theorem Th52: :: GFACIRC1:52

for x, y, z being set
for s being State of (GFA1CarryCirc (x,y,z))
for a1, a2, a3 being Element of BOOLEAN st a1 = s . [<*x,y*>,and2c] & a2 = s . [<*y,z*>,and2a] & a3 = s . [<*z,x*>,and2] holds
(Following s) . (GFA1CarryOutput (x,y,z)) = (a1 'or' a2) 'or' a3