as proven below

USAGE SUMMARY

The phrase "as proven below" is correct and usable in written English.
It can be used to indicate that evidence or examples supporting a statement will follow in the text. Example: "The theory is supported by various studies, as proven below."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

2 human-written examples

As proven below, the population after chromosomal multiplication will deviate from HWE.

BMC Cancer

These very important prior results all focused on reconstruction from a single time series; however, as proven below, they can be extended to the more practically significant case where multiple observation functions are used to generate <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0018295.e009.PNG" class= inline-graphic"/>.

Plosone

Human-verified similar examples from authoritative sources

Similar Expressions

58 human-written examples

The following result was proven by Matsen, Mossel and Steel in [ 26] for the two state random cluster model but, as proved below, it can be easily generalized to any evolutionary model.

Algorithms for Molecular Biology

So, as it would be proven below, at the bottom-up stage of the DP algorithm it would be sufficient to assign to each node a in the tree G four values: left(a), right(a), Z(a), and X(a).

BioMed Research International

As to why the theorem proven below has been missed by all of the world's philosopher, the answer is simple.

Duke University

In other words, a search within the IC triangle ensures that the node D interconnecting to C will be found, as proved below.

EURASIP Journal on Wireless Communications and Networking

"Are they as proven as David Wright?

The New York Times - Sports

The positive shift of Voc indicates that the hydrogen-induced defects lead to a relatively faster recombination rate as proven by TRPL measurements (shown below).

Nanoscale Research Letters

Plus, it's very enjoyable to watch the process, as proven by the adorable photos below.

Huffington Post

Thus, half of the N/2-pt FFT-B output values will be zero, as proved by the Eq. (12) below.

EURASIP Journal on Wireless Communications and Networking

We prove below item (ii).

Journal of Inequalities and Applications

Expert writing Tips

Best practice

Use "as proven below" to signal that you are about to provide concrete evidence or a logical argument that supports a previous statement. This helps guide the reader through your reasoning and strengthens your claims.

Common error

While grammatically correct, "as proven below" can sound overly formal in casual writing. Consider using simpler phrases like "as you can see below" or "see below for details" in less formal settings.

Linguistic Context

The phrase "as proven below" functions as a transitional phrase, specifically a causal connector. It signals that evidence or justification will be presented to support a preceding claim. Ludwig AI confirms this is a grammatically sound construction.

Expression frequency: Rare

Frequent in

Science

66%

News & Media

22%

Academia

12%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

In summary, the phrase "as proven below" is a grammatically correct causal connector that indicates supporting evidence will follow. As confirmed by Ludwig AI, it is most appropriate for formal writing, particularly in scientific or academic contexts, where rigorous justification is valued. While alternatives exist, varying in formality and emphasis, overuse in casual settings should be avoided. The phrase serves to strengthen an argument by directing the reader towards evidence that validates a preceding claim. With only three exact examples available, the phrase's occurrence can be qualified as rare.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

as demonstrated below

Replaces "proven" with "demonstrated", suggesting a visual or practical display of evidence, less formal.

as shown below

Substitutes "proven" with "shown", implying a more direct and obvious presentation of evidence, less formal.

as evidenced below

Uses "evidenced" instead of "proven", indicating that evidence will be presented, retaining a similar level of formality.

as will be proven below

Adds "will be" to explicitly indicate future proof, slightly more emphatic about the upcoming evidence.

the proof follows below

Restructures the phrase to emphasize the "proof" itself, more formal and direct.

the following proves this

Changes the structure to focus on what "proves" the point, less common in formal writing.

this is proven below

Emphasizes the fact that something "is proven", shifting focus slightly.

proof is provided below

Highlights that "proof is provided", changing the emphasis from the act of proving.

the evidence below suggests

Uses "evidence" and "suggests", making the claim slightly weaker than a direct proof.

the data below confirms

Uses "data" and "confirms", suitable for empirical or quantitative contexts, less general.

FAQs

What is an alternative to "as proven below" that sounds less formal?

You can use alternatives like "as shown below", "as demonstrated below", or "see below" depending on the context.

How should I use "as proven below" in a sentence?

Use "as proven below" to introduce evidence or explanations that support a claim you've already made. For example, "The hypothesis is valid, as proven below."

Is "as proven below" suitable for all types of writing?

While grammatically correct, "as proven below" is more suited for formal and academic writing. For informal contexts, consider using alternatives like "as you can see below".

What is the difference between "as proven below" and "as demonstrated below"?

"As proven below" implies a logical or mathematical proof is coming, while "as demonstrated below" suggests a practical demonstration or example will be provided.