theorem
  Bottom lattice G = (1).G
proof
  set L = lattice G;
  reconsider E = (1).G as Element of L by GROUP_3:def 1;
  now
    let A be Element of L;
    reconsider H = A as strict Subgroup of G by GROUP_3:def 1;
    thus A "/\" E = SubMeet(G).(A,E) by LATTICES:def 2
      .= H /\ (1).G by Def11
      .= E by GROUP_2:85;
  end;
  hence thesis by RLSUB_2:64;
end;
