = IExec(J,p,IExec(Mi,p,s)).a by Th6
    .= ( IExec(J,p,IExec(Mi,p,s))).a
    .= ( IExec(J,p,Exec(i,Initialized s))).a by A1
    .= IExec(J,p,Exec(i,Initialized s)).a;
end;
