reserve E,X,Y,x for set;
reserve A,B,C for Subset of E;

theorem
  A` c= A iff A = [#]E
proof
  thus A` c= A implies A = [#]E
  proof
    assume A` c= A;
    hence A = A \/ A` by XBOOLE_1:12
      .= [#]E by Th10;
  end;
  thus thesis by XBOOLE_1:37;
end;
