reserve i,j for Nat;
reserve i,j for Nat,
  x for variable,
  l for quasi-loci;
reserve C for initialized ConstructorSignature,
  c for constructor OperSymbol of C;
reserve a,a9 for quasi-adjective,
  t,t1,t2 for quasi-term,
  T for quasi-type,

  c for Element of Constructors;

theorem Th38:
  for C being ConstructorSignature holds C is initialized iff
  ex m being OperSymbol of a_Type C, a being OperSymbol of an_Adj C st
  m is nullary & a is nullary
  proof
    let C be ConstructorSignature;
    hereby assume C is initialized; then
      consider m, a being OperSymbol of C such that
A1:   the_result_sort_of m = a_Type & the_arity_of m = {} &
      the_result_sort_of a = an_Adj & the_arity_of a = {};
      reconsider m as OperSymbol of a_Type C by A1,ABCMIZ_1:def 32;
      reconsider a as OperSymbol of an_Adj C by A1,ABCMIZ_1:def 32;
      take m, a;
      thus m is nullary by A1;
      thus a is nullary by A1;
    end;
    given m being OperSymbol of a_Type C, a being OperSymbol of an_Adj C
    such that
A2: m is nullary & a is nullary;
    take m,a;
    the_result_sort_of non_op C = an_Adj C &
    the_result_sort_of ast C = a_Type C by ABCMIZ_1:38;
    hence thesis by A2,ABCMIZ_1:def 32;
  end;
