TransformPROOF.natural_step_lift: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformPROOF
Lines 651-668 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=651&end_line=668

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
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle

def natural_step_lift(+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},
  -conversion: {True{} == Nat.is_eq(U32.to_nat(index), cursor) : Bool},
  same: {Transforms.natural_decided(input, axes, plan, cursor, index, source, target, candidate, Shape.BTrue{conversion}) ==
    Transforms.natural_step(input, axes, plan, cursor, source, target) : Transforms.NaturalCopy<input, axes, plan, cursor>},
  certificate: Transforms.StepCertificate<input, axes, plan, index, source, target>) ->
  Transforms.NaturalCertificate<input, axes, plan, cursor, source, target>:
  Transforms.StepCertificate{pair, exact, meaning} = certificate
  Transforms.NaturalCertificate{Transforms.NaturalCopied{pair, index, Lifecycle.natural_equal(U32.to_nat(index), cursor, conversion), candidate},
    Equal.trans(Transforms.NaturalCopy<input, axes, plan, cursor>,
      Transforms.NaturalCopied{pair, index, Lifecycle.natural_equal(U32.to_nat(index), cursor, conversion), candidate},
      Transforms.natural_decided(input, axes, plan, cursor, index, source, target, candidate, Shape.BTrue{conversion}),
      Transforms.natural_step(input, axes, plan, cursor, source, target),
      Equal.cong(Core.Tensor<input> & Result<&2, &1, Transforms.Error, Core.Tensor<Layout.output(input, axes, plan)>>,
        Transforms.NaturalCopy<input, axes, plan, cursor>,
        result => Transforms.natural_result(input, axes, plan, cursor, index, Lifecycle.natural_equal(U32.to_nat(index), cursor, conversion), candidate, result),
        pair, Transforms.copy_step(input, axes, plan, source, target, index), exact), same), meaning}

Uses (25):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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.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=Nat.is_eq
  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=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=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/lifecycle.bend&name=natural_equal
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=Error
  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=StepCertificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=copy_step
  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_result
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=natural_step