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 Th91:
  Subformulae (F => G) = Subformulae F \/ Subformulae G \/ {
  'not' G, F '&' 'not' G, F => G }
proof
  thus Subformulae (F => G) = Subformulae (F '&' 'not' G) \/ { F => G } by Th88
    .= Subformulae F \/ Subformulae 'not' G \/ {F '&' 'not' G} \/ {F => G}
  by Th89
    .= Subformulae F \/ (Subformulae G \/ {'not' G}) \/ {F '&' 'not' G} \/ {
  F => G } by Th88
    .= Subformulae F \/ Subformulae G \/ {'not' G} \/ {F '&' 'not' G} \/ { F
  => G } by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ {'not' G} \/ ({F '&' 'not' G} \/ {
  F => G }) by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ ({'not' G} \/ ({F '&' 'not' G} \/ {
  F => G })) by XBOOLE_1:4
    .= Subformulae F \/ Subformulae G \/ ({'not' G} \/ { F '&' 'not' G,F =>
  G }) by ENUMSET1:1
    .= Subformulae F \/ Subformulae G \/ { 'not' G,F '&' 'not' G,F => G } by
ENUMSET1:2;
end;
