reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);
reserve s,t for bound_QC-variable of A;
reserve F,G,H,H1 for Element of QC-WFF(A);
reserve x,y,z for bound_QC-variable of A,
  k,n,m for Nat,
  P for ( QC-pred_symbol of k, A),
  V for QC-variable_list of k, A;
reserve L,L9 for FinSequence;

theorem
  Subformulae(FALSUM(A)) = { VERUM(A), FALSUM(A) }
proof
  thus Subformulae(FALSUM(A)) c= { VERUM(A), FALSUM(A) }
  proof
    let a be object;
    assume a in Subformulae(FALSUM(A));
    then ex F st F = a & F is_subformula_of FALSUM(A) by Def22;
    then a = FALSUM(A) or a = VERUM(A) by Th81;
    hence thesis by TARSKI:def 2;
  end;
  let a be object;
  assume
A1: a in { VERUM(A), FALSUM(A) };
  then
A2: a = VERUM(A) or a = FALSUM(A) by TARSKI:def 2;
  reconsider a as Element of QC-WFF(A) by A1,TARSKI:def 2;
  a is_subformula_of FALSUM(A) by A2,Th81;
  hence thesis by Def22;
end;
