|- !l. WNOT (WORD l) = WORD (MAP ~ l)
|- !l1 l2. WORD l1 WAND WORD l2 = WORD (MAP2 $/\ l1 l2)
|- !l1 l2. WORD l1 WOR WORD l2 = WORD (MAP2 $\/ l1 l2)
|- !l1 l2. WORD l1 WXOR WORD l2 = WORD (MAP2 (\x y. ~(x = y)) l1 l2)
|- PBITOP WNOT
|- !w. WNOT (WNOT w) = w
|- !n1 n2. !w1 ::(PWORDLEN n1). !w2 ::(PWORDLEN n2). WCAT (WNOT w1,WNOT w2) = WNOT (WCAT (w1,w2))
|- PBITBOP $WAND
|- PBITBOP $WOR
|- PBITBOP $WXOR