as already proved

USAGE SUMMARY

The phrase "as already proved" is correct and usable in written English.
You can use it to refer back to something that has been previously established as true or to emphasize something that has been previously established as true. For example, "His innocence has been proven beyond a reasonable doubt, as already proved in court."

✓ Grammatically correct

Science

News & Media

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

As already proved [11 13], the resultant mean-map's importance stems from the fact that it is a tool for introducing the stability and stabilizability concepts, which we recall in the following.

Journal of Inequalities and Applications

As already proved in [16] and in [7], in the case of unbounded domains, one has ( G k s k s − 1 ( u ) ) x i = G k s k s − 1 ′ ( u ) u x i, a.e. in Ω, i = 1, …, n.

Boundary Value Problems

Bacterial disinfection can be obtained through fogging of product as already proved [ 2].

BMC Infectious Diseases

Human-verified similar examples from authoritative sources

Similar Expressions

56 human-written examples

Still, the project takes as already proven the existence of the Xia as a precursor empire to the better-established Shang, pointing to a site uncovered at Erlitou, Henan Province, in 1959 as the probable capital.

The New York Times

Altered hemodynamics and venous overlay are a common problem in diagnostic MRA, which can be solved by time-resolved MRA, which was not part of the current study, but could deliver purely arterial images without venous overlay and therefore increase diagnostic accuracy for the calf station as already proven in a previous study [ 9].

European Radiology

Secondly, as already proven by mathematical analysis [50], fast reincorporation of dissociated labels into the same photobleached area retards FRAP kinetics substantially slower (∼by half) than the true actin disassembly rate [6], [50].

Plosone

Arabidopsis thaliana has been largely adopted for mendelian genetics investigations and genomics but it is also a promising species for the pursuit of quantitative genetics studies, as already proven by the isolation of genes underlying QTLs [44].

Plosone

These findings indicate the critical roles of CCN2/CTGF in periodontal tissue development and strongly suggest the utility of CCN2/CTGF in periodontal tissue regeneration, as already proven in articular cartilage.

Cell Communication and Signaling

As Reichartz already proved in Hands Off [A.I.], as well as in his virtual interpretation of Ai Weiwei's Stools, he is fast becoming a master of 3D animation and textures.

Vice

One such narcocorridos, by Mexican band Enigma Norteño, details the exploits of El Chapo, with lyrics such as "I already proved my power once… and if I did it once, I'll do it to them again".

Independent

Proof of Theorem 1.1 As we already proved in Lemma 2.2, critical points of φ over SE are critical points of φ over E. Hence they are nonconstant classic N -periodic solutions of (1.7) with the symmetric structure (1.11).

Advances in Difference Equations

Expert writing Tips

Best practice

Use "as already proved" to succinctly reference information or results that have been rigorously demonstrated earlier in a text or in prior research. This avoids unnecessary repetition and strengthens your argument.

Common error

Avoid using "as already proved" if the point has not been explicitly and thoroughly demonstrated, either within the current text or in a readily citable source. Ensure there is clear evidence to support the claim, or choose a more tentative phrasing.

Linguistic Context

The phrase "as already proved" functions as an adverbial phrase, modifying a verb or clause to indicate that a statement is based on previously established evidence. Ludwig AI confirms that it's correct and usable. The phrase serves to reinforce the validity of a subsequent claim.

Expression frequency: Rare

Frequent in

Science

67%

News & Media

33%

Formal & Business

0%

Less common in

Academia

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "as already proved" is a grammatically sound adverbial phrase used to lend authority to a statement by referencing established evidence. Ludwig AI confirms its correctness. While relatively rare in occurrence, it is primarily found in scientific and news contexts. When employing this phrase, ensure that the referenced information has indeed been thoroughly demonstrated. For increased clarity or depending on the context, alternatives such as "as previously demonstrated" or "it is a proven fact" might be considered.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

it is a proven fact

Emphasizes that something is an already proven and accepted fact.

as previously demonstrated

Replaces "proved" with "demonstrated", emphasizing the act of showing or exhibiting evidence.

as has been established

Focuses on the state of being established or confirmed, rather than the act of proving.

as earlier indicated

Substitutes "proved" with "indicated", suggesting a less rigorous form of evidence or support.

as we have shown

Uses a more direct and personal tone, referring to the speaker's or writer's own demonstration.

it has already been verified

Highlights the aspect of verification or confirmation of something already established.

it's been previously validated

Emphasizes the validation or confirmation of a prior finding or result.

the evidence suggests

Presents a weaker assertion than "proved", indicating that the evidence points in a particular direction without definitive proof.

the facts confirm

Shifts the focus to the confirmatory nature of the facts.

this has been borne out

Implies confirmation through experience or results over time.

FAQs

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

Use "as already proved" to refer back to something that has been previously established as true. For example, "The efficacy of the treatment has been confirmed, as already proved in our earlier study."

What are some alternatives to "as already proved"?

You can use alternatives like "as previously demonstrated", "as has been established", or "it is a proven fact" depending on the context.

When is it appropriate to use "as already proved"?

It's appropriate when you are referencing information or a conclusion that has been definitively demonstrated and you want to avoid repeating the proof.

Is "as already proved" the same as "as already proven"?

While both are grammatically acceptable, "as already proved" is more concise. Both can be used to refer to something that has previously been shown to be true.