theorem Th24:
  the_result_sort_of o1 <= the_result_sort_of o2 implies Result(o1
  ,A) c= Result(o2,A)
proof
  reconsider M = the Sorts of A as OrderSortedSet of S by Th17;
A1: Result(o2,A) = ((the Sorts of A) * the ResultSort of S).o2 by
MSUALG_1:def 5
    .= (the Sorts of A).((the ResultSort of S).o2) by FUNCT_2:15
    .= (the Sorts of A).(the_result_sort_of o2) by MSUALG_1:def 2;
  assume the_result_sort_of o1 <= the_result_sort_of o2;
  then
A2: M.(the_result_sort_of o1) c= M.(the_result_sort_of o2) by Def16;
  Result(o1,A) = ((the Sorts of A) * the ResultSort of S).o1 by MSUALG_1:def 5
    .= (the Sorts of A).((the ResultSort of S).o1) by FUNCT_2:15
    .= (the Sorts of A).(the_result_sort_of o1) by MSUALG_1:def 2;
  hence thesis by A2,A1;
end;
