Sentence examples for exists a proof from inspiring English sources

This universal/existential dichotomy is a familiar one to logicians in formal logics there exists a proof for a formula \(X\) if and only if \(X\) is true in all models for the logic.

Since we think that there exists a proof which does not use Zorn's lemma, in a future work we plan to present such a proof based only on Theorem 4.1 from [15].

The negation $\neg A$ of a formula $A$ is proven once it has been shown that there cannot exist a proof of $A$, which means providing a construction that derives falsum from any possible proof of $A$.

Thus we obtain a general limitation result saying that there cannot exist a formal proof procedure by which any given arithmetical sentence can be proved to hold or not to hold.

We have thus proved that the mapping satisfies the assumptions of Schauder's fixed point theorem and hence there exists a function with The proof of existence of a solution of (1.1) is complete.

(2) There exists a gap in the proof of the John-Nirenberg inequality given in [2].

However, there exists a gap in the proof process of above Theorem CC.

There exists a gap in the proof of the John-Nirenberg inequality given in [2].

Multidisciplinary biopyschosocial rehabilitation for sub-acute pain in adults of working age has been analysed in a systematic review [ 12], which concluded that there exists a moderate degree of proof of the positive effectiveness of multidisciplinary rehabilitation.

So, by the previous part of the proof, there exists a solution of (1.2) such that (2.17).

By Lemma 3.5 and its proof, there exists a unique pair ( Φ ¯, U ¯ ) ∈ X × ℱ such that S ( Φ ¯, U ¯ ) = ( Φ ¯, U ¯ ) and Φ ¯ is the unique sequence in X such that A n, λ = Φ ¯ n, λ for each n ∈ J, λ ∈ Y. Namely, Φ ¯ is the unique solution of Equation (3.12) as well as Equation (3.11).