reserve R for Ring,
  I for Ideal of R,
  a, b for Element of R;

theorem Th7:
  Class(EqRel(R,[#]R),a) = the carrier of R
proof
  set E = EqRel(R,[#]R);
  thus Class(E,a) c= the carrier of R;
  let x be object;
  assume x in the carrier of R;
  then reconsider x as Element of R;
  x-a in [#]R;
  then [x,a] in E by Def5;
  hence thesis by EQREL_1:19;
end;
