reserve A for QC-alphabet;
reserve n,k,m for Nat;
reserve F,G,G9,H,H9 for Element of QC-WFF(A);
reserve t, t9, t99 for Element of dom tree_of_subformulae(F);
reserve x for set;
reserve x,y for set;

theorem Th26:
  (tree_of_subformulae(F)).t is universal implies t^<*0*> in dom
  tree_of_subformulae(F) & (tree_of_subformulae(F)).(t^<*0*>) = the_scope_of (
  tree_of_subformulae(F)).t
proof

  set G = (tree_of_subformulae(F)).t;
  consider H such that
A1: H = the_scope_of G;
  assume
A2: G is universal;
  then H is_immediate_constituent_of G by A1,QC_LANG2:50;
  then consider m such that
A3: t^<*m*> in dom tree_of_subformulae(F) and
  H = (tree_of_subformulae(F)).(t^<*m*>) by Th7;
  m = 0 by A2,A3,Th23;
  hence thesis by A2,A3,Th23;
end;
