reserve x for set,
  i for Instruction of SCM+FSA,
  a,b for Int-Location,
  f for FinSeq-Location,
  l, l1 for Nat,
  s,s1,s2 for State of SCM+FSA,
  P,P1,P2 for Instruction-Sequence of SCM+FSA;

theorem
  for I being keeping_0 parahalting really-closed Program of SCM+FSA,
      J being parahalting really-closed Program of SCM+FSA
 holds IExec(I ";" J,P,s).f = IExec(J,P,IExec(I,P,s)).f
proof
  let I be keeping_0 parahalting really-closed Program of SCM+FSA,
      J be parahalting really-closed Program of SCM+FSA;
A1: not f in dom Start-At (IC IExec(J,P,IExec(I,P,s)) + card I,SCM+FSA)
 by SCMFSA_2:103;
  IExec(I ";" J,P,s) = IncIC(IExec(J,P,IExec(I,P,s)),card I) by SCMFSA6B:20;
  hence thesis by A1,FUNCT_4:11;
end;
