Claim: Mekhilta of Rabbi Shimon bar Yochai (a Halakic midrash on Exodus from the school of Rabbi Akiva) was implied in the title Sifre de-Bei Rav in contradistinction to R. Shimon b. Yochai's midrash.
Evidence: The Mekhilta of Rabbi Shimon bar Yochai (Hebrew: מכילתא דרבי שמעון בר יוחאי‎, Mekhilta de-Rabbi Shimon bar Yoḥai) is a Halakic midrash on Exodus from the school of Rabbi Akiva, attributed to Shimon bar Yochai. No midrash of this name is mentioned in Talmudic literature, but medieval authors refer to one which they call either "Mekhilta de-R. Simeon b. Yohai" or "Mekhilta Ahrita de-R. Shimon", or simply "Mekhilta Akheret" ("another mekhilta"). It is clear, therefore, that the Mekhilta of R. Shimon was implied in the title Sifre de-Bei Rav; and it is mentioned in the Midrash Tehillim under the Hebrew name Middot R. Shimon b. Yohai.