Sparse-entry miss cleanup — proof internals

theorem Complexity.RAM.RegisterStore.Machine.entryMissCleanupTM_hoareTime_frame_internal {n : ℕ} (tapes : EntryMatchTapes n) (entry : Entry) (rest queryBits : List Bool) (initialWork matchedWork : Fin n → Tape) (inp₀ out₀ : Tape) (hmatch : ReadableEntryMatch tapes entry rest queryBits initialWork matchedWork) (hinput : TM.Parked inp₀) (houtput : TM.Parked out₀) : (entryMissCleanupTM tapes).HoareTime (fun (inp : Tape) (work : Fin n → Tape) (out : Tape) => inp = inp₀ ∧ work = matchedWork ∧ out = out₀) (fun (inp : Tape) (work : Fin n → Tape) (out : Tape) => inp = inp₀ ∧ EntryScanReady tapes rest queryBits initialWork work ∧ out = out₀) (entryMissCleanupTime tapes entry queryBits initialWork)