
theorem Th41:
  for f being set, x,y being non pair object holds InputVertices
  1GateCircStr(<*x,y*>,f) is without_pairs
proof
  let f be set, x,y be non pair object;
  set p = <*x,y*>;
  let z be pair object;
  assume
A1: z in InputVertices 1GateCircStr(p,f);
  InputVertices 1GateCircStr(p,f) = {x,y} by Th40;
  hence thesis by A1,TARSKI:def 2;
end;
