reserve A,B,p,q,r,s for Element of LTLB_WFF,
  n for Element of NAT,
  X for Subset of LTLB_WFF,
  g for Function of LTLB_WFF,BOOLEAN,
  x,y for set;

theorem untn(p,q) in tau X implies p in tau X & q in tau X & p 'U' q in tau X
  proof
    assume A1: untn(p,q) in tau X;
    then p '&&' (p 'U' q) in tau X by Th21;
    hence thesis by A1,Th21,Th20;
  end;
