Sentence examples for a proof has been from inspiring English sources

In a footnote, Bell added that "Since the completion of this paper such a proof has been found".

A formal proof has been provided for the case of K = 2 transmitters and S = 2 channels.

A different proof has been recently given in [44], where the Ehrhard symmetrization [55] plays the same role of Steiner symmetrization in De Giorgi's proof [53] of the isoperimetric inequality.

Although a shorter proof has been given later by Cicalese and Leonardi [45] using the regularity theory for area minimizing sets of finite perimeter, the proof by symmetrization uses no deep results from geometric and functional analysis, is geometrically intuitive and can be adapted to other situations where a complete regularity theory is not available.

Although this mechanism has been suggested before, specifically for p27 in the Pten/Nkx3.1 and MMTV-erbB2 models, and for p21 in the MMTV-Wnt1 model, this is the first time that a genetic proof has been used to assess the veracity of this model.

Until now, a poor level of proof has been published, questioning the pertinence of such a strategy.

Later on, a new and interesting proof has been offered Trudinger and Wang [65, 66], and this allows to cover the case of general subelliptic operators.

Finally, an elegant and short proof has been given by Cabré in [30] using the properties of solutions of the Neumann problem for the Laplacian.

The Annals considered publishing the paper with a disclaimer of sorts: This proof has been mostly, but not entirely, checked.

Until now, however, proof has been lacking.

The proof has been finished.