theorem Th4A:
  for q being Element of Args(o,T) holds
  i in dom q implies the_sort_of (q/.i) = (the_arity_of o)/.i
  proof
    let q be Element of Args(o,T);
    assume Z0: i in dom q;
    then i in dom the_arity_of o by MSUALG_3:6;
    then q/.i = q.i in (the Sorts of T).((the_arity_of o)/.i)
    by Z0,PARTFUN1:def 6,MSUALG_6:2;
    hence the_sort_of (q/.i) = (the_arity_of o)/.i by SORT;
  end;
