MatrixIndexProof.position_digits: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend as MatrixIndexProof
Lines 115-130 of bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&start_line=115&end_line=130

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/coordinate_proofs.bend as Coordinates
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix

def position_digits(+output: Shape.Shape, +rows: Nat, +columns: Nat,
  extents: {Shape.extents(output) == [rows, columns] : List<&2, Nat>}, +position: Nat,
  +fits: {True{} == Nat.is_lt(position, Shape.numel(Shape.extents(output))) : Bool}) ->
  {Shape.indices(Shape.extents(output), Shape.unflatten(Shape.extents(output),
    Coordinates.fin_from(Shape.numel(Shape.extents(output)), position, fits))) ==
    [Matrix.row_of(columns, position), Matrix.column_of(columns, position)] : List<&2, Nat>}:
  +bound = Shape.numel(Shape.extents(output))
  +index = Coordinates.fin_from(bound, position, fits)
  Equal.trans(List<&2, Nat>, Shape.indices(Shape.extents(output), Shape.unflatten(Shape.extents(output), index)),
    Shape.digits(Shape.extents(output), Shape.Fin.value(bound, index)), [Matrix.row_of(columns, position), Matrix.column_of(columns, position)],
    Coordinates.digits_unflatten(Shape.extents(output), index),
    Equal.trans(List<&2, Nat>, Shape.digits(Shape.extents(output), Shape.Fin.value(bound, index)),
      Shape.digits(Shape.extents(output), position), [Matrix.row_of(columns, position), Matrix.column_of(columns, position)],
      Equal.cong(Nat, List<&2, Nat>, value => Shape.digits(Shape.extents(output), value), Shape.Fin.value(bound, index), position,
        Coordinates.fin_from_value(bound, position, fits)),
      Equal.cong(List<&2, Nat>, List<&2, Nat>, dims => Shape.digits(dims, position), Shape.extents(output), [rows, columns], extents)))

Uses (18):
  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_lt
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/coordinate_proofs.bend&name=digits_unflatten
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/coordinate_proofs.bend&name=fin_from
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/coordinate_proofs.bend&name=fin_from_value
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Fin.value
  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=digits
  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=indices
  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=unflatten
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=column_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=row_of