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 s being State of SCM+FSA st
  Initialize ((intloc 0) .--> 1) c= s holds s.intloc 0 =1
proof
  let s be State of SCM+FSA;
set iS = Initialize ((intloc 0) .--> 1);
A1:  dom iS = dom((intloc 0) .--> 1) \/ dom SA0 by FUNCT_4:def 1;
    intloc 0 in dom((intloc 0) .--> 1) by FUNCOP_1:74;
    then
A2: intloc 0 in dom iS by A1,XBOOLE_0:def 3;
    IC SCM+FSA <> intloc 0 by SCMFSA_2:56;
    then not intloc 0 in dom SA0 by TARSKI:def 1;
    then
 iS.intloc 0 = ((intloc 0) .--> 1).intloc 0 by FUNCT_4:11
      .= 1 by FUNCOP_1:72;
  hence thesis by A2,GRFUNC_1:2;
end;
