theorem :: FACIRC_2:9

for a, b, c being set st c = [<*>,((0 -tuples_on BOOLEAN) --> FALSE)] holds
( 1 -BitAdderStr (<*a*>,<*b*>) = (1GateCircStr (<*>,((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowStr (a,b,c)) & 1 -BitAdderCirc (<*a*>,<*b*>) = (1GateCircuit (<*>,((0 -tuples_on BOOLEAN) --> FALSE))) +* (BitAdderWithOverflowCirc (a,b,c)) & 1 -BitMajorityOutput (<*a*>,<*b*>) = MajorityOutput (a,b,c) )