Sentence examples for analogous proof from inspiring English sources

An analogous proof applies to the Ma tests.

Analogous proof holds if one request is served.

Also, by the analogous proof of Proposition 2.3 and 2.4, (2.24).

With Theorem 2.1 and by means of the analogous proof of Theorem 4.1, we easily obtain the following corollary.

Applying an analogous proof to that of Lemma 2.1(a) in [7], we obtain the following result, which in the Euclidean setting was first given by Zhang [4].

Then T has a PPF dependent fixed point in R c. Proof By the analogous proof as in Theorem 2.3, we can construct a nondecreasing sequence { ϕ n } in R c converging to ϕ ∈ R c.

We have observed that even with almost evident analogous proofs, this decoding procedure is applied to the BCH codes over the chains of arbitrary finite local commutative rings with identity and also to the BCH codes over the direct product of the chain of local commutative rings with identity.

Proof Analogous to the proof of Theorem 2.6 in [2].

Proof It is analogous to the proof of the lines of Theorem 3.3.

Proof: (i) and (ii) can be proven using convexity arguments, or in a way analogous to our proof of Propositions 4.3 and 4.4, respectively.

where f 0 ( x ) = x 2. Proof Analogous to the proof of Theorem 2.4 in [2].