If in the end, bedikoth are to be included, why are chakiroth mentioned? For if in the chakiroth, if one of the witnesses says "I do not know," their testimony is invalidated. If this happens in the bedikoth, even if both of them say "We do not know," their testimony stands. Both in the chakiroth and in the bedikoth, if they contradict each other, their testimony is invalidated.
(Ibid. 17:4) ("This abomination has been done) in Israel": This tells me only of an Israelite (i.e., that he is to be killed). Whence do I derive (the same for) converts, women, and bondsmen? From (Ibid. 5) "Then you shall take out that man and that woman who did this evil thing".