reserve Al for QC-alphabet;
reserve i,j,n,k,l for Nat;
reserve a for set;
reserve T,S,X,Y for Subset of CQC-WFF(Al);
reserve p,q,r,t,F,H,G for Element of CQC-WFF(Al);
reserve s for QC-formula of Al;
reserve x,y for bound_QC-variable of Al;

theorem Th16:
  T is being_a_theory iff Cn(T) = T
proof
  thus T is being_a_theory implies Cn(T) = T
  proof
    assume
A1: T is being_a_theory;
A2: T c= Cn(T) by Th13;
 Cn(T) c= T
    by A1,Def2;
    hence thesis by A2;
  end;
  thus thesis by Th11;
end;
