theorem Th45:
  x is Element of LTLStates(v) iff ex s st s=x
proof
  x is Element of LTLStates(v) implies ex s st s=x
  proof
    assume x is Element of LTLStates(v);
    then x in LTLStates(v);
    then consider y be Element of LTLNodes(v) such that
A1: y=x and
A2: y is elementary strict LTLnode over v;
    reconsider y as elementary strict LTLnode over v by A2;
    take y;
    thus thesis by A1;
  end;
  hence thesis by Th44;
end;
