theorem
(
and2 . <*0,0*> = 0 &
and2 . <*0,1*> = 0 &
and2 . <*1,0*> = 0 &
and2 . <*1,1*> = 1 &
and2a . <*0,0*> = 0 &
and2a . <*0,1*> = 1 &
and2a . <*1,0*> = 0 &
and2a . <*1,1*> = 0 &
nor2 . <*0,0*> = 1 &
nor2 . <*0,1*> = 0 &
nor2 . <*1,0*> = 0 &
nor2 . <*1,1*> = 0 )