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 Iloc being Subset of Int-Locations holds s1 | (Iloc \/
  FinSeq-Locations) = s2 | (Iloc \/ FinSeq-Locations) iff (for x being
  Int-Location st x in Iloc holds s1.x = s2.x) & for x being FinSeq-Location
  holds s1.x = s2.x
proof
  set FSL = FinSeq-Locations;
  let Iloc be Subset of Int-Locations;
A1: (for x being FinSeq-Location holds s1.x = s2.x) implies for x being
  FinSeq-Location st x in FSL holds s1.x = s2.x;
A2: (for x being FinSeq-Location st x in FSL holds s1.x = s2.x) implies for
  x be FinSeq-Location holds s1.x = s2.x
  by SCMFSA_2:def 5;
  [#] FSL = FSL;
  hence thesis by A1,A2,Th27;
end;
