theorem Th125: :: GFACIRC1:125

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,2)) . (GFA3AdderOutput (x,y,z)) = (a1 'xor' a2) 'xor' a3 & (Following (s,2)) . [<*x,y*>,xor2] = a1 'xor' a2 & (Following (s,2)) . x = a1 & (Following (s,2)) . y = a2 & (Following (s,2)) . z = a3 )