Sentence examples for there existed proof from inspiring English sources

Angelo Colagrande, representing bereaved surgeon Vincenzo Vittorini, said he was certain that the court acted in "good faith," but that there existed proof of the experts' guilt.

There exist proofs that some schemes are divergent [70] or convergent [71] for some types of drift and diffusion coefficients.

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.

In Cook's piece, he says, "There exists no proof that censorship helps expedite a safe release, and there is no proof that accurate information about a victim harms him," suggesting the practice is to benefit employers, not kidnappees.

In a follow-up piece on Gawker, he wrote, "There exists no proof that censorship helps expedite a safe release, and there is no proof that accurate information about a victim harms him... Censorship historically has only covered up a host of corporate incompetence and handwringing".

Proof There exists n 0 such that for n ≥ n 0 we have ∥ a x + x n ∥ > 1.

Proof There exist an X 1 -midconvex function f 1 : X 1 → R and an X 2 -midconvex function f 2 : X 2 → R such that.

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].

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.

Proof Assume there exist x ∈ X and r > 0 such that { T n ( x ) } ⊂ B ( x ; r ).

Part 2, showing necessity by indirect proof: Assuming there exists a scoped program path such that for all scoped program paths it either holds that (40).