let L be non empty Lattice-like Boolean upper-bounded' lower-bounded' distributive' LattStr ; :: thesis: L is complemented'
for b being Element of L ex a being Element of L st a is_a_complement'_of b

proof

let b be Element of L; :: thesis: ex a being Element of L st a is_a_complement'_of b
consider a being Element of L such that
A1: a is_a_complement_of b by LATTICES:def 19;
take a ; :: thesis: a is_a_complement'_of b
A2: b "/\" a = Bottom L by A1;
b "\/" a = Top L by A1;
hence ( b "\/" a = Top' L & a "\/" b = Top' L & b "/\" a = Bot' L & a "/\" b = Bot' L ) by A2, Th20, Th21; :: according to SHEFFER1:def 6 :: thesis: verum

end;

hence L is complemented' ; :: thesis: verum