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;
