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 Th12: comp {}LTLB_WFF = {[<*>LTLB_WFF,<*>LTLB_WFF]}
  proof
    hereby
      let x be object;
      assume x in comp {}l;
      then consider Q such that
A1:   Q = x and
A2:   rng Q = tau {}l and rng (Q `1) misses rng (Q `2);
      rng Q`1 = {}l by A2;
      then A3: Q`1 = <*>l by RELAT_1:41;
      rng Q`2 = {}l by A2;
      then A4: Q`2 = <*>l by RELAT_1:41;
      ex z,y be object st z in l** & y in l** & Q = [z,y] by ZFMISC_1:def 2;
      then x = [<*>l,<*>l] by A1,A3,A4;
      hence x in {[<*>l,<*>l]} by TARSKI:def 1;
    end;
    let x be object;
    set Q = [<*>l,<*>l];
    assume x in {Q};
    then A5: x = Q by TARSKI:def 1;
    A6: rng Q`1 misses rng Q`2;
    rng Q = tau {}l;
    hence x in comp {}l by A6,A5;
  end;
