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

theorem
  for s being State of SCM+FSA st s.intloc 0 = 1
   holds DataPart Initialized s = DataPart s
proof
  let s be State of SCM+FSA;
  assume
A1: s.intloc 0 = 1;
A2: intloc 0 in dom s by SCMFSA_2:42;
    Initialized s = Initialize(s +* ((intloc 0) .--> 1)) by FUNCT_4:14;
  then Initialized s = Initialize s by A1,A2,FUNCT_7:96;
  hence thesis by MEMSTR_0:79;
end;
