let L be B_Lattice; :: thesis: for X, Y being Element of L holds X "/\" Y misses X \ Y
let X, Y be Element of L; :: thesis: X "/\" Y misses X \ Y
(X "/\" Y) "/\" (X \ Y) = ((X "/\" Y) "/\" (Y `)) "/\" X by LATTICES:def 7
.= (X "/\" (Y "/\" (Y `))) "/\" X by LATTICES:def 7
.= (X "/\" (Bottom L)) "/\" X by LATTICES:20
.= (Bottom L) "/\" X by LATTICES:15
.= Bottom L by LATTICES:15 ;
hence X "/\" Y misses X \ Y by Def4; :: thesis: verum