The phrase "allows one to prove" is correct and usable in written English.
It can be used when discussing the capability or permission to demonstrate or establish a point, theory, or argument.
Example: "This theorem allows one to prove the validity of the hypothesis under certain conditions."
Alternatives: "enables one to demonstrate" or "permits one to establish".
This allows one to prove new results about the eigenvalue problem, especially about the uniqueness and the approximation of solutions, and about the structure of fixed point sets.
allows one to prove a stronger version of the above theorem (see the Remark after Theorem 1.8 in [28]): Let (G) be a residually nilpotent finitely generated group.
In particular, Orlicz spaces are often generated by convex φ-functions [6], and the convexity allows one to prove several important properties for such spaces.
We note that Weisfeiler's Approximation Theorem [35], in conjunction with finiteness results for Galois cohomology of algebraic groups over number fields (cf. [21, §6]), allows one to prove Conjecture 6.1 for (K) a number field details will be published elsewhere.
The reasoning given above allows one to prove that under the same assumptions this map is differentiable in the sense of Fréchet and the differential of this map is the double operator integral begin{aligned} iint frac{f(s_1 -f(s_1 -fs_2-s_2},dE_A(s_1)K,dE_A(s_2).
The principle allows one to prove, for arbitrary \(n\), that there are at least \(n\) objects.
Notice also that the Hypothesis 2.1 iii) should allow one to prove the convergence in time to equilibrium of the mean-field limits.
In [18] the reduced basis method has been applied to this problem to obtain some stable solutions, allowing one to prove the efficiency of the given method to obtain solutions for different values of the parameters.
The theorem proved allows one to find all extreme points of the set of a b-bistochastic q.s.o. on 2D simplex, which can be considered as one of the future studies that can be done.
The technique allows one to noninvasively quantify local perfusion; it has recently been matched with perfusion values determined by invasive microsphere examination, proving accurateness of this measurement methodology [ 28].
Additionally these measurements allow one to definitely prove the existence of crystal type B on the samples.
