let BL be Boolean Lattice; :: thesis: the carrier of BL is Field of BL
the carrier of BL c= the carrier of BL ;
then reconsider F = the carrier of BL as non empty Subset of BL ;
for a, b being Element of BL st a in F & b in F holds
( a "/\" b in F & a ` in F ) ;
hence the carrier of BL is Field of BL by Def9; :: thesis: verum