Sentence examples for another proof which from inspiring English sources

We first give a proof of Theorem 3 for d = 2, 3 and then we give another proof which is valid for all d ≥ 2. We could have given only the second proof but we prefer to give them both as the first is simpler (but breaks down at d = 4 ).

But what's interesting to me now is another new proof, which is what do you use the Internet for?

They gave a sufficient (A_{p} -type condition (see (6.1) below), A_{p} -typea two-weight, weak type ((p,p)) inequality for (I_{alpha})(see also [22] for another, simpler proof), whicondition a problem posee by Sawyer and Wheeden in [23].

However, we give here another simple direct proof which works also to prove that part (b) holds, which seems not to have been explicitly stated before.

Another interesting analysis of finitary proof, which, however, does not provide as detailed a philosophical justification, was proposed by Kreisel (1960).

surely the proof which you desire has been already furnished.

"Unfortunately," they write, his proof, "which has been read by many prominent experts, is incomplete".

"Proof," which opened Oct. 24 at the Walter Kerr, recouped its money in just 10 weeks.

They say they need proof, which has not been given to them.

I'm also curious about "Proof," which I saw at the Manhattan Theater Club.

We give a new proof which gives a polynomial bound in 1/epsilon in this case.