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 Th16:
  p is atomic implies p.x = (the_pred_symbol_of p)!Subst(
  the_arguments_of p,(A)a.0.-->x)
proof
  ex F being Function of QC-WFF(A),QC-WFF(A) st p.x = F.p &
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;
