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
  thus EqR1 /\ (EqR1 "\/" EqR2) c= EqR1 by XBOOLE_1:17;
  EqR1 c= EqR1 \/ EqR2 & EqR1 \/ EqR2 c= EqR1 "\/" EqR2 by Def2,XBOOLE_1:7;
  then EqR1 c= EqR1 "\/" EqR2;
  hence thesis by XBOOLE_1:19;
end;
