PermuteBuildProof.cell_keeps: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend as PermuteBuildProof
Lines 247-258 of bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend&start_line=247&end_line=258

import Base
import bendtorch-core@0.1.0.0/src/tensor/permute_build.bend as Build
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

def cell_keeps(+d: Nat, -a: Array<F32>, +request: Build.Request, +position: Nat, inside: Bool, -valid: Model.Balanced(F32, d, a)) ->
  Fact<{Pair.snd(F32, Array<F32> & Array<F32>, Build.cell(Build.recipe(request), position, (a, Array.new(F32, 0n, 0.0)), inside)) == (a, Array.new(F32, 0n, 0.0)) : Array<F32> & Array<F32>}>:
  match inside:
    case False{}:
      Fact{{==}}
    case True{}:
      +index = Build.at(Build.recipe(request), position)
      Fact{Equal.trans(Array<F32> & Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, Build.take(Array.new(F32, 0n, 0.0), Array.get(F32, a, index))),
        (Refinement.first(F32, Array.get(F32, a, index)), Array.new(F32, 0n, 0.0)), (a, Array.new(F32, 0n, 0.0)),
        take_first(Array.new(F32, 0n, 0.0), Array.get(F32, a, index)),
        Equal.cong(Array<F32>, Array<F32> & Array<F32>, x => (x, Array.new(F32, 0n, 0.0)), Refinement.first(F32, Array.get(F32, a, index)), a,
          Refinement.law_get_retains(F32, d, a, index, valid)))}

Uses (21):
  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=Array.new
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=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=first
  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/permute_build.bend&name=Request
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build.bend&name=at
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build.bend&name=cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build.bend&name=recipe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build.bend&name=take
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend&name=Fact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permute_build_proof.bend&name=take_first