This paper introduces the first general and rigorous formalization of the classic busy-window principle for uniprocessors. The essence of the principle is identified as a minimal set of generic, high-level hypotheses that allow for a unified and general abstract response-time analysis, which is independent of specific scheduling policies, workload models, and preemption policy details. From this abstract core, the paper shows how to obtain concrete analysis instantiations for specific

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... or schedulers via a sequence of refinement steps, and provides formally verified response-time bounds for eight common schedulers and workloads, including the widely used fixed-priority (FP) and earliest-deadline first (EDF) scheduling policies in the context of fully, limited-, and non-preemptive sporadic tasks. All definitions and proofs in this paper have been mechanized and verified with the Coq proof assistant, and in fact form the common core and foundation for verified response-time analyses in the Prosa open-source framework for formally proven schedulability analyses.