reserve m, n for Nat,
  x for set,
  i for Instruction of SCM+FSA,
  I for Program of SCM+FSA,
  a 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 Th2:
  for s being State of SCM+FSA
  for I being parahalting Program of SCM+FSA
   st Initialize((intloc 0).-->1) c= s
  for P being Instruction-Sequence of SCM+FSA
   st I c= P
  holds P halts_on s
proof
  let s be State of SCM+FSA;
  let I be parahalting Program of SCM+FSA;
A1: Start-At(0,SCM+FSA) c= Initialize((intloc 0).-->1) by FUNCT_4:25;
  assume
A2: Initialize((intloc 0).-->1) c= s;
  let P be Instruction-Sequence of SCM+FSA
  such that
A3: I c= P;
   Start-At(0,SCM+FSA) c= s by A2,A1,XBOOLE_1:1;
   then s is 0-started by MEMSTR_0:29;
  hence thesis by A3,AMISTD_1:def 11;
end;
