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

theorem Th42:
  for M being Reflexive symmetric non empty MetrStruct holds
  fam_class_metr(M) is Classification of the carrier of M
proof
  let M be Reflexive symmetric non empty MetrStruct;
  fam_class_metr(M) = fam_class(the distance of M) by Th35;
  hence thesis by Th31;
end;
