theorem :: FTACELL1:17

for ap, bm, cp being non pair set
for dm, cin being set
for s being State of (BitFTA1Circ (ap,bm,cp,dm,cin))
for a1, a2, a3 being Element of BOOLEAN st a1 = s . ap & a2 = s . bm & a3 = s . cp holds
( (Following (s,2)) . (BitFTA1CarryOutput (ap,bm,cp,dm,cin)) = ((a1 '&' ('not' a2)) 'or' (('not' a2) '&' a3)) 'or' (a3 '&' a1) & (Following (s,2)) . (BitFTA1AdderOutputI (ap,bm,cp,dm,cin)) = 'not' ((a1 'xor' ('not' a2)) 'xor' a3) )