Indirect sparse-store load instructions -- proof internals

theorem Complexity.RAM.RegisterStore.Machine.scanner_updateQuery_of_indirect_internal {n : ℕ} (tapes : BinaryInstructionTapes n) (store : Store) (destination : ℕ) (work : Fin n → Tape) (hscanner : EntryScanReady tapes.indirectLoadLookup.scan.entry (List.flatMap Entry.encode store) [] work work) : EntryScanReady tapes.update.entry (List.flatMap Entry.encode store) destination.bits (Function.update work tapes.update.entry.query ((Tape.init (List.map Γ.ofBool destination.bits)).move Dir3.right)) (Function.update work tapes.update.entry.query ((Tape.init (List.map Γ.ofBool destination.bits)).move Dir3.right))

theorem Complexity.RAM.RegisterStore.Machine.indirectLoadInstructionTM_hoareTime_frame_internal {n : ℕ} (tapes : BinaryInstructionTapes n) (store : Store) (destination addressRegister : ℕ) (emittedBits : List Bool) (initialWork : Fin n → Tape) (inp₀ out₀ : Tape) (hcanonical : Canonical store) (hinitial : EntryLookupStaticReady tapes.lhsLookup store initialWork) (hreplacement : (initialWork tapes.update.replacement).HasBinaryNat 0) (hinput : TM.Parked inp₀) (houtput : out₀.HasBinaryPrefix emittedBits) : (indirectLoadInstructionTM tapes destination addressRegister).HoareTime (fun (inp : Tape) (work : Fin n → Tape) (out : Tape) => inp = inp₀ ∧ work = initialWork ∧ out = out₀) (fun (inp : Tape) (work : Fin n → Tape) (out : Tape) => inp = inp₀ ∧ IndirectLoadInstructionResult tapes store destination addressRegister initialWork work ∧ out.HasBinaryPrefix (emittedBits ++ List.flatMap Entry.encode (write store destination (read store (read store addressRegister))))) (indirectLoadInstructionTime tapes store destination addressRegister)

Exact semantic and time contract for one indirect sparse-register load.