reserve A for QC-alphabet;
reserve i,j,k for Nat;
reserve f for Substitution of A;
reserve x,y 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,l1,l2,ll for FinSequence of QC-variables(A);
reserve r,s for Element of CQC-WFF(A);

theorem Th15:
  VERUM(A).x = VERUM(A)
proof
  ex F being Function of QC-WFF(A),QC-WFF(A) st VERUM(A).x = F.VERUM(A) &
for q holds F.VERUM(A) = VERUM(A) &
(q is atomic implies F.q =
(the_pred_symbol_of q)!Subst(the_arguments_of q,(A)a.0.-->x)) &
(q is negative implies F.q = 'not' (F.the_argument_of q) ) &
(q is conjunctive implies F.q = (F.the_left_argument_of
  q) '&' (F.the_right_argument_of q)) & (q is universal implies F.q = IFEQ(
  bound_in q,x,q,All(bound_in q,F.the_scope_of q))) by Def3;
  hence thesis;
end;
