proven
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proven
Shown by evidence or scientific methods to exist or to be true.
Es ist eine nachgewiesene Tatsache, dass regelmäßige Bewegung der Gesundheit förderlich ist.
It is a proven fact that regular exercise is beneficial to health.
'Nachgewiesen' (proven) is the past participle of the verb 'nachweisen' (to prove/demonstrate). It is very often used as an adjective and means that something is supported by evidence.
Die Wirksamkeit des Medikaments wurde in Studien nachgewiesen.
The effectiveness of the medication was proven in studies.
This word is often used in scientific or formal contexts. Common combinations are 'eine nachgewiesene Wirkung' (a proven effect), 'ein nachgewiesener Effekt' (a proven effect), or 'wissenschaftlich nachgewiesen' (scientifically proven).
Das Produkt hat eine wissenschaftlich nachgewiesene Wirkung gegen Hautalterung.
The product has a scientifically proven effect against skin aging.
A very common structure is the phrase 'Es ist nachgewiesen, dass ...' (It has been proven that ...). This introduces a fact that is supported by evidence.
Es ist nachgewiesen, dass Schlaf für die Regeneration des Körpers wichtig ist.
It has been proven that sleep is important for the body's regeneration.
occupied / topped / proven
'belegt' and 'nachgewiesen' can both mean that something is confirmed by facts, sources, or investigations. In this sense, they are very similar. 'nachgewiesen' often sounds a bit more precise and fits especially well in science, medicine, or official investigations. 'belegt' fits well when you support a statement with sources, figures, or examples. They can be confused because 'belegt' also has completely different meanings, for example 'occupied' or 'topped with cheese'. With facts, however, the meaning is: there is evidence for it.
Bei der Untersuchung wurde der Fehler im System eindeutig nachgewiesen.
During the investigation, the error in the system was clearly proven.
Die Aussage ist durch mehrere alte Briefe gut belegt.
The statement is well supported by several old letters.