let L be B_Lattice; :: thesis: for X, Y, Z being Element of L holds X \ (Y "\/" Z) = (X \ Y) "/\" (X \ Z)
let X, Y, Z be Element of L; :: thesis: X \ (Y "\/" Z) = (X \ Y) "/\" (X \ Z)
thus X \ (Y "\/" Z) = X "/\" ((Y ` ) "/\" (Z ` )) by LATTICES:51
.= (X "/\" X) "/\" ((Y ` ) "/\" (Z ` )) by LATTICES:18
.= ((X "/\" X) "/\" (Y ` )) "/\" (Z ` ) by LATTICES:def 7
.= (X "/\" (X "/\" (Y ` ))) "/\" (Z ` ) by LATTICES:def 7
.= (X \ Y) "/\" (X \ Z) by LATTICES:def 7 ; :: thesis: verum