let L be non empty join-commutative meet-commutative distributive join-idempotent upper-bounded' lower-bounded' distributive' complemented' LattStr ; :: thesis: L is lower-bounded
ex c being Element of L st
for a being Element of L holds
( c "/\" a = c & a "/\" c = c )
proof
take Bot' L ; :: thesis: for a being Element of L holds
( (Bot' L) "/\" a = Bot' L & a "/\" (Bot' L) = Bot' L )
let a be Element of L; :: thesis: ( (Bot' L) "/\" a = Bot' L & a "/\" (Bot' L) = Bot' L )
thus ( (Bot' L) "/\" a = Bot' L & a "/\" (Bot' L) = Bot' L ) by Th5; :: thesis: verum
end;
hence L is lower-bounded ; :: thesis: verum