for L being non empty multMagma
for B being non empty AlgebraStr over L
for A being non empty Subset of B
for X being Subset-Family of B st ( for Y being set holds
( Y in X iff ( Y c= the carrier of B & ex C being Subalgebra of B st
( Y = the carrier of C & A c= Y ) ) ) ) holds
meet X is opers_closed