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 Th20: Q in compn P implies Q is complete
  proof
    assume
A1: Q in compn P;
    then consider Q1 be PNPair such that
    Q1 = Q and
A2: Q1 in comp untn P;
    consider x such that
    Q1 in x and
A3: x in {comp R where R is PNPair : R in untn P} by A2,TARSKI:def 4;
    ex R be PNPair st x = comp R & R in untn P by A3;
    hence Q is complete by Th19,A1,Th13;
  end;
