reserve n for Element of NAT;
reserve i for Integer;
reserve G,H,I for Group;
reserve A,B for Subgroup of G;
reserve N for normal Subgroup of G;
reserve a,a1,a2,a3,b,b1 for Element of G;
reserve c,d for Element of H;
reserve f for Function of the carrier of G, the carrier of H;
reserve x,y,y1,y2,z for set;
reserve A1,A2 for Subset of G;

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;
