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 J being good really-closed MacroInstruction of SCM+FSA holds
  (ProperTimesBody a,J,s,p or J is parahalting) & k < s.a & (s.
  intloc 0 = 1 or a is read-write) implies StepTimes(a,J,p,s).(k+1) | ((
  UsedILoc J) \/ FinSeq-Locations)
   = IExec(J,p+*times*(a,J),StepTimes(a,J,p,s).k) | ((
  UsedILoc J) \/ FinSeq-Locations)
proof let J be good really-closed MacroInstruction of SCM+FSA;
  set UFLI = FinSeq-Locations;
  set I = J;
  assume that
A1: ProperTimesBody a,I,s,p or I is parahalting and
A2: k < s.a and
A3: s.intloc 0 = 1 or a is read-write;
  set ST = StepTimes(a,I,p,s);
A4: ST.k.intloc 0 = 1 by A1,A2,Th11,Th12;
  set au = 1-stRWNotIn ({a} \/ UsedILoc I);
A5: ProperTimesBody a,I,s,p by A1,Th11;
  then
A6: ST.k.au+k = s.a by A2,A3,Th13;
A7: k-k < s.a-k by A2,XREAL_1:9;
  I is_halting_on ST.k,p+*times*(a,I) by A2,A5;
  then I is_halting_on Initialized ST.k,p+*times*(a,I) by A4,SCMFSA8B:42;
  hence thesis by A4,A6,A7,Th16;
  set UILI = UsedILoc I;
end;
