GradientPROOF.write_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 348-369 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=348&end_line=369

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/autograd/gradient.bend as Gradient

def write_inv(+shape: Shape.Shape, -original: Core.Tensor<shape>, -contribution: Core.Dynamic, +cursor: Nat,
  -before: Core.Tensor<shape>, -read_owner: Core.Tensor<shape>, +index: U32, +accumulated: F32, +value: F32,
  owner: Core.Dynamic, pair: Core.Tensor<shape> & Result<&2, &2, Core.Error, Unit>,
  -exact: {U32.to_nat(index) == cursor : Nat},
  -meaning: Core.CheckedUpdateMeaning(shape, read_owner, index, F32.add(accumulated, value), pair),
  -inv: Inv(shape, original, contribution, cursor, before),
  -read: {Core.checked_observe(shape, before, index) == Some{accumulated} : Maybe<&2, F32>},
  -kept: @+position: U32 -> {Core.checked_observe(shape, read_owner, position) == Core.checked_observe(shape, before, position) : Maybe<&2, F32>},
  -word: {Core.checked_observe_dynamic(contribution, index) == Some{value} : Maybe<&2, F32>}) ->
  Holds<StepInv(shape, original, contribution, cursor, Gradient.step_write(shape, owner, pair))>:
  (written, result) = pair
  match result:
    case Fail{error}:
      Holds{Unit{}}
    case Done{unit}:
      Holds{other => inside => {\{Holds: proof => proof} :
        Holds<{Core.checked_observe(shape, written, other) ==
          partial(Nat.is_lt(U32.to_nat(other), 1n+cursor), Core.checked_observe(shape, original, other), Core.checked_observe_dynamic(contribution, other)) : Maybe<&2, F32>}> ->
        {Core.checked_observe(shape, written, other) ==
          partial(Nat.is_lt(U32.to_nat(other), 1n+cursor), Core.checked_observe(shape, original, other), Core.checked_observe_dynamic(contribution, other)) : Maybe<&2, F32>}}(
        position_inv(shape, original, contribution, cursor, before, read_owner, written, index, accumulated, value, unit,
          other, Shape.bool_case(Nat.is_eq(U32.to_nat(index), U32.to_nat(other))), inside, exact, meaning, inv, read, kept, word))}

Uses (26):
  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=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  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_write
  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=partial
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/gradient_PROOF.bend&name=position_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/shape/core.bend&name=bool_case
  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=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