AUTHID changes namespace only for tables, not for procedure calls?

Hi,

just one question to ensure, that I don't make a mistake in assumptions. I'm familiar with the concept of defining a procedure with the rights of AUTHID CURRENT_USER. With synonyms and grants setup properly, I could ensure, that one and the same procedure could select from tables with the same name but from different schemas. Fine. But this won't work in the same way for procedures itself, isn't it? Scenario:

Schema 1: has table dummy, and three procedures. P1 calling P2, P2 selecting dummy and calling P3 and P3 do nothing specific.

Schema 2: has the same: table dummy, and three procedures. P1 calling P2, P2 selecting dummy and calling P3 and P3 do nothing specific.