Sentence examples for and the proofs of from inspiring English sources

Suggestions(5)

and the proof of

and the testimonies of

and the certificates of

and the tests of

and the assertions of

The phrase "and the proofs of" is correct and usable in written English.
It can be used when discussing evidence or validation of a claim, theory, or argument in various contexts, such as academic writing or legal documents.
Example: "In the research paper, the author presented the hypotheses and the proofs of their validity through extensive experimentation."
Alternatives: "and the evidence of" or "and the demonstrations of".

Exact(26)

In Section 3, we give some lemmas and the proofs of the theorems.

Journal of Inequalities and Applications

The conclusion and the proofs of the main results are arranged in Sections 4 and 5.

Journal of Inequalities and Applications

Some auxiliary results and the proofs of the main results are given in Section 3.

Journal of Inequalities and Applications

Our main results are presented in Section 2 and the proofs of the main results are provided in Section 3.

Journal of Inequalities and Applications

So the truncated method is different and the proofs of our main results are more complicated and difficult.

Journal of Inequalities and Applications

In Section 2, we will consider R1 and the proofs of R2 will be given in Section 3.

Journal of Inequalities and Applications

Similar(34)

This paper presents a novel approach to preparing sulfur-tolerant noble metal catalysts and the proof-of-concept experimental results.

Journal of Catalysis

Learn about the fare zones and the proof-of-payment system.

WikiHow

The concept and results of the proof-of-principle experiment are given.

Surface and Coatings Technology

It concerns a trip to the Eastbourne Grand Hotel, where Debussy adjusted the orchestration, and corrected the proofs, of La Mer.

The Guardian - Books

And the proof of voluntariness was placed on the State.

Cornell University

More suggestions(14)

and the documents of

and the validations of

and the explanations of

and the papers of

and the examinations of

and the manifestations of

and the confessions of

and the rationales of

and the evidences of

and the directories of

and the evidence of

and the views of

and the costs of

and the people of

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