Sentence examples for be proved directly using from inspiring English sources

The following theorem can be proved directly using formulas (2.4) and (2.5).

A limiting argument allows to weaken the sign condition; however, this generalization can also be proved directly using another way based on the following lemma, see Section 4.

The desired result can be proved directly through Theorem 3.1.

Similarly, for (widehat{beta}<1) and (alphabetabe proved directly.

And he thought that every arithmetical statement that can be proved by making a detour through higher mathematics, can also be proved directly in Peano Arithmetic.

Therefore, introgression of apomixis into diploid sexuals cannot be proven directly with the present seed dataset.

So this implication is proved directly.

The following corollaries have been proved directly in [20].

The uniqueness of a solution to Problem 1 is proved directly.

This result is proven directly in [3], Theorem 1, using Jensen's operator inequality on the sum of the operators.

Proof Property (i) is proven directly as follows.