theorem
  ConSet(X) = LConSet(X)/\RConSet(X)
proof
  ConSet(X) c= LConSet(X) & ConSet(X) c= RConSet(X) by Th45,Th46;
  hence ConSet(X) c= LConSet(X)/\RConSet(X) by XBOOLE_1:19;
  thus LConSet(X)/\RConSet(X) c= ConSet(X)
  proof
    let x be object;
    assume
A1: x in LConSet(X)/\RConSet(X);
    then x in RConSet(X) by XBOOLE_0:def 4;
    then
A2: ex R being R-congruence of X st x=R;
    x in LConSet(X) by A1,XBOOLE_0:def 4;
    then ex L being L-congruence of X st x=L;
    then x is Congruence of X by A2,Th36;
    hence thesis;
  end;
end;
