reserve x for set;
reserve i,j for Integer;
reserve n,n1,n2,n3 for Nat;
reserve K,K1,K2,K3 for Field;
reserve SK1,SK2 for Subfield of K;
reserve ek,ek1,ek2 for Element of K;
reserve p for Prime;
reserve a,b,c for Element of GF(p);
reserve F for FinSequence of GF(p);
reserve Px,Py,Pz for Element of GF(p);

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;
