theorem
  for M being unital non empty multMagma
  for R being compatible Equivalence_Relation of M
  holds 1_(M ./. R) = Class(R,1_M)
proof
  let M be unital non empty multMagma;
  let R be compatible Equivalence_Relation of M;
  reconsider E = Class(R,1_M) as Element of M ./. R by EQREL_1:def 3;
  for X being Element of M ./. R holds X * E = X & E * X = X by Lm1;
  hence thesis by GROUP_1:def 4;
end;
