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;
reserve q for sequence of LTLStates(v);
reserve U for Choice_Function of BOOL Subformulae v;
reserve v for neg-inner-most LTL-formula;
reserve U for Choice_Function of BOOL Subformulae v;
reserve N,N1,N2,M1 for strict LTLnode over v;
reserve s,s1 for elementary strict LTLnode over v;

theorem
  w |= 'X' v implies w |= * (init v)
proof
  assume
A1: w |= 'X' v;
  for H be LTL-formula st H in 'X' CastLTL(Seed v) holds w|= H
  proof
    let H being LTL-formula;
    assume H in 'X' CastLTL(Seed v);
    then
    ex x being LTL-formula st H=x & ex u being LTL-formula st u in CastLTL(
    Seed v) & x='X' u;
    hence thesis by A1,TARSKI:def 1;
  end;
  hence thesis;
end;
