CKD "associated with" DM

Does CKD "associated with" DM mean the same as "caused by" or "due to," and thus I would code 250.4x and 585.x?

Here are the provider's diagnoses (and codes she has chosen, which I need to fine tune):

Benign hypertension, 401.1

CKD stage 2 associated with type 2 DM, 250.40

Type 2 DM well controlled, 250.00

I've read the ICD-9 guidelines and searched similar posts in this forum. I just want to make sure "associated with" means I thus assign 250.40 (diabetes with renal manifestation) plus 585.2 (CKD as the manifestation).

I'm thinking the final coding would be:

250.40, 583.81, 403.90, 585.2

....am I correct?

Thanks in advance!

CKD "associated with" DM