GatherPROOF.cell_keeps: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend as GatherPROOF
Lines 265-276 of bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&start_line=265&end_line=276

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/storage/refinement.bend as Refinement
import bendtorch-core@0.1.0.0/src/tensor/gather.bend as Gather
import bendtorch-core@0.1.0.0/src/tensor/parallel_proofs.bend as Generic

def cell_keeps(+plan: Gather.Plan, +at: Nat, +da: Nat, -A: Array<F32>, +di: Nat, -I: Array<U32>, inside: Bool,
  -valid: Model.Balanced(F32, da, A), -index_valid: Model.Balanced(U32, di, I)) ->
  Generic.Fact<{Pair.snd(F32, Array<F32> & Array<U32>, Gather.cell(plan, at, (A, I), inside)) == (A, I) : Array<F32> & Array<U32>}>:
  match inside:
    case False{}:
      Generic.Fact{{==}}
    case True{}:
      Generic.Fact{{\{Generic.Fact: q => q} :
        Generic.Fact<{Pair.snd(F32, Array<F32> & Array<U32>, Gather.looked(plan, at, A, Array.get(U32, I, U32.from_nat(Gather.entry(plan, at))))) == (A, I) : Array<F32> & Array<U32>}> ->
        {Pair.snd(F32, Array<F32> & Array<U32>, Gather.looked(plan, at, A, Array.get(U32, I, U32.from_nat(Gather.entry(plan, at))))) == (A, I) : Array<F32> & Array<U32>}}(
        looked_keeps(plan, at, da, A, I, Array.get(U32, I, U32.from_nat(Gather.entry(plan, at))),
          Refinement.law_get_retains(U32, di, I, U32.from_nat(Gather.entry(plan, at)), index_valid), valid))}

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=Balanced
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/refinement.bend&name=law_get_retains
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=entry
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather.bend&name=looked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/gather_PROOF.bend&name=looked_keeps
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/parallel_proofs.bend&name=Fact