reserve x,y,z,X for set,
  T for Universe;

theorem Th2:
  for Y be non empty set for J being 1-sorted-yielding
ManySortedSet of Y, i being Element of Y holds (Carrier J).i = the carrier of J
  .i
proof
  let Y be non empty set;
  let J be 1-sorted-yielding ManySortedSet of Y, i be Element of Y;
  ex R being 1-sorted st R = J.i & (Carrier J).i = the carrier of R by
PRALG_1:def 15;
  hence thesis;
end;
