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;
reserve t for Element of dom tree_of_subformulae(F),
  s for Element of dom tree_of_subformulae(G);
reserve t for Element of dom tree_of_subformulae(F),
  s for FinSequence;
reserve C for Chain of dom tree_of_subformulae(F);
reserve G for Subformula of F;
reserve t, t9 for Entry_Point_in_Subformula_Tree of G;

theorem
  t <> t9 implies not t,t9 are_c=-comparable
proof
  assume
A1: t <> t9;
  (tree_of_subformulae(F)).t = G & (tree_of_subformulae(F)).t9 = G by Def5;
  hence thesis by A1,Th18;
end;
