Sentence examples for whose proofs from inspiring English sources

This methodology is supported by a set of theorems, whose proofs are presented in this paper.

Next we prepare two lemmas, whose proofs can be found in Fan and Pan [4].

Next, we state the regularity results whose proofs are the same as the ones in [23].

We have Theorems 2 and 3, whose proofs are presented in "Appendices 1 and 2", respectively.

Theorem 11, therefore, brings another theorems whose proofs are obvious, thus omitted here.

5.4, relies on Propositions 1 and 2, whose proofs are presented in Sects 5.2 and 5.3.

That hypothesis is now universally accepted.But the big idea of Dr Gold's whose proof or disproof is pending is the "deep, hot biosphere".

"I never expected to have a play on Broadway," said Mr. Auburn, whose "Proof" began Off Broadway at the nonprofit Manhattan Theater Club.

We require the following lemma whose proof is immediate.

We will need the following result whose proof is elementary.

Theorem 1, whose proof is quite simple, reads as follows.