theorem Th53: :: GFACIRC1:53

for x, y, z being set st x <> [<*y,z*>,and2a] & y <> [<*z,x*>,and2] & z <> [<*x,y*>,and2c] holds
for s being State of (GFA1CarryCirc (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)) . (GFA1CarryOutput (x,y,z)) = ((a1 '&' ('not' a2)) 'or' (('not' a2) '&' a3)) 'or' (a3 '&' a1) & (Following (s,2)) . [<*x,y*>,and2c] = a1 '&' ('not' a2) & (Following (s,2)) . [<*y,z*>,and2a] = ('not' a2) '&' a3 & (Following (s,2)) . [<*z,x*>,and2] = a3 '&' a1 )