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The phrase "a basic condition for the existence" is correct and usable in written English.
It can be used when discussing fundamental requirements or prerequisites for something to exist or occur.
Example: "Access to clean water is a basic condition for the existence of a healthy community."
Alternatives: "a fundamental requirement for existence" or "an essential prerequisite for being".
Exact(1)
A basic condition for the existence of peace, for achieving it and for preserving it, is security".
Similar(59)
"This is a basic condition for any negotiations".
She can't even articulate basic conditions for the use of nuclear weapons.
Recent work has shown that contractivity is a necessary condition for the existence of an attractor for some basic types of IFSs, such as affine, projective and Möbius IFSs.
Now we provide a sufficient condition for the existence.
Hence, a necessary condition for the existence of is that.
Using Lyapunov functional approach, a sufficient condition for the existence of admissible controller is presented.
A necessary condition for the existence of a (v,k,λ -PMD is λv(v−1)≡0 (mod k).
A necessary condition for the existence of ASS is that this equation has three positive solutions.
Indeed, in [34] it is demonstrated that the existence of at least one positive-feedback loop is is a necessary condition for the existence of multiple steady states.
We derive a condition for the existence of a cost-optimal homeostatic state.
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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