TransformPROOF.inverse_axes_naturals: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend as TransformPROOF
Lines 1995-2005 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=1995&end_line=2005

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/axis_spec.bend as Axis
import bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend as AxisAlgebra
import bendtorch-core@0.1.0.0/src/tensor/transform_totality.bend as Totality
import bendtorch-core@0.1.0.0/src/tensor/permutation_mapping.bend as Mapping

def inverse_axes_naturals(+input: Shape.Shape, +axes: List<&2, U32>, +accepted: {True{} == Layout.bijective(input, axes) : Bool}) ->
  {Shape.naturals(Totality.inverse_axes(input, axes)) == Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes)) : List<&2, Nat>}:
  words_bounded_exact(Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes)), Shape.rank(input),
    %Equal.sym(Nat, U32.to_nat(Shape.rank(input)), Shape.rank_dimensions(Shape.dimensions(input)), AxisAlgebra.rank_exact(input)) :
      {True{} == Axis.bounded(Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes)), _) : Bool}
    Mapping.and_left(Axis.bounded(Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes)), Shape.rank_dimensions(Shape.dimensions(input))),
      Axis.unique(Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes))),
      Mapping.and_right(Nat.is_eq(List.length(&2, Nat, Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes))), Shape.rank_dimensions(Shape.dimensions(input))),
        Bool.and(Axis.bounded(Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes)), Shape.rank_dimensions(Shape.dimensions(input))),
          Axis.unique(Axis.inverse_axes(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes)))),
        AxisAlgebra.facts_inverse_valid(Shape.rank_dimensions(Shape.dimensions(input)), Shape.naturals(axes), AxisAlgebra.shape_facts(input, axes, accepted)))))

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=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  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.to_nat
  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=dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=naturals
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=rank
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=rank_dimensions
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=facts_inverse_valid
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=rank_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=shape_facts
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=bounded
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=inverse_axes
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=unique
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=bijective
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permutation_mapping.bend&name=and_left
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/permutation_mapping.bend&name=and_right
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=words_bounded_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_totality.bend&name=inverse_axes