The law if non-Kosher Sechach is mixed together with the Kosher Sechach, or is sitting on top of it:

We consider the non-Kosher Sechach as nullified when all the following conditions are fulfilled:

1. There is enough Kosher Sechach to give majority of shade on its own
2. There is a lot more Kosher Sechach then non-Kosher Sechach
3. The non-Kosher Sechach cannot give majority of shade on its own, or can give majority of shade on its own but there is so much Kosher Sechach that even if one were to remove all the non-Kosher Sechach and an equal amount of Kosher Sechach then the Kosher Sechach would still give majority shade, then it is valid.

The reason for this is: Because we view the non-Kosher Sechach as nullified to the Kosher Sechach.[1]

If the above conditions are lacking: If any of the above conditions are lacking, such as if the Kosher Sechach cannot give majority shade on its own, or can but there is more non-Kosher Sechach then kosher, or not but there is enough non-Kosher Sechach to give majority of shade on its own, and if one were to remove all the non-Kosher Sechach and an equal amount of Kosher Sechach then the Kosher Sechach would not give majority shade, then it is invalid.[2]

Other Opinions in a case that the mixture of Sechach are both from the same species: However there are opinions[3] which say that in a case that the Kosher and Non-Kosher Sechach are of the same species, such as an attached tree branch which is resting on the Sechach of a Sukkah which itself is made of cut branches of that tree, then if there is more kosher Sechach then non-kosher Sechach and there is not enough non-kosher Sechach for it to give majority of shade on its own, then we view the non-kosher Sechach as nullified to the kosher Sechach to the point that it itself can now be joined in with the kosher Sechach to produce majority shade. Meaning that in such a case if the kosher Sechach alone cannot produce majority shade then the non-kosher Sechach may join it in order for it to do so and validate the Sukkah.

The reason for this opinion is: because when the non-kosher Sechach is nullified to the kosher Sechach it itself becomes kosher Sechach, as the Torah [Halacha Limoshe Misinai] did not require that all the majority shade be given by Kosher Sechach but rather only that majority of it be given by the Kosher Sechach.

The law according to this opinion if the non-kosher Sechach can give majority of shade on its own: Then although it cannot be nullified to the Kosher Sechach, and thus the Kosher Sechach must be able to give majority shade on its own, nevertheless it also does not invalidate any of the Kosher Sechach.

The Final Ruling: The main Halachic opinion is like the former. Nevertheless by a time of need, such as there is no other Sukkah available, and it is not possible to remove the mixed non-Kosher Sechach, then one may rely on this latter opinion in order so one not nullify himself from fulfilling the Mitzvah of Sukkah.  [See Q&A 3]

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[1] 626/3-11; This is opposed to the previous case in which we always view the Sechach under the non-Kosher Sechach as non-existent, being that there the two Sechachs are not mixed and thus there is no law of nullification, while here it is mixed and thus as long as the non-Kosher Sechach is nullified by having fulfilled the above conditions it is valid, and we do not require one to view as if an equal amount of non-Kosher Sechach is non-existent.

[2] Thus in conclusion, when we cannot nullify the non- kosher Sechach then we give the Sukkah the same laws as that of one which has the Non-Kosher Sechach hovering over the Sukkah, in which we view all the kosher Sechach that is under it as non-existent.

[3] Rashi