theorem Th8: :: FTACELL1:8

for ap, bp, cp, dp being non pair set
for cin being set st cin <> [<*dp,(GFA0AdderOutput (ap,bp,cp))*>,and2] & not cin in InnerVertices (BitGFA0Str (ap,bp,cp)) holds
for s being State of (BitFTA0Circ (ap,bp,cp,dp,cin))
for a1, a2, a3, a4, a5 being Element of BOOLEAN st a1 = s . ap & a2 = s . bp & a3 = s . cp & a4 = s . dp & a5 = s . cin holds
( (Following (s,2)) . (GFA0AdderOutput (ap,bp,cp)) = (a1 'xor' a2) 'xor' a3 & (Following (s,2)) . ap = a1 & (Following (s,2)) . bp = a2 & (Following (s,2)) . cp = a3 & (Following (s,2)) . dp = a4 & (Following (s,2)) . cin = a5 )