theorem :: GFACIRC1:124

for x, y, z being set st z <> [<*x,y*>,xor2] holds
for s being State of (GFA3AdderCirc (x,y,z))
for a1a2, a1, a2, a3 being Element of BOOLEAN st a1a2 = s . [<*x,y*>,xor2] & a1 = s . x & a2 = s . y & a3 = s . z holds
(Following s) . (GFA3AdderOutput (x,y,z)) = a1a2 'xor' a3