TensorChainPROOF.conclude: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/tensor_chain_PROOF.bend as TensorChainPROOF
Lines 433-456 of bendtorch-core@0.1.0.0/src/autograd/tensor_chain_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_chain_PROOF.bend&start_line=433&end_line=456

import Base
import bendtorch-core@0.1.0.0/src/autograd/gradient.bend as Gradient
import bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend as Backward
import bendtorch-core@0.1.0.0/src/autograd/tensor_chain_LAWS.bend as Laws

def conclude(-entries: List<&1, Backward.Entry>, -copy: List<&1, Gradient.Slot>, -gradients: List<&1, Gradient.Slot>, +count: Nat,
  -gs: List<&1, Gradient.Slot>, same: {copy == gradients : List<&1, Gradient.Slot>},
  succeeded: {Laws.result(Backward.sweep(entries, Done{gradients}, count)) == Done{gs} : Laws.Slots()},
  out: Run<entries, copy, count, gradients, Nil{}>) -> {Laws.chained(entries, gradients, count, Nil{}) == Done{gs} : Laws.Slots()}:
  match out:
    case Kept{done, found, swept, pulled}:
      Equal.trans(Laws.Slots(), Laws.chained(entries, gradients, count, Nil{}), Done{found}, Done{gs}, pulled,
        Equal.trans(Laws.Slots(), Done{found}, Laws.result(Backward.sweep(entries, Done{copy}, count)), Done{gs},
          Equal.sym(Laws.Slots(), Laws.result(Backward.sweep(entries, Done{copy}, count)), Done{found},
            Equal.cong(Backward.Swept(), Laws.Slots(), pair => Laws.result(pair), Backward.sweep(entries, Done{copy}, count), (done, Done{found}), swept)),
          Equal.trans(Laws.Slots(), Laws.result(Backward.sweep(entries, Done{copy}, count)), Laws.result(Backward.sweep(entries, Done{gradients}, count)),
            Done{gs},
            Equal.cong(List<&1, Gradient.Slot>, Laws.Slots(), list => Laws.result(Backward.sweep(entries, Done{list}, count)), copy, gradients, same),
            succeeded)))
    case Stopped{done, error, swept}:
      Empty.absurd({Laws.chained(entries, gradients, count, Nil{}) == Done{gs} : Laws.Slots()},
        done_fail(error, gs,
          Equal.trans(Laws.Slots(), Fail{error}, Laws.result(Backward.sweep(entries, Done{copy}, count)), Done{gs},
            Equal.sym(Laws.Slots(), Laws.result(Backward.sweep(entries, Done{copy}, count)), Fail{error},
              Equal.cong(Backward.Swept(), Laws.Slots(), pair => Laws.result(pair), Backward.sweep(entries, Done{copy}, count), (done, Fail{error}), swept)),
            Equal.trans(Laws.Slots(), Laws.result(Backward.sweep(entries, Done{copy}, count)), Laws.result(Backward.sweep(entries, Done{gradients}, count)),
              Done{gs},
              Equal.cong(List<&1, Gradient.Slot>, Laws.Slots(), list => Laws.result(Backward.sweep(entries, Done{list}, count)), copy, gradients, same),
              succeeded))))

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  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/autograd/gradient.bend&name=Slot
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Entry
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=Swept
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_backward.bend&name=sweep
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_chain_LAWS.bend&name=Slots
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_chain_LAWS.bend&name=chained
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_chain_LAWS.bend&name=result
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_chain_PROOF.bend&name=Run
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_chain_PROOF.bend&name=done_fail