Sentence examples for defined in the proof 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.

where V ( j ) ( x ) is defined in the proof of Theorem 2.1.

Remark 3.1 We have noticed in the proof of Theorem 3.1 that B 1 ≈ A ¯, where A ¯ is defined in the same proof.

Let 0 < r ′ = min { r 1, r 2 }, where r 1 and r 2 will be defined in the following proof.

Now we show that the operator Ω F, defined in the beginning of proof of Theorem 3.4, satisfies the assumptions of Lemma 3.10.

Now we show that the operator ({mathcal{N}}), defined in the beginning of proof of Theorem 2.4, satisfies the assumptions of Lemma 1.4.