reserve X,Z for set;
reserve x,y,z for object;
reserve A,B,C for Subset of X;

theorem Th51:
  for A being set, D being a_partition of A holds
    D = the carrier of QuotientOrder(PreorderFromPartition(D))
proof
  let A be set, D be a_partition of A;
  D = Class EqRelOf PreorderFromPartition(D) by Th50;
  hence thesis by Def7;
end;
