
theorem
  for f,x being set, p being FinSequence holds x in the carrier of
  1GateCircStr(p,f,x) & for y being set st y in rng p holds y in the carrier of
  1GateCircStr(p,f,x)
proof
  let f,x be set;
  let p be FinSequence;
  set A = the carrier of 1GateCircStr(p,f,x);
  A = rng p \/ {x} & x in {x} by CIRCCOMB:def 5,TARSKI:def 1;
  hence thesis by XBOOLE_0:def 3;
end;
