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The phrase 'demonstrated a high level' is correct and usable in written English.
You can use this phrase when you want to indicate that someone has exhibited a high level of accomplishment in a particular area. For example, "Sarah demonstrated a high level of proficiency in her math class and achieved top marks in her final exams."
Exact(60)
He has neutralised controversies and in giving up his political status he has demonstrated a high level of political skill.
"During its long tenure as the company's outside auditors, Arthur Andersen has provided many years of quality service and has demonstrated a high level of professionalism," FedEx said.
This evaluation demonstrated a high level of technical proficiency.
His assignment was awarded a B grade as it fulfilled the task requirements and demonstrated a high level of creativity.
Cytotoxicity evaluation assay demonstrated a high level of safety profile of the synthesized sulfonium salts against normal cell line.
Analysis of the tissue expression patterns of xPKD1 demonstrated a high level of expression in the kidney.
The enthusiastic agent had a smiling face, frequently nodded its head, demonstrated a high level of animated gestures, and spoke in an enthusiastic voice.
On the other side hot-box measures demonstrated a high level of thermal resistance of the system reaching U-values around 0,20 W m-2 K-1.
The encapsulated cells demonstrated a high level of cell survival (90% for co-culture condition, day 7) and spreading throughout the hydrogel matrix in both culture conditions.
Currently, we are carrying out studies using the SIR method, which has demonstrated a high level of precision in clinical practice and provides us with a meaningful LIC value in μmol Fe/g to include in clinical reports.
We have therefore demonstrated a high level theoretical link between brain oscillations [25], differential excitability in brain networks (e.g. [26]) and abnormal rhythm generation, which are crucial concepts for epilepsy.
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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