proof established

USAGE SUMMARY

The phrase "proof established" is correct and usable in written English. You can use it in contexts where you want to indicate that evidence or arguments have been successfully presented to support a claim or conclusion. For example, "The proof established that the theory was valid." Alternative expressions include "evidence confirmed" and "validation achieved."

✓ Grammatically correct

Science

News & Media

Encyclopedias

Human-verified examples from authoritative sources

Exact Expressions

4 human-written examples

Euclid's proof established that there will always be primes, but it says nothing about how far apart any two might be.

The New Yorker

This proof established that the classical Greek construction problem of squaring the circle (constructing a square with an area equal to that of a given circle) by compass and straightedge is insoluble.

Encyclopedia Britannica

Thus, when a different proof arose later on using Montel's idea of normal families, this proof established itself as standard [2].

Complex Analysis and its Synergies

The recommendations proposed have been classed as grade A, B or C as follows: (i) a grade A recommendation is based on scientific proof established by studies with a high level of evidence such as adequately-powered comparative, randomised trials without major bias, or comparative, randomised meta-analyses or decision analyses based on well-conducted studies.

The Journal of Headache and Pain

Human-verified similar examples from authoritative sources

Similar Expressions

56 human-written examples

They include reversing the burden of proof; establishing a tribunal that would take the financial sting out of libel; preventing large and medium-sized corporations from suing; protecting service providers from the chilling effect of takedown notices; and stemming the tide of libel tourism.

The Guardian - Opinion

An indirect proof establishes its conclusion by showing the impossibility of its opposite.

SEP

If successful, this proof establishes that there is a first mover of all moved movers which is not itself material.

SEP

The proof establishes the equivalence of the cb-norm distance and the Bures distance for completely positive maps.

Journal of Functional Analysis

The Peres proof establishes the KS result in full strength, with great simplicity, and, moreover, in an intuitively accessible way, since it operates in three dimensions; we refer the reader to Peres (1995: 197 99).

SEP

Indeed, Hilbert saw that something stronger is true: not only does a consistency proof establish truth of real formulas provable by ideal methods, but it yields finitary proofs of finitary general propositions if the corresponding free-variable formula is derivable by ideal methods (1928, 474).

SEP

In the absence of proof establishing some other date, the one appearing in the printed or electronic matter must be accepted as correct.

BMC Evolutionary Biology

Expert writing Tips

Best practice

When using "proof established", ensure the context clearly indicates what evidence or arguments led to the establishment of proof. For example, "The research provided data, and the analysis provided in its context finally provided the "proof established" that linked the effects of certain medications and its effects to the disease.

Common error

Avoid using "proof established" when the evidence is suggestive but not definitive. Instead, use phrases like "evidence suggests" or "indications point to".

Linguistic Context

The primary grammatical function of "proof established" is to act as a declarative phrase indicating that a claim, theory, or fact has been successfully validated or demonstrated through presented evidence. Ludwig AI confirms its usability.

Expression frequency: Rare

Frequent in

Science

50%

News & Media

25%

Encyclopedias

25%

Less common in

Formal & Business

0%

Wiki

0%

Social Media

0%

Ludwig's WRAP-UP

In summary, the phrase "proof established" is used to indicate that a claim has been successfully validated. Ludwig AI shows that while grammatically correct, its usage is relatively rare, primarily appearing in scientific, news, and encyclopedic contexts. When writing, it's crucial to use this phrase accurately, ensuring the context warrants such a strong declaration of validation. Consider alternatives like "evidence confirmed" or "validation achieved" if the evidence doesn't fully establish proof. When using the phrase "proof established", make sure the context is appropriate to give your readers the best content.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

evidence confirmed

Focuses on the confirmation of evidence rather than the establishment of proof.

claim validated

Specifically refers to the validation of a claim.

validation achieved

Emphasizes the successful validation of a claim or hypothesis.

demonstrated validity

Highlights the act of showing something to be valid.

assertion confirmed

Highlights the confirmation of an assertion.

findings corroborated

Emphasizes the corroboration of research findings.

authenticity verified

Specific to confirming the authenticity of something.

truth substantiated

Focuses on supporting the truth of a statement or claim.

determination affirmed

Suggests a firm decision or conclusion has been confirmed.

legitimacy ascertained

Focuses on determining the legitimacy of something.

FAQs

How can I use "proof established" in a sentence?

You can use "proof established" to indicate that evidence or arguments have successfully validated a claim or conclusion. For example, "The rigorous study provided the "proof established" that the new treatment was effective."

What are some alternatives to "proof established"?

Some alternatives include "evidence confirmed", "validation achieved", or "claim validated", depending on the specific context.

In what contexts is "proof established" commonly used?

"Proof established" is often used in academic, scientific, and legal contexts to describe a situation where a claim has been successfully proven through evidence.

What is the difference between "proof established" and "evidence presented"?

"Evidence presented" simply means that evidence has been shown, while "proof established" indicates that the evidence has successfully proven a claim. "Proof established" implies a stronger level of validation.