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, f being FinSeq-Location
     st not f in dom p
    holds not f in dom Initialized p
proof
  let p be PartState of SCM+FSA;
  let f be FinSeq-Location;
  assume
A1:  not f in dom p;
  assume f in dom Initialized p;
  then f in dom p \/ {intloc 0} \/ {IC SCM+FSA} by Th3;
  then
A2: f in (dom p \/ {intloc 0}) or f in {IC SCM+FSA} by XBOOLE_0:def 3;
  per cases by A2,A1,XBOOLE_0:def 3;
  suppose
    f in {intloc 0};
    then f = intloc 0 by TARSKI:def 1;
    hence contradiction by SCMFSA_2:58;
  end;
  suppose
    f in {IC SCM+FSA};
    then f = IC SCM+FSA by TARSKI:def 1;
    hence contradiction by SCMFSA_2:57;
  end;
end;
