Sentence examples for by the proof from inspiring English sources

Moreover, the least fixed point is recursive by the proof.

By the proof of Theorem 4.1, we know.

Then (92) holds by the proof of Lemma 6.

By the proof of Theorem 2.2,   as, and exists.

By the proof of Theorem 3.1, we have as, (3.39).

Moreover, by the proof of Lemma 2.7, we obtain (414).

By the proof of Theorem 4.2, we have, so.

By the proof of Lemma 3.6, we have (3.40).

By previous lemma and by the proof of Lemma 2.13.

By the proof of Lemma 2.4, we know and.

By the proof of Theorem 2.4, there exists such that.