
theorem Th7:
  for I being non empty set for A be 1-sorted-yielding
  ManySortedSet of I for x being Element of I holds (Carrier A).x = [#](A.x)
proof
  let I be non empty set;
  let A be 1-sorted-yielding ManySortedSet of I;
  let x be Element of I;
  ex R being 1-sorted st R=A.x & (Carrier A).x = the carrier of R by
PRALG_1:def 15;
  hence thesis;
end;
