reserve p,p1,p2,h for Instruction-Sequence of SCM+FSA;
reserve k, l, n for Nat,
  j for Integer,
  i,i1 for Instruction of SCM+FSA;
reserve s, s1, s2 for State of SCM+FSA,
  a for read-write Int-Location,
  b for Int-Location,
  I, J for MacroInstruction of SCM+FSA,
  Ig for good MacroInstruction of SCM+FSA,
  i, j, k, m, n for Nat;
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, n for Nat;
reserve a for read-write Int-Location;
reserve P for Instruction-Sequence of SCM+FSA;

theorem
  for I being good parahalting really-closed MacroInstruction of SCM+FSA,
      a being read-write Int-Location st I does not destroy a
   holds Initialize((intloc 0).-->1)  is Times(a,I)-halted
proof
  let I be good parahalting really-closed MacroInstruction of SCM+FSA;
  let a be read-write Int-Location;
  assume
A1: I does not destroy a;
  now
   let s be State of SCM+FSA;
   let P be Instruction-Sequence of SCM+FSA;
    (Initialized s).intloc 0 = 1 by SCMFSA_M:5;
   hence Times(a,I) is_halting_on Initialized s,P by A1,Th56;
  end;
  hence thesis by SCMFSA8C:5;
end;
