as we have shown

USAGE SUMMARY

The phrase "as we have shown" is correct and usable in written English.
It is typically used to refer back to evidence or arguments previously presented in a text or discussion. Example: "The results of our study indicate a significant correlation between the variables, as we have shown in the previous section."

✓ Grammatically correct

Science

News & Media

Formal & Business

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

"We are totally against his views as we have shown," said Ahmed Versi, editor of the newspaper Muslim News.

The New York Times

The challenge is to show the same resolve with them as we have shown in Asia.

The Economist

The truth of it rests on reliable evidence, and, as we have shown, it can be deduced by a simple consideration of natural philosophy.

The New Yorker

As we have shown before, there are far more PhDs produced each year than there are job openings.

The Economist

As we have shown in other work, this same divergence between countries also held for the income tax.

The New York Times

As we have shown, this is not possible.

Journal of Cloud Computing

Patient-centered versions of deontology cannot easily escape this problem, as we have shown.

SEP

As we have shown in Step 1, { T n x n } and { u n } are bounded.

Fixed Point Theory and Applications

As we have shown here, charging is not only confined to ballistospores of Agaricomycetes.

AMB Express

As we have shown in Example 3.1, this reasoning is not correct.

Journal of Inequalities and Applications

Instead, as we have shown, it is possible to introduce flexibility in two ways.

Journal of Economic Structures

Expert writing Tips

Best practice

When using "as we have shown", ensure that the referenced information is clear and easily accessible to the reader. Cite specific sections or figures if possible.

Common error

Avoid using "as we have shown" if the information hasn't been explicitly presented or adequately supported within the current context. Always ensure the reader has access to the evidence you're referencing.

Linguistic Context

The phrase "as we have shown" functions as an explicit textual reference. It signals to the reader that the subsequent statement is supported by information already presented, often reinforcing an argument or conclusion. As Ludwig AI suggests, this phrase serves to connect different parts of a text by reminding the reader of previous findings.

Expression frequency: Very common

Frequent in

Science

51%

News & Media

33%

Formal & Business

4%

Less common in

Encyclopedias

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "as we have shown" is a versatile phrase used to refer back to previously presented information. Ludwig AI confirms its correctness and usability. It is most common in scientific and news contexts, serving to validate arguments and strengthen conclusions. When employing this phrase, ensure clarity by referencing specific sections or figures. Alternatives like "as previously demonstrated" or "as evidenced above" can be used to add formality or emphasis. Avoid assuming prior knowledge; always ensure your readers have access to the referenced material. The phrase contributes to creating a cohesive and well-supported narrative.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

as the data shows

Directly links the statement to the data presented.

as the evidence suggests

Highlights the suggestive nature of the evidence.

as previously demonstrated

Emphasizes a more formal and rigorous presentation of evidence.

it has already been shown

Emphasizes the established nature of the information.

as demonstrated earlier

Similar to "as previously demonstrated" but with a simpler structure.

as evidenced above

Focuses on the evidence presented in the preceding text.

we have already established that

Highlights the action of establishing a fact or conclusion.

as we previously mentioned

Highlights a prior mention of the topic, less emphasis on proof.

as indicated before

Refers to a previous indication or suggestion.

the foregoing has shown

More formal and literary alternative.

FAQs

How can I use "as we have shown" in a sentence?

Use "as we have shown" to refer back to information, data, or arguments that you've previously presented in your writing. For instance, "The data indicates a strong correlation, "as we have shown" in the previous section."

What are some alternatives to "as we have shown"?

You can use alternatives like "as previously demonstrated", "as evidenced above", or "as the data shows" to introduce information that has already been established.

Is it appropriate to use "as we have shown" in formal writing?

Yes, "as we have shown" is appropriate for formal writing, especially in academic papers, reports, and articles. It's a clear and direct way to refer to previously presented evidence. Consider alternatives like "as previously demonstrated" for an even more formal tone.

What's the difference between "as we have shown" and "as we will show"?

"As we have shown" refers to information that has already been presented, while "as we will show" refers to information that will be presented later in the text. Make sure you use the correct phrase based on whether you're referring to past or future content.