TransposePROOF.natural_valid_layout: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend as TransposePROOF
Lines 141-151 of bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/transpose_PROOF.bend&start_line=141&end_line=151

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

def natural_valid_layout(+shape: Shape.Shape, +axes: List<&2, U32>, accepted: {True{} == Axis.valid(Shape.rank_dimensions(Shape.dimensions(shape)), Shape.naturals(axes)) : Bool}) ->
  {True{} == Layout.bijective(shape, axes) : Bool}:
  %Equal.sym(Nat, Shape.rank_dimensions(axes), List.length(&2, Nat, Shape.naturals(axes)), Shape.rank_naturals(axes)) :
    {True{} == Bool.and(Nat.is_eq(_, Shape.rank_dimensions(Shape.dimensions(shape))), Bool.and(Layout.bounded(axes, Shape.rank(shape)), Layout.unique(axes))) : Bool}
  %Equal.sym(Bool, Layout.unique(axes), Axis.unique(Shape.naturals(axes)), Algebra.unique(axes)) :
    {True{} == Bool.and(Nat.is_eq(List.length(&2, Nat, Shape.naturals(axes)), Shape.rank_dimensions(Shape.dimensions(shape))), Bool.and(Layout.bounded(axes, Shape.rank(shape)), _)) : Bool}
  %Equal.sym(Bool, Layout.bounded(axes, Shape.rank(shape)), Axis.bounded(Shape.naturals(axes), U32.to_nat(Shape.rank(shape))), Algebra.bounded(axes, Shape.rank(shape))) :
    {True{} == Bool.and(Nat.is_eq(List.length(&2, Nat, Shape.naturals(axes)), Shape.rank_dimensions(Shape.dimensions(shape))), Bool.and(_, Axis.unique(Shape.naturals(axes)))) : Bool}
  %Equal.sym(Nat, U32.to_nat(Shape.rank(shape)), Shape.rank_dimensions(Shape.dimensions(shape)), Algebra.rank_exact(shape)) :
    {True{} == Bool.and(Nat.is_eq(List.length(&2, Nat, Shape.naturals(axes)), Shape.rank_dimensions(Shape.dimensions(shape))), Bool.and(Axis.bounded(Shape.naturals(axes), _), Axis.unique(Shape.naturals(axes)))) : Bool}
  accepted

Uses (24):
  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/shape/core.bend&name=rank_naturals
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_algebra.bend&name=bounded
  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=unique
  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=unique
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/axis_spec.bend&name=valid
  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/layout.bend&name=bounded
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/layout.bend&name=unique