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 Th1:
  for s being State of SCM+FSA, x being set st x in dom s holds x is
  Int-Location or x is FinSeq-Location or x = IC SCM+FSA
proof
  let s be State of SCM+FSA;
  let x be set;
  assume
A1: x in dom s;
  x in Data-Locations SCM+FSA \/ {IC SCM+FSA} by A1,MEMSTR_0:13;
  then
  x in Data-Locations SCM+FSA or x in {IC SCM+FSA}
  by XBOOLE_0:def 3;
  then x in Int-Locations or x in FinSeq-Locations or x = IC SCM+FSA
   by SCMFSA_2:100,TARSKI:def 1,XBOOLE_0:def 3;
  hence thesis by AMI_2:def 16,SCMFSA_2:def 5;
end;
