theorem
  for X,Y being Subgroup of A holds
  (X qua Subgroup of G) /\ (Y qua Subgroup of G) = X /\ Y
proof
  let X,Y be Subgroup of A;
  reconsider Z = X /\ Y as Subgroup of G by GROUP_2:56;
  the carrier of X /\ Y = (carr X) /\ (carr Y) by GROUP_2:def 10;
  then (X qua Subgroup of G) /\ (Y qua Subgroup of G) = Z by GROUP_2:80;
  hence thesis;
end;
