reserve X for non empty set;

theorem Th5:
  for A being set, x,y being Element of EqRelLatt A holds x [= y iff x c= y
proof
  let A be set, x,y be Element of EqRelLatt A;
  reconsider x9 = x,y9 = y as Equivalence_Relation of A by MSUALG_5:21;
A1: x9 /\ y9 = x9 iff x9 c= y9 by XBOOLE_1:17,28;
  x "/\" y = (the L_meet of EqRelLatt A).(x9,y9) by LATTICES:def 2
    .= x9 /\ y9 by MSUALG_5:def 2;
  hence thesis by A1,LATTICES:4;
end;
