theorem :: GFACIRC1:123

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