Prove2Me

Checking terminal witnesses from a stored reporting frontier

Proved
ThreeSum.LightReportingTerminalStored.program_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 II be a finite set of raw items, ww a wanted label, and k≤Jk\le J. Suppose the retained frontier at level kk has its exact count, query mask, and left/right prefix-mask arrays stored at root aa, with the correct capacity in a+3a+3. Independently, let stored integer arrays L,RL,R, integer a0,δa_0,\delta, and natural pp have exact residue buckets and the required occurrence and cover data for ww's output.

Assume the terminal layout, source-value and sum word bounds, terminal space and word bounds, S≤ΩS\le\Omega, and depth

d+∣Fk∣+(2h(J−k)h(J−k))+512hJ+11≤Δ.d+|\mathcal F_k|+\binom{2h(J-k)}{h(J-k)}+512hJ+11\le\Delta.

The routine returns a Boolean satisfying

r=1  ⟺  ∃P∈Fk, H(P),r=1\iff \exists P\in\mathcal F_k,\ H(P),

where Fk\mathcal F_k is the frontier of I,wI,w and H(P)H(P) is the guarded terminal test: an admissible enumerated completion has bucket-matching u,vu,v with a0+Lu=Rva_0+L_u=R_v. It preserves memory before the terminal masks and uses the frontier-scan time bound plus 600600.

This connects stored frontier records to terminal checking.

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_Bundle04
import Definitions.Def_ThreeSum1962Source_Bundle05
import Definitions.Def_ThreeSum1962Source_Bundle07
import Definitions.Def_ThreeSum1962Source_Bundle08
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 Definitions.Def_ThreeSum1962Source_Bundle14
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.Combinatorics.Colex
import Mathlib.Data.Bool.Basic
import Mathlib.Data.Fin.Embedding
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Finset.Basic
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.ProdSigma
import Mathlib.Data.List.Range
import Mathlib.Data.List.Sublists
import Mathlib.Data.List.TakeDrop
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.Order.ConditionallyCompleteLattice.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.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Push
import Mathlib.Tactic.Ring
import Mathlib.Tactic.SplitIfs
import Mathlib.Tactic.Tauto
import Theorems.Thm_ThreeSum_LightReportingTerminalFrontier_program_meets
import Theorems.Thm_ThreeSum_RawReporting_partitionWord_length
import Theorems.Thm_ThreeSum_RawReporting_word_children
import Theorems.Thm_ThreeSum_ReportingHostMasks_blockSet_localRow
import Theorems.Thm_ThreeSum_ReportingHostMasks_localChildren_mem
import Theorems.Thm_ThreeSum_Reporting_frontier_length_le_mass


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.BlockForced
end ThreeSum.BlockForced
namespace ThreeSum.BlockIndex
end ThreeSum.BlockIndex
namespace ThreeSum.BlockIndexedQuery
end ThreeSum.BlockIndexedQuery
namespace ThreeSum.BlockMaskLayout
end ThreeSum.BlockMaskLayout
namespace ThreeSum.BlockRows
end ThreeSum.BlockRows
namespace ThreeSum.BlockSourceEncoding
end ThreeSum.BlockSourceEncoding
namespace ThreeSum.GlobalEncoding
end ThreeSum.GlobalEncoding
namespace ThreeSum.LightBlockQuery
end ThreeSum.LightBlockQuery
namespace ThreeSum.LightBlockSourceBuild
end ThreeSum.LightBlockSourceBuild
namespace ThreeSum.LightReportingTerminalMasks
end ThreeSum.LightReportingTerminalMasks
namespace ThreeSum.LightSourceResidues
end ThreeSum.LightSourceResidues
namespace ThreeSum.LocalCoverBounds
end ThreeSum.LocalCoverBounds
namespace ThreeSum.RawIncidences
end ThreeSum.RawIncidences
namespace ThreeSum.RawPrefixCounts
end ThreeSum.RawPrefixCounts
namespace ThreeSum.RawReporting
end ThreeSum.RawReporting
namespace ThreeSum.ReportingHostFrontierLayout
end ThreeSum.ReportingHostFrontierLayout
namespace ThreeSum.ReportingHostMasks
end ThreeSum.ReportingHostMasks
namespace ThreeSum.ReportingHostTerminalFrontier
end ThreeSum.ReportingHostTerminalFrontier
namespace ThreeSum.SourceBuckets
end ThreeSum.SourceBuckets
namespace ThreeSum.StoredReporting
end ThreeSum.StoredReporting
namespace ThreeSum.SubsetAddress
end ThreeSum.SubsetAddress
namespace ThreeSumApsp
end ThreeSumApsp

universe u_1 u_2 u_3
Formal statement
theorem ThreeSum.LightReportingTerminalStored.program_meets : ∀ {lim : Light.Limits} {α : Type u_1} {β : Type u_2} {γ : Type u_3} [Fintype.{u_1} α] [Fintype.{u_2} β]
  [Fintype.{u_3} γ] [inst : DecidableEq.{u_1 + 1} α] [DecidableEq.{u_2 + 1} β] [DecidableEq.{u_3 + 1} γ] {μ : Nat → Int}
  {h J k srcL srcR offsetsL offsetsR flatL flatR NL NR occ maps candidates histL histR root masks masksL masksR base
    bitBase rowOut work d : Nat}
  (av : Int) (p : Nat) (shift : Int) (left right : Nat → Int)
  (I : Finset.{max (max u_3 u_2) u_1} (ThreeSum.RawIncidences.RawItem.{u_1, u_2, u_3} h J α β γ))
  (w : ThreeSum.RawReporting.Wanted.{u_1} h J α) (hk : @LE.le.{0} Nat instLENat k J)
  (HF :
    @ThreeSum.ReportingHostFrontierLayout.At.{u_1, u_2, u_3} α β γ inst h J μ I w root
      (@ThreeSum.ReportingHostFrontierLayout.capacity.{u_1, u_2, u_3} α β γ inst h J I w) k)
  (hcap :
    @Eq.{1} Int
      (μ
        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) root
          (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3)))))
      (@Nat.cast.{0} Int instNatCastInt
        (@ThreeSum.ReportingHostFrontierLayout.capacity.{u_1, u_2, u_3} α β γ inst h J I w)))
  (HL :
    ThreeSum.SourceBuckets.Stored μ
      (fun (i : Nat) =>
        ThreeSum.LightSourceResidues.key p (ThreeSum.BlockSourceEncoding.modulus h J)
          (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0))) (left i))
      NL (ThreeSum.BlockSourceEncoding.modulus h J) offsetsL flatL)
  (HR :
    ThreeSum.SourceBuckets.Stored μ
      (fun (i : Nat) => ThreeSum.LightSourceResidues.key p (ThreeSum.BlockSourceEncoding.modulus h J) shift (right i))
      NR (ThreeSum.BlockSourceEncoding.modulus h J) offsetsR flatR)
  (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)
          (@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
              (@List.length.{0}
                (List.{0}
                  (Finset.{0}
                    (Fin
                      (@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.ReportingHostFrontier.frontier.{u_1, u_2, u_3} α β γ inst h J I w k)))
            (ThreeSum.LightReportingTerminalMasks.count h J k))
          (@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)
  (hsrcL : @LE.le.{0} Nat instLENat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) srcL NL) masks)
  (hsrcR : @LE.le.{0} Nat instLENat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) srcR NR) masks)
  (hoffsetsL :
    @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) offsetsL
          (ThreeSum.BlockSourceEncoding.modulus h J))
        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
      masks)
  (hoffsetsR :
    @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) offsetsR
          (ThreeSum.BlockSourceEncoding.modulus h J))
        (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
      masks)
  (hflatL : @LE.le.{0} Nat instLENat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) flatL NL) masks)
  (hflatR : @LE.le.{0} Nat instLENat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) flatR NR) masks)
  (hocc : @LE.le.{0} Nat instLENat (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) occ J) masks)
  (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)))
      masks)
  (hcandidates :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) candidates
        (ThreeSum.GlobalEncoding.scheduleSize h))
      masks)
  (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)))
      masks)
  (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)))
      masks)
  (hslot :
    @LE.le.{0} Nat instLENat
      (ThreeSum.ReportingHostFrontierLayout.slot root
        (@ThreeSum.ReportingHostFrontierLayout.capacity.{u_1, u_2, u_3} α β γ inst h J I w)
        (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) k
          (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1)))))
      masks)
  (hmasks :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) masks
        (ThreeSum.LightReportingTerminalMasks.count h J k))
      masksL)
  (hmasksL :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) masksL
        (ThreeSum.LightReportingTerminalMasks.count h J k))
      masksR)
  (hmasksR :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) masksR
        (ThreeSum.LightReportingTerminalMasks.count h J k))
      base)
  (hstop :
    @LE.le.{0} Nat instLENat
      (ThreeSum.LightReportingTerminalPreparation.stop base
        (@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))
        (ThreeSum.LightReportingTerminalMasks.count h J k))
      bitBase)
  (hbits :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) bitBase
        (@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)))
      rowOut)
  (hrowOut :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) rowOut
        (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2))))
      work)
  (hspace : @LE.le.{0} Nat instLENat (ThreeSum.LightReportingTerminal.space work h J) lim.space)
  (hword :
    @LE.le.{0} Int Int.instLEInt (@Nat.cast.{0} Int instNatCastInt (ThreeSum.LightReportingTerminal.word h J)) lim.word)
  (hoccRead :
    ∀ (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) occ j))
          (@Nat.cast.{0} Int instNatCastInt
            (@ThreeSum.BlockCoefficientRows.occurrenceIndices h J
              (@ThreeSum.BlockEncoding.outputOccurrences h J
                (@Prod.snd.{0, 0} (Fin (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))))
                  (ThreeSum.GlobalEncoding.GlobalOutput h J)
                  (@Prod.snd.{u_1, 0} α
                    (Prod.{0, 0} (Fin (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))))
                      (ThreeSum.GlobalEncoding.GlobalOutput h J))
                    w)))
              j)))
  (hcover : ThreeSum.BlockSourceCoverInput.Input μ h maps candidates histL histR)
  (hreadL :
    ∀ (i : Nat),
      @LT.lt.{0} Nat instLTNat i NL →
        @Eq.{1} Int (μ (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) srcL i)) (left i))
  (hreadR :
    ∀ (j : Nat),
      @LT.lt.{0} Nat instLTNat j NR →
        @Eq.{1} Int (μ (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) srcR j)) (right j))
  (hvaluesL :
    ∀ (i : Nat),
      @LT.lt.{0} Nat instLTNat i NL →
        @LE.le.{0} Int Int.instLEInt (@abs.{0} Int instLatticeInt Int.instAddGroup (left i)) lim.word)
  (hvaluesR :
    ∀ (j : Nat),
      @LT.lt.{0} Nat instLTNat j NR →
        @LE.le.{0} Int Int.instLEInt (@abs.{0} Int instLatticeInt Int.instAddGroup (right j)) lim.word)
  (ha : @LE.le.{0} Int Int.instLEInt (@abs.{0} Int instLatticeInt Int.instAddGroup av) lim.word)
  (htarget :
    ∀ (i : Nat),
      @LT.lt.{0} Nat instLTNat i NL →
        @LE.le.{0} Int Int.instLEInt
          (@abs.{0} Int instLatticeInt Int.instAddGroup
            (@HAdd.hAdd.{0, 0, 0} Int Int Int (@instHAdd.{0} Int Int.instAdd) av (left i)))
          lim.word)
  (hcountWord :
    @LE.le.{0} Int Int.instLEInt
      (@Nat.cast.{0} Int instNatCastInt (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat) NL NR))
      lim.word),
  Light.Meets lim ThreeSum.LightReportingTerminalStored.program
    (@OfNat.ofNat.{0} Nat (nat_lit 40) (instOfNatNat (nat_lit 40))) d
    (@List.cons.{0} Int av
      (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt srcL)
        (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt srcR)
          (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt offsetsL)
            (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt flatL)
              (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt offsetsR)
                (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt flatR)
                  (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt NL)
                    (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt NR)
                      (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt (ThreeSum.BlockSourceEncoding.modulus h J))
                        (@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 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 k)
                                              (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt root)
                                                (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt masks)
                                                  (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt masksL)
                                                    (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt masksR)
                                                      (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt base)
                                                        (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt bitBase)
                                                          (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt rowOut)
                                                            (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt work)
                                                              (@List.nil.{0} Int))))))))))))))))))))))))))))))
    μ (@ThreeSum.LightReportingTerminalStored.time.{u_1, u_2, u_3} α β γ inst h J p shift left right NL NR I w k)
    fun (r : Int) (ν : Nat → Int) =>
    And
      (Or (@Eq.{1} Int r (@OfNat.ofNat.{0} Int (nat_lit 0) (@instOfNat (nat_lit 0))))
        (@Eq.{1} Int r (@OfNat.ofNat.{0} Int (nat_lit 1) (@instOfNat (nat_lit 1)))))
      (And
        (Iff (@Eq.{1} Int r (@OfNat.ofNat.{0} Int (nat_lit 1) (@instOfNat (nat_lit 1))))
          (∃ (pre :
            List.{0}
              (Finset.{0}
                (Fin
                  (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                    (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h)))),
            And
              (@Membership.mem.{0, 0}
                (List.{0}
                  (Finset.{0}
                    (Fin
                      (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                        (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h))))
                (List.{0}
                  (List.{0}
                    (Finset.{0}
                      (Fin
                        (@HMul.hMul.{0, 0, 0} Nat Nat Nat (@instHMul.{0} Nat instMulNat)
                          (@OfNat.ofNat.{0} Nat (nat_lit 512) (instOfNatNat (nat_lit 512))) h)))))
                (@List.instMembership.{0}
                  (List.{0}
                    (Finset.{0}
                      (Fin
                        (@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.ReportingHostFrontier.frontier.{u_1, u_2, u_3} α β γ inst h J I w k) pre)
              (@ThreeSum.ReportingHostTerminalBatch.Hit h J av p shift left right NL NR
                (@Prod.snd.{0, 0} (Fin (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))))
                  (ThreeSum.GlobalEncoding.GlobalOutput h J)
                  (@Prod.snd.{u_1, 0} α
                    (Prod.{0, 0} (Fin (@OfNat.ofNat.{0} Nat (nat_lit 3) (instOfNatNat (nat_lit 3))))
                      (ThreeSum.GlobalEncoding.GlobalOutput h J))
                    w))
                k pre)))
        (Light.Kept μ ν masks)) := by
  sorry
Source
https://github.com/c0ldzy17/three-sum-lean/blob/2b639655e07421b9ac743de9090459bab473a7c0/Submission/ThreeSum/LightReportingTerminalStored.lean#L47-L149

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