Sentence examples for the next proof from inspiring English sources

The next proof will be given in two steps.

The next proof is similar to Theorem 1.

Thus limn→∞T3nx = z and z is a best proximity point of T in A i. For the next proof we will follow the idea in [8], how to use a variational principle to prove a fixed point theorem.

For the convenience of our discussion, we start with the following lemmas, which will be useful in the next proofs.

In the following proposition, we will give other properties of the Fibonacci and Lucas numbers, which will be necessary in the next proofs.

Andrei Linde, a Stanford University physicist, noted that his favorite model was still in the running and exclaimed in an e-mail message, "Great day for cosmology!" The stage is set for a race to achieve the next milestone, proof of inflation theory.

The next best proof of ovulation is provided by the post-ovulatory rise in progesterone production following an oestrogen peak and fall.

I'm no pro, but the creaking of my abdomen the next morning is proof enough that just a few spins will awaken even the most neglected of cores.

"As the number of such connected devices is expected to grow to more than four times the number of connected computers in the next few years, proof of an 'internet of things'-based attack has significant security implications for device owners," David Knight, general manager of ProofPoint's security division, said.

But by the next day, the proof is in the poop.

Sentry Safe developed the next generation disaster proof drive in a collaboration with Maxtor Storage Solutions.