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The phrase "environment of mutual trust" is correct and can be used in written English.
It is typically used to describe a situation or setting where there is a relationship of trust and respect between all parties involved. Example: "In order for a successful team project, it is important to create an environment of mutual trust, where each team member feels valued and supported."
Exact(8)
An environment of mutual trust and confidence is essential, with all parties pursuing an agreed strategy.
The remarkable improvement in the Dutch economy post 1982 has been linked to that nation's culture of a search for consensus in combination with a far-reaching institutional consultation structure that has produced an environment of mutual trust and cooperation.
The level of accountability, transparency and togetherness has created an environment of mutual trust, respect and caring.
Rather than succumb to the narrative of perpetual conflict, I chose the path of engagement because the struggle for peace and justice requires mainstream American Jewish and Muslim communities making common cause, which is only possible in an environment of mutual trust.
In short, egos have no place in this environment of mutual trust and respect.
By creating an environment of mutual trust between the communities and other actors involved (often development partners and/or funding agencies) success was feasible, despite the wider instability in the region.
Similar(52)
Another important result of the agreements was the emergence of mutual trust between the two nations, and a healthier international environment overall.
On the other hand, creating an environment where you can be open about these things will promote a feeling of mutual trust and honest communication.
The changing competitive environment prompted H to use his language advantage to form a more stable relationship of mutual trust with the police, landlords, and contracted factories.
There is a deep-seated attitude of mutual trust.
Eventually we reached a degree of mutual trust.
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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