let L be B_Lattice; :: thesis: for X, Y being Element of L holds X \ (X \ Y) = X "/\" Y
let X, Y be Element of L; :: thesis: X \ (X \ Y) = X "/\" Y
X \ (X \ Y) = X "/\" ((X `) "\/" ((Y `) `)) by LATTICES:23
.= X "/\" ((X `) "\/" Y)
.= (X "/\" (X `)) "\/" (X "/\" Y) by LATTICES:def 11
.= (Bottom L) "\/" (X "/\" Y) by LATTICES:20 ;
hence X \ (X \ Y) = X "/\" Y ; :: thesis: verum