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 Th6:
 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 IExec(Ig ";" J,p,s).a = IExec(J,p,IExec(Ig,p,s)).a
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: J is_halting_on IExec(I,p,s),p by A2,SCMFSA7B:19;
A4: not a in dom Start-At (IC IExec(J,p,IExec(I,p,s)) + card I,SCM+FSA)
by SCMFSA_2:102;
  I is_halting_on Initialized s,p by A1,SCMFSA7B:19;
  then
  IExec(I ";" J,p,s) = IExec(J,p,IExec(I,p,s)) +*
     Start-At (IC IExec(J,p,IExec(I,p,s)) + card I,SCM+FSA) by A3,Th5;
  hence thesis by A4,FUNCT_4:11;
end;
