let L be non empty join-commutative meet-commutative distributive join-idempotent upper-bounded' lower-bounded' distributive' complemented' LattStr ; :: thesis: Top L = Top' L
set Y = Top' L;
( L is upper-bounded & ( for a being Element of L holds
( (Top' L) "\/" a = Top' L & a "\/" (Top' L) = Top' L ) ) ) by Th4, Th12;
hence Top L = Top' L by LATTICES:def 17; :: thesis: verum