Sentence examples for defined in the proof of from inspiring English sources

as defined in the proof of Lemma 3.3(c).

and is defined in the proof of Lemma 2.3.

where is defined in the proof of Lemma 1.3.

Let X, Y be defined in the proof of Theorem 5.1, and let (D(A_{2})) and (A_{2}) be defined in the proof of Theorem 3.2.

Pick n and M defined in the proof of Lemma 3.2.

Proof Let ( S, d ) be the generalized metric space defined in the proof of Theorem 2.1.

Let H be a cubic graph on n vertices w 1,…,w n, and let G be the graph defined as in the proof of Theorem 3. Set p=f(n+3)−(n+3).

Let U and V be the sets defined as in the proof of Theorem 2.5.

Let,, and be defined as in the proof of Lemma 4.5(2).

We take where and are defined as in the proof of Theorem 4.2.

Let (S, d) be the generalized metric space defined as in the proof of Theorem 2.2.