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The phrase "all this under" is correct and usable in written English.
It can be used when referring to something that is being discussed or explained within a specific context or condition.
Example: "All this under the assumption that everyone agrees with the plan."
Alternatives: "all this within" or "all this in the context of".
Exact(32)
Karadžić has asked for 17 hours to outline his explanation for all this, under his alleged command.
All this under microwave irradiation.
All this under the interrogator's sleek appearance and courtly manner.
Also important was having all this under one roof.
All this under the banner of protecting U.S. national security.
"I wish they had kept all this under wraps," he said.
Similar(28)
Best of all, this under-appreciated species drives profit back to traditional New England fishing communities.
Unless, of course, all this colour, all this under-and-over stitch-work, is a lulling tease of make-believe.
All this in under a fortnight.
Yes, all this for under $800.
All this for just a hair under $300.
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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