Sentence examples for proof in the first from inspiring English sources

This ends the proof in the first case.

Similar to the proof in the first step, we have bigl| nabla u_{varepsilon}-u bigr| _{L^{q}(0,l;L^{r})}rightarrow0 quad mbox{as } varepsilonabla u_{varepsilon}-u bigr

Then ⪯ ˜ and ⪯ g are the same order if and only if there exists a generator ℛ of ⪯ ˜ satisfying that if g : X → R is a measurable mapping such that g and f are ⪯-comonotonic for all f ∈ R, then g ∈ R. Proof In the first place, let us see that ⪯ ˜ and ⪯ g are the same order under the existence of a generator satisfying the above condition.

Proof In the first statement additionally, intermediate trees also have zero costs.

The proof was in the first set.

Hence, one may continue the proof as in the first subcase.

Then, by the same proof as in the first part of Lemma 2.2, one gets.

For any (tin J) and (xin mathit{PC}_{beta}), following the method of proof used in the first step together with condition (H2), we get Vert xVert _{mathit{PC}_{beta}}leq bigl(p^Qbigl Vert xVert _{mathit{PC}_{beta}}bigr Psi_{1}+Vbigl Vert xVert _{mathit{PC}_{beta}}bigr Psi _{2}bigr)T^{beta}.

Crescas's purpose in criticizing and rejecting several of these propositions was to show that the traditional Aristotelian proofs (founded in the first place on physical doctrines) were not valid.

In addition, cetuximab (Erbitux®) has demonstrated good response rates in previously treated patients with metastatic colorectal cancer and recently proofed effective in the first line setting [ 29- 31].

Gödel gave a sketch of the proof in the 1951 second printing of Gödel 1940.