theorem :: FSCIRC_2:24

for x, y, c being set st x <> [<*y,c*>,and2] & y <> [<*x,c*>,and2a] & c <> [<*x,y*>,and2a] & c <> [<*x,y*>,'xor'] holds
for s being State of (BitSubtracterWithBorrowCirc (x,y,c))
for a1, a2, a3 being Element of BOOLEAN st a1 = s . x & a2 = s . y & a3 = s . c holds
( (Following (s,2)) . (BitSubtracterOutput (x,y,c)) = (a1 'xor' a2) 'xor' a3 & (Following (s,2)) . (BorrowOutput (x,y,c)) = ((('not' a1) '&' a2) 'or' (a2 '&' a3)) 'or' (('not' a1) '&' a3) )