as previously proved

USAGE SUMMARY

The phrase "as previously proved" is correct and usable in written English.
It can be used when referring back to a statement or argument that has already been established or demonstrated earlier in the text. Example: "The theorem holds true, as previously proved in section 2 of this paper."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

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

Advances in Difference Equations

Therefore, weekly nab-paclitaxel was more desirable as previously proved in solvent-based paclitaxel [ 7].

BMC Cancer

Irrespectively of the real initiation codon, a formyl-Met was assumed to be the starting amino acid for all the proteins as previously proved for other mitochondrial genomes [ 37, 38].

BMC Genomics

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

There was no need for attenuation correction of the dynamic study because the factors that respectively relate gradient and intercept based on raw count rates to Ki and V 0) are identical, and cancel out in their ratio, as previously proven [29].

EJNMMI Research

Then ( g u ˆ, g u ˆ ) and ( g u ˜, g u ˜ ) are two common coupled points of coincidence of F and g and, as was previously proved, it must be g u ˆ = g u ˜, and so u ˆ = g u ˆ = g u ˜ = u ˜.

Fixed Point Theory and Applications

The intensive care unit contains a complex assortment of monitors and life-support equipment that can sustain life in situations that previously proved fatal, such as adult respiratory distress syndrome, multiorgan failure, kidney failure, and sepsis.

Encyclopedia Britannica

Yet it has previously proved a folly to believe that common sense or technical knowledge would act as a failsafe.

BMJ Quality and Safety

In this paper, we provide a theoretical proof of the fact that the only unitals contained in the 2- 28,4,5) Hölz design are Hermitian and Ree unitals (as was previously proven by a computer search by Tonchev, [V.D. Tonchev, Unitals in the Hölz design on 28 points, Geom. Dedicata 38 (3) (1991) 357 363]).

Journal of Combinatorial Theory, Series A

The anti-theophylline aptamer was attached at the same point as had previously proven successful in the design of theophylline-dependent cleavases and ligases [ 13, 14].

BMC Biotechnology

Then r ( t ) ≥ 0 ∀ t ∈ R 0 + is deduced from the fact that ι ( t ) ≥ 0 ∀ t ∈ R 0 +, as it was previously proven.

Advances in Difference Equations

Five transcription factors were identified as documented PDR18 regulators previously proven to bind to its promoter region, and, thus, were selected as candidates for, directly or indirectly, controlling 2,4-D-induced PDR18 up-regulation.

Biochemical Journal

Expert writing Tips

Best practice

When using "as previously proved", ensure that the prior proof is clearly referenced or easily accessible within the current document or context. This enhances clarity and credibility.

Common error

Avoid using "as previously proved" without providing context or a specific reference. This can leave the reader unsure of what you're referring to, weakening your argument.

Linguistic Context

The phrase "as previously proved" functions as an adverbial phrase, modifying a statement by indicating that it has been established or demonstrated earlier. As seen in the Ludwig examples, it is used to reference a prior argument or finding, strengthening the current assertion.

Expression frequency: Rare

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Encyclopedias

0%

Ludwig's WRAP-UP

In summary, "as previously proved" is an adverbial phrase used to reference a prior demonstration or establishment of a fact, primarily found in formal and scientific writing. Ludwig AI confirms its grammatical correctness and while examples are limited, its usage in credible sources reinforces its proper application. To ensure clarity, always provide sufficient context or a specific reference when using this phrase. While "proved" is more common in British English and "proven" is favored in American English, both can be used. Alternative phrases like "as demonstrated before" or "as established earlier" can also be used depending on the context.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

as demonstrated before

This alternative substitutes "proved" with "demonstrated" implying an earlier exhibition or explanation.

as established earlier

This alternative uses "established" to suggest something was confirmed or proven at an earlier point.

as shown previously

Replaces "proved" with "shown", which indicates a presentation or demonstration occurred before.

as already proven

Uses "already" to emphasize that the proof happened before the current statement.

as has been demonstrated

Uses a passive voice to emphasize the demonstration rather than the action of proving.

as it has been established

Similar to "as established earlier", but with more emphasis on the process of establishing.

as can be seen from above

This refers back to something shown or proven earlier, directing the reader's attention to that section.

as validated before

Implies formal validation has occurred to confirm a previous statement or claim.

as substantiated earlier

Replaces "proved" with "substantiated", focusing on providing evidence or support for a claim made earlier.

as verified previously

Focuses on the act of verifying, which implies a check has been conducted and confirmed the statement.

FAQs

How can I use "as previously proved" in a sentence?

Use "as previously proved" to refer to a statement or argument that has already been established. For example, "The theorem holds true, "as previously proved" in section 2 of this paper".

What are some alternatives to "as previously proved"?

You can use alternatives such as "as demonstrated before", "as established earlier", or "as shown previously" depending on the context.

Is "as previously proved" or "as previously proven" more correct?

Both "as previously proved" and "as previously proven" are acceptable, though "proved" is more common in British English, while "proven" is more prevalent in American English. Consider your audience when choosing.

What's the difference between "as previously proved" and "as previously stated"?

"As previously proved" indicates that something has been demonstrated with evidence, while "as previously stated" simply refers to something mentioned before, without necessarily implying proof.