as proved previously

USAGE SUMMARY

The phrase "as proved previously" is correct and usable in written English.
It can be used to refer back to information or evidence that has already been established or demonstrated earlier in the text. Example: "The results of the experiment align with the hypothesis, as proved previously in our earlier analysis."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

1 human-written examples

Although warm-rainy temperature favours bacterial growth, enteric viruses could be damaged by rising temperatures, as proved previously, when EV and RV were studied in fresh water at 22°C and 20°C [ 39, 40].

Environmental Health: A Global Access Science Source

Human-verified similar examples from authoritative sources

Similar Expressions

59 human-written examples

As proven previously, one transcriptionally active autonomous element can cause trans-mobilization of a range of related, but not directly derived elements [ 13].

BMC Genomics

This is a simple and well-known consequence of our choice of concave rate functions, as has been proved previously in [12]: when there are no constraints, an even (equal across time) allocation is optimal.

EURASIP Journal on Wireless Communications and Networking

Predictors included gender, pre-test score, highest mathematics course (pre-algebra or lower, algebra, geometry or higher), how many conjectures the participant had proved previously as an ordered factor variable (to account for tiring), and sample (video game camp or private high school).

Cognitive Research: Principles and Implications

Hence, as is proven previously, we infer that is nonnegative on.

Advances in Difference Equations

These results suggest that the microvilli (filopodia or lamellipodia) of CD4 T cells closely react with the QNPA substrates via high-affinity STR-biotin conjugation as we have proven previously [22] and extend filopodia of widths depending on the diameter of the QNPAs to identify the size of the structures underneath the cells using filopodia as illustrated in Figure 3c.

Nanoscale Research Letters

"Are they as proven as David Wright?

The New York Times - Sports

Concerning malaria vaccine clinical research, the preerythrocytic candidate FMP011 adjuvanted with AS01 failed to induce protection although immunogenicity was proved, as previously happened with AS02 [ 99].

BioMed Research International

Herbal remedies containing aristolochic acids were previously categorized as proven group 1 human carcinogens by the WHO cancer agency, the International Agency for Research on Cancer.

The Journal of Urology

Bill O'Reilly of Fox News, who had previously praised Lichter's work as proving that the media was liberal, was incensed and rejected the study.

The New York Times

As previously proved in Theorem 3.3, we see that the operator (mathcal{Q}) is continuous, uniformly bounded, and equicontinuous.

Advances in Difference Equations

Expert writing Tips

Best practice

Use "as proved previously" to efficiently refer to established facts or findings, avoiding repetition and maintaining clarity in your writing.

Common error

Avoid using "as proved previously" in casual or informal writing. Opt for simpler phrases like "as we saw earlier" or "as mentioned before" to maintain a natural tone.

Linguistic Context

The phrase "as proved previously" functions as an adverbial phrase, modifying a verb or clause by providing context about when or how something was established. Ludwig AI confirms this by presenting various examples of its usage across different domains.

Expression frequency: Uncommon

Frequent in

Science

60%

News & Media

20%

Formal & Business

10%

Less common in

Wiki

5%

Encyclopedias

3%

Social Media

2%

Ludwig's WRAP-UP

In summary, "as proved previously" is a grammatically sound adverbial phrase used to reference prior evidence or demonstrations. While correct, it leans toward formal and scientific writing, as Ludwig AI analysis and examples suggest. When writing, it's crucial to ensure the context aligns with the phrase's formality. For more casual settings, consider alternative expressions such as "as we saw earlier". Although its usage is not as frequent as simpler alternatives, it effectively connects current statements with previously demonstrated information, enhancing credibility and conciseness.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

as previously demonstrated

Replaces "proved" with "demonstrated", focusing on the act of showing evidence.

as previously established

Substitutes "proved" with "established", highlighting the confirmed or settled nature of the information.

as has been shown before

Uses a more informal and conversational tone.

as prior research indicates

Specifically references research as the source of proof.

in accordance with prior findings

Emphasizes agreement with existing research.

consistent with earlier evidence

Highlights the consistency of new information with previous evidence.

as validated in previous studies

Focuses on validation through prior research.

it has been previously verified that

Emphasizes the verification process.

building on earlier proofs

Suggests a progression from previous proofs.

as confirmed by earlier analysis

Highlights the confirmation through prior analysis.

FAQs

How can I rephrase "as proved previously" to sound more formal?

Consider using alternatives like "as previously demonstrated", "as previously established", or "in accordance with prior findings" to maintain a formal tone in your writing.

Is "as proved previously" suitable for informal conversations?

While grammatically correct, "as proved previously" may sound too formal for casual conversations. Simpler alternatives like "as we saw earlier" or "as mentioned before" are often more appropriate.

What is the difference between "as proved previously" and "as previously reported"?

"As proved previously" implies that something has been conclusively demonstrated, while "as previously reported" simply indicates that something has been mentioned before, without necessarily implying proof.

Can I use "as proved previously" at the beginning of a sentence?

Yes, "as proved previously" can be used at the beginning of a sentence to introduce a statement that builds upon previously established information. For example: "As proved previously, the theorem holds true under these conditions."