
theorem Th40:
  for x1,x2 being set, X being non empty finite set for f being
Function of 2-tuples_on X, X for S being Signature of X st x1 in the carrier of
  S & x2 in the carrier of S & not Output 1GateCircStr(<*x1,x2*>,f) in
  InputVertices S holds InputVertices (S +* 1GateCircStr(<*x1,x2*>,f)) =
  InputVertices S
proof
  let x1,x2 be set, X be non empty finite set;
  let f be Function of 2-tuples_on X, X;
A1: rng <*x1,x2*> = {x1,x2} by FINSEQ_2:127;
  let S be Signature of X;
  assume x1 in the carrier of S & x2 in the carrier of S;
  then rng <*x1,x2*> c= the carrier of S by A1,ZFMISC_1:32;
  hence thesis by Th35;
end;
