TransformPROOF.natural_decided_certificate: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformPROOF
Lines 670-681 of bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&start_line=670&end_line=681

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/layout.bend as Layout
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/transforms.bend as Transforms

def natural_decided_certificate(+input: Shape.Shape, +axes: List<&2, U32>, +plan: Layout.Plan<input, axes>, +cursor: Nat, +index: U32,
  source: Core.Tensor<input>, target: Core.Tensor<Layout.output(input, axes, plan)>,
  -candidate: {index == U32.from_nat(cursor) : U32},
  decision: Shape.BoolCase<Nat.is_eq(U32.to_nat(index), cursor)>,
  same: {Transforms.natural_decided(input, axes, plan, cursor, index, source, target, candidate, decision) ==
    Transforms.natural_step(input, axes, plan, cursor, source, target) : Transforms.NaturalCopy<input, axes, plan, cursor>}) ->
  Transforms.NaturalCertificate<input, axes, plan, cursor, source, target>:
  match decision:
    case Shape.BFalse{equal}:
      Transforms.NaturalCertificate{Transforms.NaturalError{source}, same, Unit{}}
    case Shape.BTrue{equal}:
      natural_step_lift(input, axes, plan, cursor, index, source, target, candidate, equal, same, step_certificate(input, axes, plan, index, source, target))

Uses (18):
  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=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.from_nat
  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/shape/core.bend&name=BoolCase
  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=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=Plan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=output
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=natural_step_lift
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=step_certificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=NaturalCertificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=NaturalCopy
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=natural_decided
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=natural_step