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) `)) "\/" (Y "/\" (X "/\" (X `))) by LATTICES:def 7
.= (X "/\" ((X "/\" Y) `)) "\/" (Y "/\" (Bottom L)) by LATTICES:20
.= (X "/\" ((X "/\" Y) `)) "\/" (Bottom L) by LATTICES:15
.= X "/\" ((X "/\" Y) `) by LATTICES:14
.= X "/\" ((X `) "\/" (Y `)) by LATTICES:23
.= (X "/\" (X `)) "\/" (X "/\" (Y `)) by LATTICES:def 11
.= (Bottom L) "\/" (X "/\" (Y `)) by LATTICES:20
.= X "/\" (Y `) by LATTICES:14 ;
hence X \+\ (X "/\" Y) = X \ Y ; :: thesis: verum