reserve l, m, n for Nat;
reserve a,b for Int-Location,
  f for FinSeq-Location,
  s,s1,s2 for State of SCM+FSA;

theorem
  for p being PartState of SCM+FSA holds (Initialized p).intloc 0 =
  1 & (Initialized p).IC SCM+FSA =  0
proof
  let p be PartState of SCM+FSA;
  intloc 0 in {intloc 0} by TARSKI:def 1;
  then
A1: intloc 0 in dom q;
A2: Initialized p = Initialize(p +* q) by FUNCT_4:14;
  intloc 0 <> IC SCM+FSA by SCMFSA_2:56;
  then not intloc 0 in {IC SCM+FSA} by TARSKI:def 1;
  then not intloc 0 in dom SA0;
  hence (Initialized p).intloc 0 = (p +* q).intloc 0 by A2,FUNCT_4:11
    .= q.intloc 0 by A1,FUNCT_4:13
    .= 1 by FUNCOP_1:72;
  IC SCM+FSA in {IC SCM+FSA} by TARSKI:def 1;
  then IC SCM+FSA in dom SA0;
  hence (Initialized p).IC SCM+FSA = SA0.IC SCM+FSA by A2,FUNCT_4:13
    .=  0 by FUNCOP_1:72;
end;
