
theorem
  for a,b,c being set st c = [<*>, (0-tuples_on BOOLEAN)-->FALSE] holds
  1-BitGFA0Str(<*a*>,<*b*>) =
  1GateCircStr(<*>,(0-tuples_on BOOLEAN)-->FALSE) +* BitGFA0Str(a, b, c) &
  1-BitGFA0Circ(<*a*>,<*b*>) =
  1GateCircuit(<*>, (0-tuples_on BOOLEAN)-->FALSE) +* BitGFA0Circ(a, b, c) &
  1-BitGFA0CarryOutput(<*a*>,<*b*>) = GFA0CarryOutput(a, b, c)
proof
  let a,b be set;
A1: <*a*>.1 = a;
  <*b*>.1 = b;
  hence thesis by A1,Th3;
end;
