reserve i,k for Nat;
reserve A for QC-alphabet;
reserve x for bound_QC-variable of A;
reserve a for free_QC-variable of A;
reserve p,q for Element of QC-WFF(A);
reserve l for FinSequence of QC-variables(A);
reserve P,Q for QC-pred_symbol of A;
reserve V for non empty Subset of QC-variables(A);
reserve s,t for QC-symbol of A;

theorem
  P is QC-pred_symbol of the_arity_of P, A
proof
  set k = the_arity_of P;
  set QCP = {Q : the_arity_of Q = k };
  P in QCP;
  hence thesis;
end;
