
theorem Th37:
  for x1 being set, X being non empty finite set for f being
Function of 1-tuples_on X, X for S being Signature of X st x1 in the carrier of
S & not Output 1GateCircStr(<*x1*>,f) in InputVertices S holds InputVertices (S
  +* 1GateCircStr(<*x1*>,f)) = InputVertices S
proof
  let x1 be set, X be non empty finite set;
  set p = <*x1*>;
  let f be Function of 1-tuples_on X, X;
  let S be Signature of X;
  assume x1 in the carrier of S;
  then {x1} c= the carrier of S by ZFMISC_1:31;
  then rng p c= the carrier of S by FINSEQ_1:38;
  hence thesis by Th35;
end;
