Sentence examples for using the proof of from inspiring English sources

This is accomplished using the proof of concept design and implementation of a novel in-band, path-coupled signaling protocol for IPv4/IPv6.

Using the proof of Theorem 3.1, we have the following.

Using the proof of Theorem 3.3, we obtain (3.40).

Using the proof of [13, Theorem  2], one can easily show this lemma.

Using the proof of the composition theorem [2, Theorem 2.4], (applied to ) it follows (3.14).

Using the proof of Theorem 1 in [18], we obtain the following theorem.

Using the proof-of-concept experience, MCHIP has developed an implementation package outlining the process, training materials, tools, and key implementation considerations to help government and other stakeholders adapt and scale-up the approach (see supplementary material).

Using the proofs of Theorems 3.1 and 3.3, we get unique an additive mapping and unique quadratic mapping satisfying (3.42).

Ether, for example, uses the proof-of-stake concept, which is energy efficient, while the cryptocurrency ripple does not require mining.

We continue to use the proof of Theorem 2.3.

Finally, to prove Theorem 1.3, we use the proof of Theorem B in [11].