Sentence examples for proofs were from inspiring English sources

And what proofs were offered?

The proofs were not simply 'sketched' but presented completely.

The proofs were getting so long that progress was glacial.

Within a fortnight, a deal had been struck (Charlotte was paid £100) and proofs were being worked on.

Some of the results were given without proof in an appendix, and Huygens' complete proofs were not published until after his death.

The title, changed by the publisher after galley proofs were distributed for review, is "The Okinawa Program: How the World's Longest-Lived People Achieve Everlasting Health -- And How You Can Too," by Dr. Bradley J. Willcox, Dr. D. Craig Willcox and Dr. Makoto Suzuki (Clarkson Potter, 2001), not "The Okinawa Way".

Actually, hundreds of proofs are known today.

Formal convergence proofs are indicated.

All our proofs are analytic.

Their proofs are obvious.

Our proofs are elementary.