reserve k,n,m for Nat,
  a,x,X,Y for set,
  D,D1,D2,S for non empty set,
  p,q for FinSequence of NAT;
reserve F,F1,G,G1,H,H1,H2 for LTL-formula;
reserve sq,sq9 for FinSequence;
reserve L,L9 for FinSequence;
reserve j for Nat;
reserve j1 for Element of NAT;
reserve V for LTLModel;
reserve Kai for Function of atomic_LTL,the BasicAssign of V;
reserve f,f1,f2 for Function of LTL_WFF,the carrier of V;
reserve BASSIGN for non empty Subset of ModelSP(Inf_seq(S));
reserve t for Element of Inf_seq(S);
reserve f,g for Assign of Inf_seqModel(S,BASSIGN);
reserve r for Element of Inf_seq(AtomicFamily);

theorem Th74:
  r |= 'X'('not' H) iff r |='not' ('X' H)
proof
  r |= 'X'('not' H) iff Shift(r,1)|='not' H by Th67;
  then r |= 'X'('not' H) iff Shift(r,1)|/= H by Th64;
  then r |= 'X'('not' H) iff not r|= 'X' H by Th67;
  hence thesis by Th64;
end;
