The phrase "with the conditions set out in" is correct and usable in written English. You can use the phrase when you want to refer to conditions previously stated in a statement or agreement. For example: "The terms of the agreement will be enforced with the conditions set out in the contract.".
On the other hand, the recipient, be it the formulator or the end user, has to check whether he complies with the conditions set out in the exposure scenario received with the substance.
Sample distribution is governed by the conditions set out in the EBB charter and standardised material transfer agreements (MTAs).
However, to try and insert this into a contract after it has been signed off, you will need to read the conditions set out in the contract's termination clause, which usually determines how to deal with breaches.
Promontory maintains that it complied with the conditions set out by the O.C.C.
Domestic regulators must ensure that their alcohol policies comply with conditions set out in trade treaties, potentially reducing their capacity to implement appropriate policies.
Payments to businesses in which academy's trustees have a beneficial interest are allowed if the trust has fully complied with its procedures and conditions set out in the trust's articles of association.
This could include looking at the terms and conditions set out in an enterprise agreement.
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MA of Applied Linguistic, Maquarie University, Australia