Prove2Me

Constructing a complete bank of retained block-source transforms

Proved
ThreeSum.LightBlockSourceBatch.Procs.meets

by wurtle · Oct 14, 2026 · Mathlib 0df444a (Lean v4.33.1)

3sumalgorithmsfine-grained-complexitythree-sum-1962word-ram

Write S,Ω,ΔS,\Omega,\Delta for machine space, word magnitude, and depth limits. Let q0,…,qN−1q_0,\ldots,q_{N-1} be global outputs with JJ blocks, and let h,J,p,ch,J,p,c be natural with c≤W=512hJc\le W=512hJ. Two arrays enumerate finite left and right inputs bijectively and preserve their values. Suppose exact residue histograms, all NN occurrence rows, and local cover data are stored before bank base aa.

Assume the specified batch-step procedures, the retained-host scratch and word bounds for the packed bank layout, S≤ΩS\le\Omega, and d+W+11≤Δd+W+11\le\Delta. For every i<Ni<N, the procedure retains both complete partial source-zeta families for qiq_i through cutoff cc, and their header pointers:

ν(a+2i)=Li,ν(a+2i+1)=Ri.\nu(a+2i)=L_i,\qquad \nu(a+2i+1)=R_i.

It preserves every cell below aa and runs within

N(Tstep(h,J,c)+200)+20.N\bigl(T_{\rm step}(h,J,c)+200\bigr)+20.

Here Li,RiL_i,R_i are the prescribed family addresses and TstepT_{\rm step} is the single-bank-step budget.

This assembles independently addressable transform families for a list of selected occurrences.

Preamble
/-
Copyright (c) 2026 Anthropic, PBC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
SPDX-License-Identifier: Apache-2.0
-/

import Aesop
import Definitions.Def_APSPSource_RemainingDefinitions
import Definitions.Def_APSPSource_ThreeSumApsp_Lang_Logic
import Definitions.Def_APSPSource_ThreeSumApsp_Lang_Regions
import Definitions.Def_APSPSource_ThreeSumApsp_Lang_Syntax
import Definitions.Def_ThreeSum1962Source_Bundle01
import Definitions.Def_ThreeSum1962Source_Bundle02
import Definitions.Def_ThreeSum1962Source_Bundle04
import Definitions.Def_ThreeSum1962Source_Bundle06
import Definitions.Def_ThreeSum1962Source_Bundle07
import Definitions.Def_ThreeSum1962Source_Bundle09
import Definitions.Def_ThreeSum1962Source_Bundle10
import Definitions.Def_ThreeSum1962Source_Bundle11
import Definitions.Def_ThreeSum1962Source_Bundle12
import Definitions.Def_ThreeSum1962Source_Bundle13
import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algebra.BigOperators.Group.Finset.Powerset
import Mathlib.Algebra.BigOperators.Group.Finset.Sigma
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Group.Equiv.Basic
import Mathlib.Algebra.Group.Int.Defs
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.Order.BigOperators.Group.List
import Mathlib.Algebra.Order.BigOperators.Group.Multiset
import Mathlib.Algebra.Order.Chebyshev
import Mathlib.Algebra.Order.Field.Basic
import Mathlib.Algebra.Order.Floor.Div
import Mathlib.Algebra.Order.Group.Abs
import Mathlib.Algebra.Order.Group.Int
import Mathlib.Algebra.Order.Group.Nat
import Mathlib.Algebra.Order.Group.Unbundled.Abs
import Mathlib.Algebra.Order.Ring.Abs
import Mathlib.Algebra.Order.Ring.Int
import Mathlib.Algebra.Order.Ring.Nat
import Mathlib.Algebra.Order.Ring.Pow
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.Coeff
import Mathlib.Algebra.Ring.Nat
import Mathlib.Analysis.Complex.ExponentialBounds
import Mathlib.Analysis.Convex.Deriv
import Mathlib.Analysis.SpecialFunctions.BinaryEntropy
import Mathlib.Analysis.SpecialFunctions.Log.Base
import Mathlib.Analysis.SpecialFunctions.Pow.Asymptotics
import Mathlib.Analysis.SpecialFunctions.Pow.NthRootLemmas
import Mathlib.Analysis.SpecificLimits.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Combinatorics.Colex
import Mathlib.Data.Bool.Basic
import Mathlib.Data.Fin.Embedding
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Max
import Mathlib.Data.Finset.Powerset
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Finset.Range
import Mathlib.Data.Finset.Sigma
import Mathlib.Data.Finset.Sort
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Fintype.Card
import Mathlib.Data.Fintype.EquivFin
import Mathlib.Data.Fintype.Fin
import Mathlib.Data.Fintype.Pi
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.Int.Cast.Lemmas
import Mathlib.Data.Int.ModEq
import Mathlib.Data.Int.Notation
import Mathlib.Data.Int.SuccPred
import Mathlib.Data.List.Basic
import Mathlib.Data.List.GetD
import Mathlib.Data.List.MinMax
import Mathlib.Data.List.Nodup
import Mathlib.Data.List.OfFn
import Mathlib.Data.List.Pi
import Mathlib.Data.List.Range
import Mathlib.Data.List.Sublists
import Mathlib.Data.Nat.Cast.Order.Ring
import Mathlib.Data.Nat.Choose.Basic
import Mathlib.Data.Nat.Choose.Bounds
import Mathlib.Data.Nat.Choose.Central
import Mathlib.Data.Nat.Choose.Sum
import Mathlib.Data.Nat.Count
import Mathlib.Data.Nat.Log
import Mathlib.Data.Nat.Notation
import Mathlib.Data.Nat.Size
import Mathlib.Data.Nat.Sqrt
import Mathlib.Data.Nat.SuccPred
import Mathlib.Data.Real.Basic
import Mathlib.Data.ZMod.Basic
import Mathlib.GroupTheory.Index
import Mathlib.LinearAlgebra.Dual.Lemmas
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.LinearAlgebra.Matrix.Dual
import Mathlib.LinearAlgebra.Matrix.ToLin
import Mathlib.Logic.Equiv.Fin.Basic
import Mathlib.Logic.Function.Basic
import Mathlib.NumberTheory.Bertrand
import Mathlib.NumberTheory.Chebyshev
import Mathlib.Order.ConditionallyCompleteLattice.Basic
import Mathlib.Order.Monotone.Basic
import Mathlib.RingTheory.Coprime.Lemmas
import Mathlib.Tactic
import Mathlib.Tactic.Abel
import Mathlib.Tactic.ByContra
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Push
import Mathlib.Tactic.Ring
import Mathlib.Tactic.SplitIfs
import Mathlib.Tactic.Tauto
import Theorems.Thm_Light_Ends_for
import Theorems.Thm_ThreeSum_BlockSourceCoverInput_Input_of_kept
import Theorems.Thm_ThreeSum_LightBlockSourceBatchStep_Procs_meets
import Theorems.Thm_ThreeSum_SubsetAddress_layerRank_lt


set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option Elab.async false
namespace Light
end Light
namespace ThreeSum.BlockCoefficientRows
end ThreeSum.BlockCoefficientRows
namespace ThreeSum.BlockEncoding
end ThreeSum.BlockEncoding
namespace ThreeSum.BlockIndex
end ThreeSum.BlockIndex
namespace ThreeSum.BlockSourceEncoding
end ThreeSum.BlockSourceEncoding
namespace ThreeSum.GlobalEncoding
end ThreeSum.GlobalEncoding
namespace ThreeSum.LightBlockSourceBatchLayout
end ThreeSum.LightBlockSourceBatchLayout
namespace ThreeSum.LightSourceResidues
end ThreeSum.LightSourceResidues
namespace ThreeSum.LightZetaStages
end ThreeSum.LightZetaStages
namespace ThreeSum.LocalCoverBounds
end ThreeSum.LocalCoverBounds
namespace ThreeSum.SubsetAddress
end ThreeSum.SubsetAddress

universe u_1 u_2
Formal statement
theorem ThreeSum.LightBlockSourceBatch.Procs.meets : ∀ {lim : Light.Limits} {P : Light.Program} {d : Nat} {β : Type u_1} {γ : Type u_2} [inst : Fintype.{u_1} β]
  [inst_1 : Fintype.{u_2} γ] [inst_2 : DecidableEq.{u_1 + 1} β] [inst_3 : DecidableEq.{u_2 + 1} γ] {pMain : Nat}
  (C : ThreeSum.LightBlockSourceBatch.Procs P pMain) {μ : Nat → Int}
  {h J cut p NL NR occ maps candidates histL histR sourceHistL sourceHistR base count : Nat} {shift : Int}
  (B : Finset.{u_1} β) (b : β → Int) (A : Finset.{u_2} γ) (a : γ → Int)
  (q : Nat → ThreeSum.GlobalEncoding.GlobalOutput h J) (vL vR : Nat → Int) (eL : Equiv.{1, u_1 + 1} (Fin NL) ↥B)
  (eR : Equiv.{1, u_2 + 1} (Fin NR) ↥A)
  (hw : @LE.le.{0} Int Int.instLEInt (@Nat.cast.{0} Int instNatCastInt lim.space) lim.word)
  (hd :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) d
          (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
            (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
              (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h)))
        (@OfNat.ofNat.{0} Nat (nat_lit 11) (instOfNatNat (nat_lit 11))))
      lim.depth)
  (hcut :
    @LE.le.{0} Nat instLENat cut
      (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
          (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h)))
  (hocc :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) occ
        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) count J))
      base)
  (hmaps :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) maps
        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
          (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
            (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))
            (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
              (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h))
          (ThreeSum.GlobalEncoding.scheduleSize h)))
      base)
  (hcandidates :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) candidates
        (ThreeSum.GlobalEncoding.scheduleSize h))
      base)
  (hleft :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) histL
        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (ThreeSum.LightLocalCoverSchedule.rows h)
          (ThreeSum.LocalCoverBounds.localPrime h)))
      base)
  (hright :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) histR
        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) (ThreeSum.LightLocalCoverSchedule.rows h)
          (ThreeSum.LocalCoverBounds.localPrime h)))
      base)
  (hsourceHistL :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) sourceHistL
        (ThreeSum.BlockSourceEncoding.modulus h J))
      base)
  (hsourceHistR :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) sourceHistR
        (ThreeSum.BlockSourceEncoding.modulus h J))
      base)
  (hspace :
    @LE.le.{0} Nat instLENat
      (ThreeSum.LightBlockSourceRetainedHost.space
        (ThreeSum.LightBlockSourceBatchLayout.work base count
          (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
            (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
              (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h))
          cut)
        h J)
      lim.space)
  (hword :
    @LE.le.{0} Int Int.instLEInt
      (@Nat.cast.{0} Int instNatCastInt (ThreeSum.LightBlockSourceRetainedHost.word NL NR h J)) lim.word)
  (hinputL :
    ∀ (j : Fin NL),
      @Eq.{1} Int (vL (@Fin.val NL j))
        (b
          (@Subtype.val.{u_1 + 1} β
            (fun (x : β) =>
              @Membership.mem.{u_1, u_1} β (Finset.{u_1} β)
                (@SetLike.instMembership.{u_1, u_1} (Finset.{u_1} β) β (@Finset.instSetLike.{u_1} β)) B x)
            (@DFunLike.coe.{u_1 + 1, 1, u_1 + 1} (Equiv.{1, u_1 + 1} (Fin NL) ↥B) (Fin NL) (fun (x : Fin NL) => ↥B)
              (@EquivLike.toFunLike.{u_1 + 1, 1, u_1 + 1} (Equiv.{1, u_1 + 1} (Fin NL) ↥B) (Fin NL) (↥B)
                (@Equiv.instEquivLike.{1, u_1 + 1} (Fin NL) ↥B))
              eL j))))
  (hinputR :
    ∀ (j : Fin NR),
      @Eq.{1} Int (vR (@Fin.val NR j))
        (a
          (@Subtype.val.{u_2 + 1} γ
            (fun (x : γ) =>
              @Membership.mem.{u_2, u_2} γ (Finset.{u_2} γ)
                (@SetLike.instMembership.{u_2, u_2} (Finset.{u_2} γ) γ (@Finset.instSetLike.{u_2} γ)) A x)
            (@DFunLike.coe.{u_2 + 1, 1, u_2 + 1} (Equiv.{1, u_2 + 1} (Fin NR) ↥A) (Fin NR) (fun (x : Fin NR) => ↥A)
              (@EquivLike.toFunLike.{u_2 + 1, 1, u_2 + 1} (Equiv.{1, u_2 + 1} (Fin NR) ↥A) (Fin NR) (↥A)
                (@Equiv.instEquivLike.{1, u_2 + 1} (Fin NR) ↥A))
              eR j))))
  (hhistReadL :
    ∀ (r : Nat),
      @LT.lt.{0} Nat instLTNat r (ThreeSum.BlockSourceEncoding.modulus h J) →
        @Eq.{1} Int (μ (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) sourceHistL r))
          (@Nat.cast.{0} Int instNatCastInt
            (ThreeSum.LightBlockSourceRetainedStages.histogram p (ThreeSum.BlockSourceEncoding.modulus h J)
              (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0))) vL NL r)))
  (hhistReadR :
    ∀ (r : Nat),
      @LT.lt.{0} Nat instLTNat r (ThreeSum.BlockSourceEncoding.modulus h J) →
        @Eq.{1} Int (μ (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) sourceHistR r))
          (@Nat.cast.{0} Int instNatCastInt
            (ThreeSum.LightBlockSourceRetainedStages.histogram p (ThreeSum.BlockSourceEncoding.modulus h J) shift vR NR
              r)))
  (hoccRead :
    ∀ (i : Nat),
      @LT.lt.{0} Nat instLTNat i count →
        ∀ (j : Nat),
          @LT.lt.{0} Nat instLTNat j J →
            @Eq.{1} Int
              (μ
                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) occ
                    (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) i J))
                  j))
              (@Nat.cast.{0} Int instNatCastInt
                (@ThreeSum.BlockCoefficientRows.occurrenceIndices h J
                  (@ThreeSum.BlockEncoding.outputOccurrences h J (q i)) j)))
  (hcover : ThreeSum.BlockSourceCoverInput.Input μ h maps candidates histL histR),
  Light.Meets lim P pMain d
    (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt J)
      (@List.cons.{0} Int
        (@HMul.hMul.{0, 0, 0} Int Int Int (@instHMul.{0} Int Int.instMul)
          (@OfNat.ofNat.{0} Int (nat_lit 512) (@instOfNat (nat_lit 512))) (@Nat.cast.{0} Int instNatCastInt h))
        (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt h)
          (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt (ThreeSum.LocalCoverBounds.localPrime h))
            (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt (ThreeSum.LocalCoverBounds.localBucketCap h))
              (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt cut)
                (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt (ThreeSum.BlockSourceEncoding.modulus h J))
                  (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt occ)
                    (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt maps)
                      (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt candidates)
                        (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt histL)
                          (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt histR)
                            (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt sourceHistL)
                              (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt sourceHistR)
                                (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt base)
                                  (@List.cons.{0} Int
                                    (@Nat.cast.{0} Int instNatCastInt
                                      (ThreeSum.SubsetAddress.downsetCap
                                        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
                                          (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                                            (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h))
                                        cut))
                                    (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt count)
                                      (@List.cons.{0} Int
                                        (@Nat.cast.{0} Int instNatCastInt
                                          (ThreeSum.LightBlockSourceBatchLayout.banks base count))
                                        (@List.cons.{0} Int
                                          (@Nat.cast.{0} Int instNatCastInt
                                            (ThreeSum.LightBlockSourceBatchLayout.stride
                                              (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
                                                (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                                                  (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h))
                                              cut))
                                          (@List.cons.{0} Int
                                            (@Nat.cast.{0} Int instNatCastInt
                                              (ThreeSum.LightBlockSourceBatchLayout.maskBase base count
                                                (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
                                                  (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                                                    (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512)))
                                                    h))
                                                cut))
                                            (@List.cons.{0} Int
                                              (@Nat.cast.{0} Int instNatCastInt
                                                (ThreeSum.LightBlockSourceBatchLayout.bitBase base count
                                                  (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
                                                    (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                                                      (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512)))
                                                      h))
                                                  cut))
                                              (@List.cons.{0} Int
                                                (@Nat.cast.{0} Int instNatCastInt
                                                  (ThreeSum.LightBlockSourceBatchLayout.rowOut base count
                                                    (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
                                                      (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                                                        (@OfNat.ofNat.{0} Nat (nat_lit 512)
                                                          (instOfNatNat (nat_lit 512)))
                                                        h))
                                                    cut))
                                                (@List.cons.{0} Int
                                                  (@Nat.cast.{0} Int instNatCastInt
                                                    (ThreeSum.LightBlockSourceBatchLayout.work base count
                                                      (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) J
                                                        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                                                          (@OfNat.ofNat.{0} Nat (nat_lit 512)
                                                            (instOfNatNat (nat_lit 512)))
                                                          h))
                                                      cut))
                                                  (@List.nil.{0} Int))))))))))))))))))))))))
    μ (ThreeSum.LightBlockSourceBatch.time count h J cut) fun (x : Int) (ν : Nat → Int) =>
    And
      (∀ (i : Nat),
        @LT.lt.{0} Nat instLTNat i count →
          @ThreeSum.LightBlockSourceBatch.BankAt.{u_1, u_2} β γ inst inst_1 inst_2 inst_3 h J ν base count cut i
            (@Nat.cast.{0} Int instNatCastInt p) shift B b A a (q i))
      (Light.Kept μ ν base) := by
  sorry
Source
https://github.com/c0ldzy17/three-sum-lean/blob/2b639655e07421b9ac743de9090459bab473a7c0/Submission/ThreeSum/LightBlockSourceBatch.lean#L85-L180

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