let X be set ; :: thesis: Bottom (BoolePoset X) = {}
thus Bottom (BoolePoset X) = "\/" {} ,(LattPOSet (BooleLatt X)) by YELLOW_0:def 11
.= "\/" {} ,(BooleLatt X) by YELLOW_0:29
.= Bottom (BooleLatt X) by LATTICE3:50
.= {} by LATTICE3:3 ; :: thesis: verum