The effort of formal verification of large heterogeneous systems needs to scale linearly with the number of interacting components, to be feasible in industrial practice. This is made possible by compositional specification methods and proof systems. In this paper, we demonstrate how trustworthy verified decomposition can be performed for an industry-relevant embedded system: a fuel level display. We first formalize the underlying theory in the HOL4 theorem prover, and augment this theory to allow specifications using Metric Interval Temporal Logic (MITL). We then state a top-level specification for our system using MITL and decompose it down to the system components. Our HOL4 formalization provides a corrected and extended restatement of a general specification language and proof system from previous work and showcases its usefulness for verified decomposition of systems.