reserve X,x for set;
reserve k,m,n for Element of NAT,
  p,q,r,s,r9,s9 for Element of HP-WFF,
  T1,T2 for Tree;
reserve T1,T2 for DecoratedTree;
reserve t,t1 for FinSequence;

theorem Th32:
  Subformulae(p '&' q) = (p '&' q)-tree(Subformulae p,Subformulae q)
proof
  ex p9,q9 being DecoratedTree of HP-WFF st p9 = HP-Subformulae.p & q9 =
  HP-Subformulae.q & HP-Subformulae.(p '&' q) = (p '&' q)-tree(p9,q9) &
  HP-Subformulae.(p => q) = (p => q)-tree(p9,q9) by Def9;
  hence thesis;
end;
