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 (F 'or' G) = Subformulae F \/ Subformulae G \/ {'not' G,
  'not' F, 'not' F '&' 'not' G, F 'or' G}
proof
  thus Subformulae (F 'or' G) = Subformulae ('not' F '&' 'not' G) \/ { F 'or'
  G } by Th88
    .= Subformulae 'not' F \/ Subformulae 'not' G \/ {'not' F '&' 'not' G}
  \/ {F 'or' G} by Th89
    .= Subformulae 'not' F \/ (Subformulae G \/ {'not' G}) \/ {'not' F '&'
  'not' G} \/ {F 'or' G} by Th88
    .= Subformulae F \/ {'not' F} \/ (Subformulae G \/ {'not' G}) \/ {'not'
  F '&' 'not' G} \/ {F 'or' G} by Th88
    .= Subformulae F \/ ((Subformulae G \/ {'not' G}) \/ {'not' F}) \/ {
  'not' F '&' 'not' G} \/ {F 'or' G} by XBOOLE_1:4
    .= Subformulae F \/ (Subformulae G \/ ({'not' G} \/ {'not' F})) \/ {
  'not' F '&' 'not' G} \/ {F 'or' G} by XBOOLE_1:4
    .= Subformulae F \/ (Subformulae G \/ {'not' G,'not' F}) \/ {'not' F '&'
  'not' G} \/ {F 'or' G} by ENUMSET1:1
    .= Subformulae F \/ Subformulae G \/ {'not' G,'not' F} \/ {'not' F '&'
  'not' G} \/ {F 'or' G} by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ {'not' G,'not' F} \/ ({'not' F '&'
  'not' G} \/ {F 'or' G}) by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ {'not' G,'not' F} \/ {'not' F '&'
  'not' G, F 'or' G} by ENUMSET1:1
    .= Subformulae F \/ Subformulae G \/ ({'not' G,'not' F} \/ {'not' F '&'
  'not' G, F 'or' G}) by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ {'not' G, 'not' F, 'not' F '&'
  'not' G, F 'or' G} by ENUMSET1:5;
end;
