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The phrase "coexistence of both" is correct and usable in written English
It can be used when discussing the simultaneous existence of two entities, ideas, or phenomena. Example: "The coexistence of both traditional and modern practices can enrich cultural experiences."
Exact(59)
A robust global economy requires the coexistence of both systems trading with each other.
Analogously, a "paradoxical" coexistence of both strong reflection and absolute transparency is explained.
iPP sample with coexistence of both phases showed an intermediate critical stress of cavitation-induced whitening.
The direct evidence for coexistence of both bottom-up and top-down mechanisms are shown.
The temperature range examined corresponds to the coexistence of, both, the nematic and the isotropic phases.
For some time his religious policy was devised so as to allow the coexistence of both religions.
Mr. McFaul suggested the coexistence of both pro-Western and authoritarian traits in Mr. Putin form a contradictory picture open to misinterpretation.
Except PBUDA homopolymers, all other polymers were observed with a broad baseline and sharp peaks with varied intensity, indicating the coexistence of both crystalline and amorphous microstructures.
Later on, structure H CH4 + iso-C5H12 hydrate was formed resulting in a coexistence of both structures.
It also provides evidence for the coexistence of both DO22 and L12 long range order (LRO) structures in the alloy.
Moreover, coexistence of both competing populations can occur in cases 2 and 6.
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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