GradientPROOF.contribution_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 394-419 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=394&end_line=419

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/elementwise_totality.bend as Totality
import bendtorch-core@0.1.0.0/src/autograd/gradient.bend as Gradient

def contribution_inv(+shape: Shape.Shape, -original: Core.Tensor<shape>, -contribution: Core.Dynamic, +cursor: Nat, +index: U32,
  total: Core.Tensor<shape>, -current: Core.Dynamic, pair: Core.Dynamic & Result<&2, &2, Core.Error, F32>,
  -exact: {U32.to_nat(index) == cursor : Nat},
  -source: {Core.dynamic_read_value(pair) == Core.checked_observe_dynamic(current, index) : Maybe<&2, F32>},
  -same: Totality.SameSource(contribution, current),
  -inv: Inv(shape, original, contribution, cursor, total)) ->
  Holds<StepInv(shape, original, contribution, cursor, Gradient.step_contribution(shape, index, total, pair))>:
  (owner, result) = pair
  match result:
    case Fail{error}:
      Holds{Unit{}}
    case Done{+value}:
      total_inv(shape, original, contribution, cursor, total, index, value, owner, Core.read_flat(shape, total, index), exact,
        {\{Core.SourceRead: meaning => meaning} : Core.SourceRead<shape, total, index> ->
          {Core.read_value(shape, Core.read_flat(shape, total, index)) == Core.checked_observe(shape, total, index) : Maybe<&2, F32>}}(
          Core.source_read_model(shape, total, index)),
        {\{Core.SourceReadKeeps: kept => kept} : Core.SourceReadKeeps<shape, total, index> ->
          @+position: U32 -> {Core.retained_read_observe(shape, Core.read_flat(shape, total, index), position) == Core.checked_observe(shape, total, position) : Maybe<&2, F32>}}(
          Core.source_read_keeps(shape, total, index)),
        inv,
        Equal.trans(Maybe<&2, F32>, Core.checked_observe_dynamic(contribution, index), Core.checked_observe_dynamic(current, index), Some{value},
          Equal.sym(Maybe<&2, F32>, Core.checked_observe_dynamic(current, index), Core.checked_observe_dynamic(contribution, index),
            {\{Holds: proof => proof} : Holds<{Core.checked_observe_dynamic(current, index) == Core.checked_observe_dynamic(contribution, index) : Maybe<&2, F32>}> ->
              {Core.checked_observe_dynamic(current, index) == Core.checked_observe_dynamic(contribution, index) : Maybe<&2, F32>}}(
              same_checked(contribution, current, same, index))),
          Equal.sym(Maybe<&2, F32>, Some{value}, Core.checked_observe_dynamic(current, index), source)))

Uses (32):
  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=F32
  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_contribution
  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=same_checked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&name=total_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=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=SourceRead
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=SourceReadKeeps
  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=dynamic_read_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=read_flat
  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=source_read_keeps
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=source_read_model
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_totality.bend&name=SameSource