TransformPROOF.step_mapped_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 623-644 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=623&end_line=644

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 step_mapped_certificate(+input: Shape.Shape, +axes: List<&2, U32>, +plan: Layout.Plan<input, axes>, +index: U32,
  source: Core.Tensor<input>, target: Core.Tensor<Layout.output(input, axes, plan)>,
  result: Result<&2, &2, Layout.Error, Layout.Mapping<input, axes, plan, index>>,
  exact: {result == Layout.map_index(input, axes, plan, index) : Result<&2, &2, Layout.Error, Layout.Mapping<input, axes, plan, index>>}) ->
  Transforms.StepCertificate<input, axes, plan, index, source, target>:
  match result:
    case Fail{error}:
      Transforms.StepCertificate{(source, Fail{Transforms.LayoutError{error}}),
        Equal.cong(Result<&2, &2, Layout.Error, Layout.Mapping<input, axes, plan, index>>,
          Core.Tensor<input> & Result<&2, &1, Transforms.Error, Core.Tensor<Layout.output(input, axes, plan)>>,
          mapped => Transforms.copy_mapped(input, axes, plan, index, source => target => (source, Done{target}), source, target, mapped),
          Fail{error}, Layout.map_index(input, axes, plan, index), exact), Unit{}}
    case Done{+mapping}:
      step_read_certificate(input, axes, plan, index, source, target, mapping, exact,
        pair => equality => Equal.trans(Core.Tensor<input> & Result<&2, &1, Transforms.Error, Core.Tensor<Layout.output(input, axes, plan)>>,
          pair, Transforms.copy_mapped(input, axes, plan, index, source => target => (source, Done{target}), source, target, Done{mapping}),
          Transforms.copy_step(input, axes, plan, source, target, index), equality,
          Equal.cong(Result<&2, &2, Layout.Error, Layout.Mapping<input, axes, plan, index>>,
            Core.Tensor<input> & Result<&2, &1, Transforms.Error, Core.Tensor<Layout.output(input, axes, plan)>>,
            mapped => Transforms.copy_mapped(input, axes, plan, index, source => target => (source, Done{target}), source, target, mapped),
            Done{mapping}, Layout.map_index(input, axes, plan, index), exact)),
        Core.read_certificate(input, source, Layout.source_index(input, axes, plan, index, mapping)))

Uses (22):
  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=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=Unit
  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/core.bend&name=read_certificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=Mapping
  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=map_index
  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/layout.bend&name=source_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=step_read_certificate
  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=StepCertificate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=copy_mapped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transforms.bend&name=copy_step