
theorem Th65:
  for x,y,z being set st z <> [<*x,y*>,xor2c] & x <> [<*y,z*>,
  and2a] & y <> [<*z,x*>,and2] & z <> [<*x,y*>,and2c] holds InputVertices
  BitGFA1Str(x,y,z) = {x,y,z}
proof
  set f1 = and2c, f2 = and2a, f3 = and2;
  set f0 = xor2c;
  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 = GFA1CarryStr(x,y,z);
  set S1 = GFA1AdderStr(x,y,z);
  InputVertices S1 = {x,y,z} & InputVertices S2 = {x,y,z} by A1,Th45,
FACIRC_1:57;
  hence thesis by CIRCCOMB:47,FACIRC_2:21;
end;
