reserve Y for non empty set,
  a for Function of Y,BOOLEAN,
  G for Subset of PARTITIONS(Y),
  P,Q for a_partition of Y;

theorem Th2:
  for R,S being Equivalence_Relation of Y holds R \/ S c= R*S
proof
  let R,S be Equivalence_Relation of Y;
  let x,y be Element of Y;
  assume
A1: [x,y] in R \/ S;
  per cases by A1,XBOOLE_0:def 3;
  suppose
A2: [x,y] in R;
    [y,y] in S by EQREL_1:5;
    hence thesis by A2,RELAT_1:def 8;
  end;
  suppose
A3: [x,y] in S;
    [x,x] in R by EQREL_1:5;
    hence thesis by A3,RELAT_1:def 8;
  end;
end;
