reserve i for Nat,
  j for Element of NAT,
  X,Y,x,y,z for set;
reserve C for initialized ConstructorSignature,
  s for SortSymbol of C,
  o for OperSymbol of C,
  c for constructor OperSymbol of C;
reserve a,b for expression of C, an_Adj C;
reserve t, t1,t2 for expression of C, a_Type C;
reserve p for FinSequence of QuasiTerms C;
reserve e for expression of C;
reserve a,a9 for expression of C, an_Adj C;

theorem Th65:
  for a being positive quasi-adjective of C
  ex v being constructor OperSymbol of C st the_result_sort_of v = an_Adj C &
  ex p st len p = len the_arity_of v & a = v-trm p
proof
  let e be positive quasi-adjective of C;
  per cases by Th53;
  suppose
    ex x being variable st e = x-term C;
    hence thesis by Th48;
  end;
  suppose
    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;
    then consider c being constructor OperSymbol of C,
    p being FinSequence of QuasiTerms C such that
A1: len p = len the_arity_of c and
A2: e = c-trm p;
    take c;
    e is expression of C, the_result_sort_of c by A1,A2,Th52;
    hence the_result_sort_of c = an_Adj C by Th48;
    take p;
    thus thesis by A1,A2;
  end;
  suppose
    ex a st e = (non_op C)term a;
    hence thesis by Def37;
  end;
  suppose
    ex a,t st e = (ast C)term(a,t);
    then e is expression of C, a_Type C by Th46;
    hence thesis by Th48;
  end;
end;
