theorem Th18:
  w in Lang(A) iff ex p, q st p in the InitS of A & q in the
  FinalS of A & p, w ==>* q, A
proof
  thus w in Lang(A) implies ex p, q st p in the InitS of A & q in the FinalS
  of A & p, w ==>* q, A
  proof
    assume w in Lang(A);
    then
    ex u st w = u & ex p, q st p in the InitS of A & q in the FinalS of A
    & p, u ==>* q, A;
    hence thesis;
  end;
  thus thesis;
end;
