Prove2Me

Gathering exactly the masks of positive reporting children

Proved
ThreeSum.LightReportingPositiveMasks.program_meets

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

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

Fix a finite raw incidence set II, wanted label ww, prefix uu, and depth k<Jk<J. Enumerate the G=(2hh)G=\binom{2h}{h} balanced children in their defined order, and let s0,…,st−1s_0,\ldots,s_{t-1} be precisely the child indices whose depth-k+1k+1 prefix counts are positive. Memory stores these indices and the left and right masks Li,RiL_i,R_i of all children.

All five arrays must fit within space SS. The index array is disjoint from both destinations; the left source is disjoint from the left destination; the right source is disjoint from both destinations; and the destinations are disjoint. Assume S≤BS\le B, 2J(512h)+1≤B2^{J(512h)+1}\le B, and d<Dd<D. The fixed pair-gather program terminates within 80t+8080t+80 steps and writes

ν(dstL+j)=Lsj,ν(dstR+j)=Rsj(j<t).\nu(\mathrm{dst}_L+j)=L_{s_j},\qquad\nu(\mathrm{dst}_R+j)=R_{s_j}\quad(j<t).

These are exactly the positive children's masks in their retained order; all other cells are preserved.

This connects physical mask gathering to the abstract reporting frontier.

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_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 Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
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.Pow
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.Sigma
import Mathlib.Data.Finset.Sort
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Fintype.Card
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.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.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_LightBlockChildrenIndexed_childPrefixes_length
import Theorems.Thm_ThreeSum_LightReportingGatherPair_program_meets


set_option autoImplicit false
set_option relaxedAutoImplicit false
set_option Elab.async false
namespace Light
end Light
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.GlobalEncoding
end ThreeSum.GlobalEncoding
namespace ThreeSum.LightBlockChildrenIndexed
end ThreeSum.LightBlockChildrenIndexed
namespace ThreeSum.LightSubsetAddress
end ThreeSum.LightSubsetAddress
namespace ThreeSum.LocalCoverBounds
end ThreeSum.LocalCoverBounds
namespace ThreeSum.QueryCoordinates
end ThreeSum.QueryCoordinates
namespace ThreeSum.RawIncidences
end ThreeSum.RawIncidences
namespace ThreeSum.RawReporting
end ThreeSum.RawReporting
namespace ThreeSum.ReportingHostMasks
end ThreeSum.ReportingHostMasks
namespace ThreeSum.ReportingHostPositive
end ThreeSum.ReportingHostPositive
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.LightReportingPositiveMasks.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 indices srcL srcR dstL dstR d : Nat}
  (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)
  (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))))
  (hk : @LT.lt.{0} Nat instLTNat k J)
  (hw : @LE.le.{0} Int Int.instLEInt (@Nat.cast.{0} Int instNatCastInt lim.space) lim.word)
  (hindices :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) indices
        (@List.length.{0} Nat
          (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
      lim.space)
  (hsrcL :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) srcL (ThreeSum.LocalCoverBounds.groupSize h))
      lim.space)
  (hsrcR :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) srcR (ThreeSum.LocalCoverBounds.groupSize h))
      lim.space)
  (hdstL :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) dstL
        (@List.length.{0} Nat
          (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
      lim.space)
  (hdstR :
    @LE.le.{0} Nat instLENat
      (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) dstR
        (@List.length.{0} Nat
          (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
      lim.space)
  (hsepIL :
    Light.Apart indices
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk))
      dstL
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
  (hsepIR :
    Light.Apart indices
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk))
      dstR
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
  (hsepLL :
    Light.Apart srcL (ThreeSum.LocalCoverBounds.groupSize h) dstL
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
  (hsepRL :
    Light.Apart srcR (ThreeSum.LocalCoverBounds.groupSize h) dstL
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
  (hsepRR :
    Light.Apart srcR (ThreeSum.LocalCoverBounds.groupSize h) dstR
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
  (hsepOut :
    Light.Apart dstL
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk))
      dstR
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
  (hreadI :
    Light.SegN μ indices
      (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk))
  (hreadL :
    Light.SegN μ srcL
      (@List.map.{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))))
        Nat
        (fun
            (next :
              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.SubsetAddress.subsetMask
            (@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.BlockIndexedQuery.leftPrefix 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)
              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) k
                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
              (@ThreeSum.StoredReporting.prefixRows 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)
                next)))
        (@ThreeSum.LightBlockChildrenIndexed.childPrefixes h J k
          (@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))
          pre hk)))
  (hreadR :
    Light.SegN μ srcR
      (@List.map.{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))))
        Nat
        (fun
            (next :
              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.SubsetAddress.subsetMask
            (@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.BlockIndexedQuery.rightPrefix 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)
              (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) k
                (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
              (@ThreeSum.BlockForced.outputRows 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)))
              (@ThreeSum.StoredReporting.prefixRows 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)
                next)))
        (@ThreeSum.LightBlockChildrenIndexed.childPrefixes h J k
          (@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))
          pre hk)))
  (hword :
    @LE.le.{0} Int Int.instLEInt
      (@Nat.cast.{0} Int instNatCastInt
        (@HPow.hPow.{0, 0, 0} Nat Nat Nat
          (@instHPow.{0, 0} Nat Nat (@NPow.toPow.{0} Nat (@Monoid.toNPow.{0} Nat Nat.instMonoid)))
          (@OfNat.ofNat.{0} Nat (nat_lit 2) (instOfNatNat (nat_lit 2)))
          (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat)
            (@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 1) (instOfNatNat (nat_lit 1))))))
      lim.word)
  (hd : @LT.lt.{0} Nat instLTNat d lim.depth),
  Light.Meets lim ThreeSum.LightReportingGatherPair.program
    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))) d
    (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt indices)
      (@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
              (@List.length.{0} Nat
                (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
            (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt (ThreeSum.LocalCoverBounds.groupSize h))
              (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt dstL)
                (@List.cons.{0} Int (@Nat.cast.{0} Int instNatCastInt dstR) (@List.nil.{0} Int))))))))
    μ
    (ThreeSum.LightReportingGatherPair.time
      (@List.length.{0} Nat
        (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
    fun (x : Int) (ν : Nat → Int) =>
    And
      (Light.SegN ν dstL
        (@List.map.{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))))
          Nat
          (fun
              (next :
                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.SubsetAddress.subsetMask
              (@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.BlockIndexedQuery.leftPrefix 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)
                (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) k
                  (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
                (@ThreeSum.StoredReporting.prefixRows 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)
                  next)))
          (@ThreeSum.ReportingHostPositive.positiveChildren.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
      (And
        (Light.SegN ν dstR
          (@List.map.{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))))
            Nat
            (fun
                (next :
                  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.SubsetAddress.subsetMask
                (@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.BlockIndexedQuery.rightPrefix 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)
                  (@HAdd.hAdd.{0, 0, 0} Nat Nat Nat (@instHAdd.{0} Nat instAddNat) k
                    (@OfNat.ofNat.{0} Nat (nat_lit 1) (instOfNatNat (nat_lit 1))))
                  (@ThreeSum.BlockForced.outputRows 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)))
                  (@ThreeSum.StoredReporting.prefixRows 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)
                    next)))
            (@ThreeSum.ReportingHostPositive.positiveChildren.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))
        (Light.SameOutside2 μ ν dstL
          (@List.length.{0} Nat
            (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk))
          dstR
          (@List.length.{0} Nat
            (@ThreeSum.LightReportingPositiveMasks.selectedIndices.{u_1, u_2, u_3} α β γ inst h J k I w pre hk)))) := by
  sorry
Source
https://github.com/c0ldzy17/three-sum-lean/blob/2b639655e07421b9ac743de9090459bab473a7c0/Submission/ThreeSum/LightReportingPositiveMasks.lean#L37-L102

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