
theorem Th129:
  for x,y,z being set st z <> [<*x,y*>,xor2] & x <> [<*y,z*>,
  nor2] & y <> [<*z,x*>,nor2] & z <> [<*x,y*>,nor2] holds InputVertices
  BitGFA3Str(x,y,z) = {x,y,z}
proof
  set f1 = nor2, f2 = nor2, f3 = nor2;
  set f0 = xor2;
  let x,y,z be set such that
A1: z <> [<*x,y*>,f0] & x <> [<*y,z*>,f2] & y <> [<*z,x*>,f3] & z <> [<*
  x,y *>,f1];
  set S2 = GFA3CarryStr(x,y,z);
  set S1 = GFA3AdderStr(x,y,z);
  InputVertices S1 = {x,y,z} & InputVertices S2 = {x,y,z} by A1,Th109,
FACIRC_1:57;
  hence thesis by CIRCCOMB:47,FACIRC_2:21;
end;
