Used and loved by millions
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com
they established that
Grammar usage guide and real-world examplesUSAGE SUMMARY
The phrase "they established that" is correct and usable in written English.
It can be used when referring to a conclusion or finding that has been determined or proven by a group or individuals. Example: "In their research, they established that regular exercise significantly improves mental health."
✓ Grammatically correct
Science
News & Media
Academia
Alternative expressions(17)
they determined that
they found that
they demonstrated that
they proved that
they showed that
they confirmed that
they ascertained that
they concluded that
it was established that
they clarified that
they discovered that
they asserted that
they achieved that
they acknowledged that
they maintained that
they stated that
they estimated that
Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Human-verified examples from authoritative sources
Exact Expressions
60 human-written examples
They established that thisclass of nonlinear mappings is general than the class of demicontractive mappings.Olaleru and Mogbademu [10, 11] used a three-step iterative scheme to approximate the fixedpoints of strongly successively pseudocontractive maps.
But they established that Black Lives Matter.
News & Media
They established that Regeni died between 10pm on 1 February and 10pm on 2 February.
News & Media
This Case We must review the instances in which appellants claim that they established that legal votes were rejected or illegal voters were included in the certifications.
News & Media
They established that he was Mark Kennedy, an undercover policeman who had been sent to spy on her circle of activist friends.
News & Media
Together, they established that the Pentagon's claim that closing Groton would save $1.6 billion over 20 years was overstated by $400 million and perhaps more.
News & Media
They established that he was in California at the time of the murder but could not place him in Los Angeles.
News & Media
"Despite that bond, they only first met at a conference in March 2018 where they established that Tim's father's father's father is Geoff's father's father.
News & Media
These results are in agreement with previous studies using conventional electrochemical techniques with gold NPs and single crystal electrodes, since they established that higher ratio of (1 0 0) domains provide higher catalytic activity for ORR.
Science
Assuming that they established that funded activities abroad threaten certain species, they failed to show that one or more of their members would thereby be directly affected apart from the members' special interest in the subject.
Academia
They established that all sticklebacks seem to have the same genes, but that rapid change in regulatory DNA allowed them to alter expression of their genes in order to adapt quickly to changing environments.
Expert writing Tips
Best practice
When using "they established that", ensure that the 'they' refers to a clearly defined group or entity, and the establishment is based on evidence or research.
Common error
Avoid using "they established that" without specifying who 'they' are or providing context for how the establishment was made. This can lead to confusion and weaken your argument.
Source & Trust
85%
Authority and reliability
4.5/5
Expert rating
Real-world application tested
Linguistic Context
The phrase "they established that" functions as a reporting verb phrase, used to introduce a statement, finding, or conclusion that a group or entity has proven or determined. Ludwig AI confirms its grammatical correctness and widespread use.
Frequent in
Science
35%
News & Media
30%
Academia
20%
Less common in
Wiki
10%
Formal & Business
5%
Reference
0%
Ludwig's WRAP-UP
In summary, the phrase "they established that" is a grammatically sound and frequently used expression to report a proven or determined fact. According to Ludwig AI, it's suitable for various contexts, including scientific research, news reporting, and academic writing. This phrase is particularly common in the sciences, news and media, and academia. When using this phrase, ensure that the reference to 'they' is explicit to avoid ambiguity. For alternative phrasing, you could consider using "they demonstrated that", "they proved that", or "they found that" for similar meanings.
More alternative expressions(6)
Phrases that express similar concepts, ordered by semantic similarity:
they demonstrated that
Replaces "established" with "demonstrated", emphasizing the act of showing or proving something.
they proved that
Uses "proved" instead of "established", highlighting the conclusive nature of the finding.
they confirmed that
Substitutes "established" with "confirmed", suggesting that the findings reinforce existing knowledge.
they determined that
Replaces "established" with "determined", focusing on the process of finding something out through investigation.
they ascertained that
Uses "ascertained" instead of "established", implying careful and thorough investigation.
they found that
A simpler alternative using "found" instead of "established", suitable for less formal contexts.
they showed that
Replaces "established" with "showed", highlighting the act of making something clear or visible.
they concluded that
Uses "concluded" instead of "established", focusing on the final judgment or decision reached.
it was established that
Changes the sentence structure to passive voice but maintains the core meaning.
they clarified that
Replaces "established" with "clarified", emphasizing the act of making something easier to understand.
FAQs
How can I use "they established that" in a sentence?
Use "they established that" to introduce a finding or conclusion reached by a group or individuals based on evidence. For example, "The researchers established that exercise improves cognitive function".
What can I say instead of "they established that"?
You can use alternatives like "they demonstrated that", "they proved that", or "they found that" depending on the context.
Is "they established that" formal or informal?
"They established that" is generally considered neutral to formal, suitable for academic, professional, and journalistic contexts. Simpler alternatives like "they showed that" can be used in informal settings.
What's the difference between "they established that" and "they determined that"?
While similar, "they established that" implies a more solid or definitive finding, while "they determined that" suggests a conclusion reached after investigation or consideration. The choice depends on the nuance you want to convey.
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Table of contents
Usage summary
Human-verified examples
Expert writing tips
Linguistic context
Ludwig's wrap-up
Alternative expressions
FAQs
Source & Trust
85%
Authority and reliability
4.5/5
Expert rating
Real-world application tested