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
 for Ig being good really-closed Program of SCM+FSA
 for J being really-closed Program of SCM+FSA holds
  (Ig is parahalting or Ig is_halting_on Initialized s,p) &
  (J is parahalting or J is_halting_on IExec(Ig,p,s),p)
  implies DataPart IExec(Ig ";" J,p,s) = DataPart IExec(J,p,IExec(Ig,p,s))
proof
 let Ig be good really-closed Program of SCM+FSA;
 let J be really-closed Program of SCM+FSA;
  set I = Ig;
  assume that
A1: I is parahalting or I is_halting_on Initialized s,p
and
A2: J is parahalting or J is_halting_on IExec(I,p,s),p;
A3: for f holds IExec(I ";" J,p,s).f = IExec(J,p,IExec(I,p,s)).f by A1,A2,Th7;
  for a holds IExec(I ";" J,p,s).a = IExec(J,p,IExec(I,p,s)).a by A1,A2,Th6;
  hence thesis by A3,SCMFSA_M:2;
end;
