A1:
for x, y, z being Element of (BooleLatt X) holds x "\/" (y "\/" z) = (x "\/" y) "\/" z
by XBOOLE_1:4;
A2:
for x, y being Element of (BooleLatt X) holds (x "/\" y) "\/" y = y
by XBOOLE_1:22;
A3:
for x, y, z being Element of (BooleLatt X) holds x "/\" (y "/\" z) = (x "/\" y) "/\" z
by XBOOLE_1:16;
for x, y being Element of (BooleLatt X) holds x "/\" (x "\/" y) = x
by XBOOLE_1:21;
then
( BooleLatt X is join-commutative & BooleLatt X is join-associative & BooleLatt X is meet-absorbing & BooleLatt X is meet-commutative & BooleLatt X is meet-associative & BooleLatt X is join-absorbing )
by A1, A2, A3;
hence
BooleLatt X is Lattice-like
; verum