reserve i,j for Nat;

theorem Th14:
 for C being initialized standardized ConstructorSignature
 for e being expression of C
  holds
   (e.{})`1 in Vars & (e.{})`2 = a_Term & e is quasi-term of C or
   (e.{})`2 = the carrier of C &
    ( (e.{})`1 in Constructors & (e.{})`1 in the carrier' of C or
      (e.{})`1 = * or (e.{})`1 = non_op )
  proof let C be initialized standardized ConstructorSignature;
   let e be expression of C;
   per cases by Th11;
   suppose ex x being Element of Vars st e = x-term C & e.{} = [x, a_Term];
    then consider x being Element of Vars such that
A1:  e = x-term C & e.{} = [x, a_Term];
    thus thesis by A1;
   end;
   suppose ex o being OperSymbol of C st e.{} = [o, the carrier of C] &
     ( o in Constructors or o = * or o = non_op ); then
    consider o being OperSymbol of C such that
A2:  e.{} = [o, the carrier of C] &
     ( o in Constructors or o = * or o = non_op );
    thus thesis by A2;
   end;
  end;
