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;
reserve L for finite Subset of Int-Locations;

theorem
  for w being FinSequence of INT,f be FinSeq-Location
  holds dom (Initialized (f.--> w)) = {intloc 0,IC SCM+FSA,f}
proof
  let w be FinSequence of INT,f be FinSeq-Location;
  dom (Initialized(f .--> w)) =
  dom(Initialize ((intloc 0) .--> 1)) \/ dom (f.--> w) by FUNCT_4:def 1
    .= ({ intloc 0,IC SCM+FSA } \/ {f}) by Th11;
  hence thesis by ENUMSET1:3;
end;
