Sentence examples for achieve the proof from inspiring English sources
If (n-k) is odd, we can do similar arguments to achieve the proof.
Choosing δ conveniently and applying the discrete Gronwall inequality, we achieve the proof of Lemma 7. ■.
Thus, to achieve the proof of (4.33) we only need to show that begin{aligned} int _I|tau ^prime (t -1|,dt -1|(n)sqrt{D(E^*)}.
Now, to achieve the proof of (5.10), we would like to replace the (E_j) with a sequence of sets converging to B in (C^1) and contradicting inequality (5.8).
Hence gammabigl overline{co}(A bigr) (t) leqgamma(A) (t),quad 0 leq t leq T. It follows that (gamma overline{co}(A))leqgamma(A)), by which we achieve the proof for the first assertion.
Since (xi_{n}) is a Cauchy sequence in (X_{T}) and contains a subsequence (xi_{m_{k}}) which converges to ξ, (xi_{n}) converges to ξ in (X_{T}), and by this we achieve the proof.
To achieve the proofs of Theorem 1 and Theorem 2, we need the following lemmas.
To achieve the proofs of Theorem 1, Theorem 2 and Theorem 3, we need the following lemmas.
This achieves the Proof of Theorem 2.
Finally, the dominated convergence theorem achieves the proof.
