let L be non empty satisfying_DN_1 ComplLLattStr ; :: thesis: L is join-associative

for x, y, z being Element of L holds (x + y) + z = x + (y + z) by Th55;

hence L is join-associative by LATTICES:def 5; :: thesis: verum

for x, y, z being Element of L holds (x + y) + z = x + (y + z) by Th55;

hence L is join-associative by LATTICES:def 5; :: thesis: verum