Here's a quote from Douglas Stinson:
“[i]f a cryptosystem can be ‘broken’ in some specific way, then it would be possible to efficiently solve some well-studied problem that is thought to be difficult. For example, it may be possible to prove a statement of the type “a given cryptosystem is secure if a given integer n cannot be factored.” [...] [B]ut it must be understood that this approach only provides a proof of security relative to some other problem, not an absolute proof of security. This is a similar situation to proving that a problem is NP-complete [...].”
Source: Stinson, D. R. (2006). Cryptography, Theory and Practice. Chapman and Hall, CRC, 3rd edition. Chapter 2, section 2.1, page 45.
Say there is a proof that a cryptosystem $X$ satisfies Stinson's definition. An attacker builds a method to break $X$ by side-channel attacks. Does that offer any trouble to the definition or to my proof? Or would you say side-channel attacks have nothing to do with provable security?