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The phrase "action has been demonstrated" is correct and usable in written English.
It can be used in contexts where you want to indicate that a specific action or behavior has been shown or proven to occur.
Example: "In the experiment, the effectiveness of the new drug was clear; the action has been demonstrated through various trials."
Alternatives: "the action has been shown" or "the action has been proven."
Exact(15)
Brillouin laser action has been demonstrated in discrete resonators based on silica8,10,57 and CaF2 (ref. 9).
The advantage of shortening the response time of the shutdown action has been demonstrated in term of the improved safety margin.
Combination therapy using medications of different classes together, each with a different mechanism of action, has been demonstrated to be a more efficacious approach to acne treatment than monotherapy.
The pleiotropic nature of statin action has been demonstrated on various macro and microvascular endothelial cells although less attention has been paid to the highly specialised retinal microvascular endothelium.
This action has been demonstrated in proteins [15], while the protective effect exerted by threalose on lipids is apparently due to the inhibition of phase transition temperature of membranes [16].
Its prooxidant action has been demonstrated in in vivo and in vitro conditions [ 2– 7].
Similar(45)
Its diverse mechanisms of action have been demonstrated to be tumor-selective and lead to partial and complete remission.
A wide range of anticancer drugs with widely differing modes of action have been demonstrated to induce apoptosis in vitro, suggesting this as a significant common final pathway through which they exert their clinical effect.
The roles of cardiac glucose uptake and insulin action have been demonstrated in mice with cardiac-specific ablation of GLUT4, which developed cardiac hypertrophy resembling that of the diabetic heart [ 37].
A large number of anti-cancer agents with widely differing modes of action have been demonstrated to induce apoptosis in vitro, suggesting this as a significant final common pathway for exerting their clinical effects.
The original observation of Snow sufficed to state that something in the water supplied by one company potentially caused cholera and to take appropriate action (closing the pump), and there was no need to wait until a mechanism of action had been demonstrated (thereby probably sacrificing the lives of thousands of people).
More suggestions(16)
activities has been demonstrated
activated has been demonstrated
processes has been demonstrated
approaches has been demonstrated
interventions has been demonstrated
measures has been demonstrated
action has been filed
action has been made
action has been implemented
action has been tried
action has been documented
action has been done
action has been stepped
action has been suspended
action has been found
action has been prodded
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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