theorem Th117: :: GFACIRC1:117

for x, y, z being set st x <> [<*y,z*>,nor2] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,nor2] holds
for s being State of (GFA3CarryCirc (x,y,z))
for a1, a2, a3 being Element of BOOLEAN st a1 = s . x & a2 = s . y & a3 = s . z holds
( (Following (s,2)) . (GFA3CarryOutput (x,y,z)) = 'not' (((('not' a1) '&' ('not' a2)) 'or' (('not' a2) '&' ('not' a3))) 'or' (('not' a3) '&' ('not' a1))) & (Following (s,2)) . [<*x,y*>,nor2] = ('not' a1) '&' ('not' a2) & (Following (s,2)) . [<*y,z*>,nor2] = ('not' a2) '&' ('not' a3) & (Following (s,2)) . [<*z,x*>,nor2] = ('not' a3) '&' ('not' a1) )