by proving that

USAGE SUMMARY

The phrase "by proving that" is correct and usable in written English.
You can use it when you want to indicate that a conclusion or assertion is supported by evidence or demonstration. Example: "The researcher strengthened her argument by proving that the new method significantly improved results."

✓ Grammatically correct

Science

News & Media

Wiki

Human-verified examples from authoritative sources

Exact Expressions

59 human-written examples

The prosecutor could do that either by proving that Huhne was not present when Pryce committed the offence, or by proving that her will had not been overborne.

The Guardian - Opinion

Mr. Duffas has done Moliere and Corneille a service by proving that "Psyche" can be staged today.

The New York Times

Messrs Page and Brin created an internet phenomenon with their search engine and refuted conventional wisdom by proving that search could make money when paired with advertising.

The Economist

We begin by proving that (2.12).

Journal of Inequalities and Applications

We begin by proving that ((x_{n})_{ninmathbb{N}}) is bounded.

Journal of Inequalities and Applications

We will show that is open in by proving that is closed in.

Fixed Point Theory and Applications

We finish this step by proving that (overline{Upsilon}_{2}) is a χ-contraction.

Advances in Difference Equations

We also provide theoretical guarantees on the performance of this algorithm, by proving that XRJN is instance-optimal.

Information Systems

We will establish the existence of the second positive solution of problem (1.2) by proving that satisfies the -condition.

Boundary Value Problems

Now, we can calculate the worst-case capacity by proving that Gaussian distribution for,, and provides the worst case.

EURASIP Journal on Wireless Communications and Networking

Fagin began this field by proving that NP = SO\(\exists\), i.e., a property is in NP iff it is expressible in second-order existential logic [Fagin, 1974].

SEP

Expert writing Tips

Best practice

Use "by proving that" to clearly indicate that an assertion is supported by evidence or a demonstration of truth. This phrase strengthens your argument and enhances credibility.

Common error

While "by proving that" is grammatically correct, avoid overuse in informal writing where simpler alternatives like "by showing that" might sound more natural.

Linguistic Context

The phrase "by proving that" functions as an adverbial phrase introducing a subordinate clause. It signifies the method or means by which a claim or statement is validated or substantiated. Ludwig AI highlights that it connects the action of proving to the establishment of a fact or truth.

Expression frequency: Very common

Frequent in

Science

33%

News & Media

32%

Wiki

11%

Less common in

Encyclopedias

7%

Formal & Business

7%

Reference

3%

Ludwig's WRAP-UP

In summary, the phrase "by proving that" serves as a robust connector to introduce evidence and validation in support of a claim. It is grammatically correct and frequently used, as confirmed by Ludwig AI, particularly in scientific, news, and general knowledge contexts. While versatile, its use should be moderated in very informal settings, opting for simpler alternatives like "by showing that" when appropriate. Remember to employ "by proving that" when you want to emphasize a validated or substantiated point. The phrase adds weight and credibility to your writing.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

by demonstrating that

Replaces "proving" with "demonstrating", offering a more general term for showing evidence.

by showing that

Uses "showing" as a simpler alternative to "proving", indicating the act of displaying evidence.

by confirming that

Substitutes "proving" with "confirming", suggesting the validation of something already suspected.

by establishing that

Replaces "proving" with "establishing", indicating a more formal and definitive validation.

by verifying that

Uses "verifying" in place of "proving", focusing on the act of checking accuracy or truth.

by validating that

Similar to confirming, but emphasizes the act of ensuring something is officially recognized as correct.

by substantiating that

Offers a more formal tone, indicating that evidence is being provided to support a claim.

through evidence that

Shifts the focus to the evidence itself, rather than the act of proving.

as evidenced by the fact that

Highlights the fact that there is evidence, adding weight to the statement.

in light of the fact that

Introduces the subsequent clause as being illuminated or clarified by existing facts.

FAQs

How can I use "by proving that" in a sentence?

The phrase "by proving that" introduces a clause that demonstrates or confirms something. For example, "The theory gained acceptance "by proving that" it could accurately predict future events".

What are some alternatives to "by proving that"?

Alternatives include "by demonstrating that", "by showing that", or "by confirming that". The best choice depends on the specific nuance you want to convey.

Is it better to say "proving that" or "showing that"?

"Proving that" implies a conclusive demonstration, while "showing that" suggests a less definitive indication. Use "proving that" when you want to emphasize the strength of the evidence.

What's the difference between "by proving that" and "due to the fact that"?

"By proving that" introduces evidence supporting a claim, while "due to the fact that" introduces a reason or cause. "By proving that" focuses on demonstration; "due to the fact that" emphasizes causation.