An institution typically comprises constitutive rules, which give shape and meaning to social interactions and regulative rules, which prescribe agent behaviour in the society. Regulative rules guide social interaction, in particular when they are coupled with reward and punishment regulations that are enforced for (non-)compliance. Institution examples include legislation and contracts. Formal institutional reasoning frameworks automate ascribing social meaning to agent interaction and determining whether those actions have social meanings that comprise (non-)compliant behaviour. Yet, institutions do not just govern societies. Rather, in what is called multi-level governance, institutional designs at lower governance levels (e.g., national legislation at the national level) are governed by higher level institutions (e.g., directives, human rights charters and supranational agreements). When an institution design is found to be non-compliant, punishments can be issued by annulling the legislation or imposing fines on the responsible designers (i.e., government). In order to enforce multi-level governance, higher governance levels (e.g., courts applying human rights) must check lower level institution designs (e.g., national legislation) for compliance; in order to avoid punishment, lower governance levels (e.g., national governments) must check their institution designs are compliant with higher-level institutions before enactment. However, checking non-compliance of institution designs in multi-level governance is non-trivial. In particular, because institutions in multi-level governance operate at different levels of abstraction. Lower level institutions govern with concrete regulations whilst higher level institutions typically comprise increasingly vague and abstract regulations. To address this issue, in this paper we propose a formal framework with a novel semantics that defines compliance between concrete lower level institutions and abstract higher level institutions. The formal framework is complemented by a sound and complete computational framework that automates compliance checking, which we apply to a real-world case study.