theorem :: GFACIRC2:20

for n being Nat
for x, y being FinSeqLen of n
for a, b being set holds
( (n + 1) -BitGFA1Str ((x ^ <*a*>),(y ^ <*b*>)) = (n -BitGFA1Str (x,y)) +* (BitGFA1Str (a,b,(n -BitGFA1CarryOutput (x,y)))) & (n + 1) -BitGFA1Circ ((x ^ <*a*>),(y ^ <*b*>)) = (n -BitGFA1Circ (x,y)) +* (BitGFA1Circ (a,b,(n -BitGFA1CarryOutput (x,y)))) & (n + 1) -BitGFA1CarryOutput ((x ^ <*a*>),(y ^ <*b*>)) = GFA1CarryOutput (a,b,(n -BitGFA1CarryOutput (x,y))) )