as demonstrated above

USAGE SUMMARY

"as demonstrated above" is a correct and usable phrase in written English.
It is typically used to refer to information or evidence that has been presented earlier in the text or in a previous paragraph. Example: "As demonstrated above, the results of the experiment clearly indicate that exercise has a positive impact on mental health."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Pump up the volume with a parka, Mizrahi says, but offset its bulk with narrow pants, as demonstrated above.

The New York Times

As demonstrated above, complete reactions between early-formed minerals and the liquid depletes the supply of the liquid, thereby curtailing the progression down the series.

Encyclopedia Britannica

However, as demonstrated above, Pythagorean pseudepigrapha were very widespread and more common than genuine Pythagorean works.

SEP

At low frequencies the loss modulus follows [20] where viscosity scales as as demonstrated above.

Nanoscale Research Letters

As demonstrated above, GaN films cannot be deposited on graphite surfaces by conventional two-step growth.

Nanoscale Research Letters

As demonstrated above, there are noticeable differences across beverages for price and income elasticities, especially for beer.

Health Economics Review

As demonstrated above, Taiwan's science education reform discourses were shaped by the democratic movement and political events of the 1990s.

Asia-Pacific Science Education

Their size and percentage in the material change non-monotonically with changing porosity, as demonstrated above from our PL measurements.

Nanoscale Research Letters

As demonstrated above, topology optimisation and shape optimisation are complementary methods: the former for drafting, the latter for fine-tuning.

Journal of Mathematics in Industry

As demonstrated above, to prove the inequality in equation (2.6) it is not necessary to use the Jensen inequality.

Journal of Inequalities and Applications

The Electoral Commission is worried the current craze for smart phone self-portraits, as demonstrated above by the prime minister, will threaten the secrecy of the ballot.

BBC

Expert writing Tips

Best practice

Ensure the information you are referencing with "as demonstrated above" is clear and readily accessible to the reader. Avoid using it to refer to information that is vague or difficult to locate.

Common error

Avoid using "as demonstrated above" if the demonstration is not clear or is too far removed from the current text. Readers should not have to search extensively to understand the reference.

Linguistic Context

The phrase "as demonstrated above" functions as a transitional phrase, specifically a referential marker. It directs the reader's attention to information, examples, or evidence that has been previously presented within the text. Ludwig AI confirms its validity and widespread use.

Expression frequency: Very common

Frequent in

Science

66%

News & Media

12%

Encyclopedias

2%

Less common in

Formal & Business

0%

Wiki

0%

Reference

0%

Ludwig's WRAP-UP

In summary, "as demonstrated above" is a frequently used and grammatically sound phrase for referencing previously presented information or evidence. As Ludwig AI confirms, this phrase is effective in formal and scientific writing to reinforce arguments and maintain clarity. While alternatives exist, they often carry slight differences in formality or emphasis. When using "as demonstrated above", ensure the reference is clear and easily accessible to the reader.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

as previously shown

Emphasizes the chronological order of the demonstration.

as illustrated earlier

Focuses on the visual or descriptive nature of the prior demonstration.

as evidenced before

Highlights the evidence-based aspect of the prior information.

as established above

Suggests a more definitive and conclusive demonstration.

as mentioned earlier

Refers to something that was previously stated but may not have been explicitly demonstrated.

as noted previously

Similar to 'mentioned earlier' but slightly more formal.

in light of the above

Positions the current statement as a consequence of the preceding information.

considering what's been shown

Less formal alternative, emphasizing consideration of the evidence.

given the preceding examples

Specifically refers back to examples that have been presented.

pursuant to the above

A formal and legalistic alternative, indicating action based on what has been presented.

FAQs

How can I use "as demonstrated above" in a sentence?

Use "as demonstrated above" to refer back to a point or evidence that has been clearly presented earlier in your text. For example, "As demonstrated above, the new policy has significantly reduced operational costs".

What are some alternatives to "as demonstrated above"?

You can use alternatives like "as previously shown", "as illustrated earlier", or "as evidenced before" depending on the context.

Is "as demonstrated above" too formal for casual writing?

While "as demonstrated above" is generally suitable for formal and academic writing, it might sound too stiff in casual contexts. Consider using a more relaxed phrase like "as you can see" or "like we said before".

What is the difference between "as demonstrated above" and "as mentioned above"?

"As demonstrated above" implies that you have provided clear evidence or an example to support a claim, while "as mentioned above" simply means that you have previously stated something, without necessarily providing a demonstration.