let G be Group; :: thesis: Top (lattice G) = (Omega). G
set L = lattice G;
reconsider E = (Omega). G as Element of (lattice G) by GROUP_3:def 1;

now

let A be Element of (lattice G); :: thesis: A "\/" E = E
reconsider H = A as strict Subgroup of G by GROUP_3:def 1;
thus A "\/" E = (SubJoin G) . (A,E) by LATTICES:def 1
.= H "\/" ((Omega). G) by Def11
.= E by Th77 ; :: thesis: verum

end;

hence Top (lattice G) = (Omega). G by RLSUB_2:65; :: thesis: verum