Sentence examples for proof of this fact from inspiring English sources

We provide an alternative self-contained proof of this fact.

In this paper, we give a purely functional analytic proof of this fact.

The remarkable proof of this fact has been preserved by Aristotle.

The proof of this fact is one of the main results of this paper.

The first proof used algebraic geometry, and a later more elementary proof of this fact is still quite complicated.

Kelly Vincent, representing the Dignity for Disability party in the South Australian upper house is living proof of this fact.

Pottery was not an unknown art, and the brilliantly painted vessels found here are emphatic proof of this fact.

The constructive proof of this fact leads to an efficient computer algorithm for the design of a lattice.

We give two proofs of this fact.

Despite the fact that the isoperimetric property of the circle among all planar figures was already well known in ancient times, the first rigorous proofs of this fact have been only obtained at the beginning of last century.

Proof The demonstration of this fact is immediate taking into account the construction of the lower solution α obtained in the previous theorem, the existence of the upper solution β with 0 < α ≤ β and the implementation of Lemma 3.2.