The test for "completely contained" is stricter than the test for added subject-matter since it is a test whether the subsequently filed missing or correct part or element was part(s) and/or element(s) was (were) identical to the corresponding extract in the priority document, or a translation thereof.
Although the RO is responsible for the decision on whether the missing or correct part(s) and/or element(s) was (were) completely contained in the priority document, the examiner must check (as far as the documents needed are available) that the decision taken was correct.
If the EPO is the RO, the examiner is only required to check for additional technical content. This entails ensuring that the missing text has been inserted into the application in such a position that it has exactly the same meaning as it had in the priority document.
If the EPO is not the RO, the identity of drawings and the word-for-word identity of (parts of) the description/claim(s) must also be checked by the examiner (unless the documents needed are not available at this stage).