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 Th70:
  w |= * N implies Shift(w,1) |= * ('X' N)
proof
  set XN = 'X' N;
  assume
A1: w |= *N;
  for H be LTL-formula st H in 'X' CastLTL(the LTLnext of N) holds w|= H
  proof
    let H be LTL-formula;
    assume H in 'X' CastLTL(the LTLnext of N);
    then H in *N by Lm1;
    hence thesis by A1;
  end;
  then
A2: w |='X' CastLTL(the LTLnext of N);
  *XN = CastLTL(the LTLnext of N) by Lm33;
  hence thesis by A2,MODELC_2:77;
end;
