Sentence examples for prove the implication from inspiring English sources

We prove the implication (i) ⇒ (ii).

It remains to prove the implication:.

Proof We first prove the implication ((i) ⇒ (ii)).

The norm inequality having already been provided by Theorem 4.14, we only have to prove the implication lim r → 0 sup x ∈ R n ∥ f ∥ L Φ ( B ( x, r ) ) φ 1 ( x, r ) = 0 ⟹ lim r → 0 sup x ∈ R n ∥ T b f ∥ L Φ ( B ( x, r ) ) φ 2 ( x, r ) = 0. (4.14).

In any case, further functional studies are required to unequivocally prove the implication of the candidate gene in controlling the proposed volatile accumulation.

Let us prove the implications as follows: (i) (ii) (iii) (iv) (i).

Billingsley ( 1995 ) proved the implication that (hb) ⇒ (h8) by a version of analytic continuation of characteristic function, but it is easy to see that (hb) also implies (h7) and hence X is M-det on ({mathbb {R}}.) In Theorem 1, Carleman's condition (h7) is the weakest checkable condition for X to be M-det on ({mathbb {R}}).

Globally, this study has proven the implication of some compounds present in AESb on the rapid maturation of ovarian follicular cells leading to a precocious puberty onset.

In this work, we prove the reverse implication, i.e. any three-dimensional Riemannian manifold is asymptotically flat if it possesses a CMC-cover satisfying certain geometric curvature estimates, a uniqueness property, a weak foliation property, while each surface has weakly controlled instability.

Now we prove the converse implication.

To finish the proof, next we prove the converse implication.