GradientPROOF.total_inv: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend as GradientPROOF
Lines 371-392 of bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&start_line=371&end_line=392

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend as CoreProof
import bendtorch-core@0.1.0.0/src/autograd/gradient.bend as Gradient

def total_inv(+shape: Shape.Shape, -original: Core.Tensor<shape>, -contribution: Core.Dynamic, +cursor: Nat,
  -before: Core.Tensor<shape>, +index: U32, +value: F32, owner: Core.Dynamic,
  pair: Core.Tensor<shape> & Result<&2, &2, Core.Error, F32>,
  -exact: {U32.to_nat(index) == cursor : Nat},
  -source: {Core.read_value(shape, pair) == Core.checked_observe(shape, before, index) : Maybe<&2, F32>},
  -keeps: @+position: U32 -> {Core.retained_read_observe(shape, pair, position) == Core.checked_observe(shape, before, position) : Maybe<&2, F32>},
  -inv: Inv(shape, original, contribution, cursor, before),
  -word: {Core.checked_observe_dynamic(contribution, index) == Some{value} : Maybe<&2, F32>}) ->
  Holds<StepInv(shape, original, contribution, cursor, Gradient.step_total(shape, index, owner, value, pair))>:
  (read_owner, result) = pair
  match result:
    case Fail{error}:
      Holds{Unit{}}
    case Done{+accumulated}:
      write_inv(shape, original, contribution, cursor, before, read_owner, index, accumulated, value, owner,
        Core.write_flat(shape, read_owner, index, F32.add(accumulated, value)), exact,
        {\{Core.CheckedUpdateModel: meaning => meaning} :
          Core.CheckedUpdateModel<shape, read_owner, index, F32.add(accumulated, value)> ->
          Core.CheckedUpdateMeaning(shape, read_owner, index, F32.add(accumulated, value),
            Core.write_flat(shape, read_owner, index, F32.add(accumulated, value)))}(
          CoreProof.checked_update_model(shape, read_owner, index, F32.add(accumulated, value))),
        inv, Equal.sym(Maybe<&2, F32>, Some{accumulated}, Core.checked_observe(shape, before, index), source), keeps, word)

Uses (28):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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=Result
  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.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Unit
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient.bend&name=step_total
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&name=Holds
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&name=Inv
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&name=StepInv
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&name=write_inv
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=CheckedUpdateMeaning
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=CheckedUpdateModel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=checked_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=checked_observe_dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=read_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=retained_read_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=write_flat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core_PROOF.bend&name=checked_update_model