ProjectionPROOF.projected_pair: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/projection_PROOF.bend as ProjectionPROOF
Lines 12-29 of bendtorch-core@0.1.0.0/src/tensor/projection_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/projection_PROOF.bend&start_line=12&end_line=29

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/flat.bend as Flat
import bendtorch-core@0.1.0.0/src/shape/LAWS.bend as ShapeLaws
import bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend as Laws

def projected_pair(+plan: Shape.BroadcastPlan,
  +map: Shape.Index<Shape.extents(Shape.left_shape(plan)), Shape.extents(Shape.right_shape(plan)), Shape.extents(Shape.output_shape(plan))>,
  +index: Shape.FlatIndex<Shape.output_shape(plan)>) ->
  {Some{(Shape.index_value(Shape.left_shape(plan), Flat.project_left_index(plan, map, index)),
    Shape.index_value(Shape.right_shape(plan), Flat.project_right_index(plan, map, index)))} ==
    Laws.offset_spec(plan, ShapeLaws.position(Shape.output_shape(plan), index)) : Maybe<&1, U32 & U32>}:
  +left = Shape.extents(Shape.left_shape(plan))
  +right = Shape.extents(Shape.right_shape(plan))
  +output = Shape.extents(Shape.output_shape(plan))
  +decoded = ShapeLaws.fin_of(Shape.numel(output), ShapeLaws.position(Shape.output_shape(plan), index))
  +left_value = Shape.index_value(Shape.left_shape(plan), Flat.project_left_index(plan, map, index))
  +right_value = Shape.index_value(Shape.right_shape(plan), Flat.project_right_index(plan, map, index))
  %ShapeLaws.project_left_index_refines(plan, map, index) :
    {Some{(left_value, right_value)} == Laws.pair_offsets(_, ShapeLaws.flatten_spec(right,
      ShapeLaws.project_right_coordinate(left, right, output, Shape.alignment(plan), decoded))) : Maybe<&1, U32 & U32>}
  %ShapeLaws.project_right_index_refines(plan, map, index) :
    {Some{(left_value, right_value)} == Laws.pair_offsets(Some{left_value}, _) : Maybe<&1, U32 & U32>}
  {==}

Uses (24):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  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=bendtorch-core@0.1.0.0/src/shape/LAWS.bend&name=fin_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/LAWS.bend&name=flatten_spec
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/LAWS.bend&name=position
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/LAWS.bend&name=project_left_index_refines
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/LAWS.bend&name=project_right_coordinate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/LAWS.bend&name=project_right_index_refines
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BroadcastPlan
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=FlatIndex
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=alignment
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=extents
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=index_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=left_shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=numel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=output_shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=right_shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/flat.bend&name=project_left_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/flat.bend&name=project_right_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend&name=offset_spec
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/projection_LAWS.bend&name=pair_offsets