let L be B_Lattice; :: thesis: for X, Y being Element of L holds (X "\/" Y) \ Y = X \ Y
let X, Y be Element of L; :: thesis: (X "\/" Y) \ Y = X \ Y
(X "\/" Y) \ Y = (X "/\" (Y ` )) "\/" (Y "/\" (Y ` )) by LATTICES:def 11
.= (X "/\" (Y ` )) "\/" (Bottom L) by LATTICES:47
.= X "/\" (Y ` ) by LATTICES:39 ;
hence (X "\/" Y) \ Y = X \ Y ; :: thesis: verum