theorem Th56:
  for X be non empty set,
  R be Equivalence_Relation of X,
  S be Class(R)-valued Function st S is onto
  holds Union S = X
  proof
    let X be non empty set,
    R be Equivalence_Relation of X,
    S be Class(R)-valued Function;
    assume A1:S is onto;
     union (Class R) = X by EQREL_1:def 4;
    hence thesis by A1,FUNCT_2:def 3;
  end;
