reserve s, s1, s2 for State of SCM+FSA,
  p, p1 for Instruction-Sequence of SCM+FSA,
  a, b for Int-Location,
  d for read-write Int-Location,
  f for FinSeq-Location,
  I for MacroInstruction of SCM+FSA,
  J for good MacroInstruction of SCM+FSA,
  k, m for Nat;

theorem
  for I being really-closed Program of SCM+FSA holds
  (I is_halting_on Initialized s,p or I is parahalting ) &
  (s.intloc 0 = 1 or a is read-write) & not a in UsedILoc I
  implies IExec(I,p,s).a = s.a
proof let I be really-closed Program of SCM+FSA;
  assume that
A1: I is_halting_on Initialized s,p or I is parahalting and
A2: s.intloc 0 = 1 or a is read-write and
A3: not a in UsedILoc I;
A4: a = intloc 0 or a is read-write by SCMFSA_M:def 2;
I is_halting_on Initialized s,p by A1,SCMFSA7B:19;
  hence IExec(I,p,s).a = (Initialized s).a by A3,Th1
    .= s.a by A2,A4,SCMFSA_M:9,37;
end;
