reserve A,X for non empty set;
reserve f for PartFunc of [:X,X:],REAL;
reserve a for Real;

theorem Th40:
  for M being Reflexive symmetric bounded non empty MetrStruct,
  R being Equivalence_Relation of M, a being non negative Real st
  a >= diameter [#]M & R = dist_toler(M,a)[*] holds
  Class R = {the carrier of M}
proof
  let M be Reflexive symmetric bounded non empty MetrStruct, R be
  Equivalence_Relation of M, a be non negative Real;
  Class(nabla the carrier of M) = {the carrier of M} by MSUALG_9:4;
  hence thesis by Th39;
end;
