reserve A,B,p,q,r for Element of LTLB_WFF,
  M for LTLModel,
  j,k,n for Element of NAT,
  i for Nat,
  X for Subset of LTLB_WFF,
  F for finite Subset of LTLB_WFF,
  f for FinSequence of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN,
  x,y,z for set,
  P,Q,R for PNPair;

theorem Th8: for P be complete PNPair st untn(A,B) in rng P
  holds A in rng P & B in rng P & A 'U' B in rng P
  proof
    let P be complete PNPair;
    assume
A1: untn(A,B) in rng P;
    tau rng P = rng P by LTLAXIO3:def 11;
    hence A in rng P & B in rng P & A 'U' B in rng P by A1,LTLAXIO3:22;
  end;
