reserve i,j for Nat;

theorem Th3:
 for C being initialized ConstructorSignature for e being expression of C holds
  e is compound iff not ex x being Element of Vars st e = x-term C
  proof let C be initialized ConstructorSignature;
    let e be expression of C;
    (ex x being variable st e = x-term C) or
    (ex c being constructor OperSymbol of C st
    ex p being FinSequence of QuasiTerms C st
    len p = len the_arity_of c & e = c-trm p) or
    (ex a being expression of C, an_Adj C st e = (non_op C)term a) or
    (ex a being expression of C, an_Adj C st
    ex t being expression of C, a_Type C st
    e = (ast C)term(a,t)) by ABCMIZ_1:53;
    hence thesis;
  end;
