
theorem
  for a,b,c being set st c = [<*>, (0-tuples_on BOOLEAN)-->TRUE] holds
  1-BitGFA1Str(<*a*>,<*b*>) =
  1GateCircStr(<*>,(0-tuples_on BOOLEAN)-->TRUE) +* BitGFA1Str(a, b, c) &
  1-BitGFA1Circ(<*a*>,<*b*>) =
  1GateCircuit(<*>, (0-tuples_on BOOLEAN)-->TRUE) +* BitGFA1Circ(a, b, c) &
  1-BitGFA1CarryOutput(<*a*>,<*b*>) = GFA1CarryOutput(a, b, c)
proof
  let a,b be set;
A1: <*a*>.1 = a;
  <*b*>.1 = b;
  hence thesis by A1,Th17;
end;
