reserve X,Y,Z for set, x,y,z for object;
reserve i,j for Nat;
reserve A,B,C for Subset of X;
reserve R,R1,R2 for Relation of X;
reserve AX for Subset of [:X,X:];
reserve SFXX for Subset-Family of [:X,X:];
reserve EqR,EqR1,EqR2,EqR3 for Equivalence_Relation of X;

theorem
  EqR1 "\/" (EqR1 /\ EqR2) = EqR1
proof
  EqR1 = EqR1 \/ (EqR1 /\ EqR2) & for EqR st EqR1 \/ (EqR1 /\ EqR2) c= EqR
  holds EqR1 c= EqR by XBOOLE_1:22;
  hence thesis by Def2;
end;
