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The phrase "are shown to exist" is correct and usable in written English.
It can be used in contexts where evidence or proof is being presented to demonstrate the existence of something.
Example: "In the study, several factors are shown to exist that contribute to the phenomenon observed."
Alternatives: "are demonstrated to exist" or "are proven to exist".
Exact(24)
Anthony Kennedy, the Court's swing vote, has in the past suggested that the right metrics — once they are shown to exist — could be used by judges to assess the fairness of new maps.
Multiple optimal configurations are shown to exist.
These five undetermined LS(2n41)s are shown to exist in this paper.
Extra-synchronous resonant vibrations are shown to exist, but with damping modeled the effect is minimal.
In particular, within this system two distinct types of horseshoe are shown to exist.
Compressibility effects are shown to exist above a Mach number of 0.3.
Similar(36)
Many relationships can be shown to exist between these geometric patterns and algebraic expressions.
After many decades of research, not a single person or place named in it has been shown to exist.
The survival instinct is shown to exist in a weird, numb state that combines defiance and resignation.
'I do not believe a connection exists, nor do I believe one will be shown to exist,' Judge Baltasar Garzón, Spain's leading anti-terrorist judge declared recently.
Good engineering agreement is shown to exist.
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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