theorem :: FACIRC_1:50

for x, y being object
for f being Function of (2 -tuples_on BOOLEAN),BOOLEAN
for s being State of (1GateCircuit (x,y,f)) holds
( (Following s) . [<*x,y*>,f] = f . <*(s . x),(s . y)*> & (Following s) . x = s . x & (Following s) . y = s . y ) by Th48;