reserve k,n,n1,m,m1,m0,h,i,j for Nat,
  a,x,y,X,X1,X2,X3,X4,Y for set;
reserve L,L1,L2 for FinSequence;
reserve F,F1,G,G1,H for LTL-formula;
reserve W,W1,W2 for Subset of Subformulae H;
reserve v for LTL-formula;
reserve N,N1,N2,N10,N20,M for strict LTLnode over v;
reserve w for Element of Inf_seq(AtomicFamily);
reserve R1,R2 for Real_Sequence;
reserve s,s0,s1,s2 for elementary strict LTLnode over v;

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;
