MatrixIndexProof.position_fits: 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 161-176 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=161&end_line=176

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_fits(+output: Shape.Shape, +rows: Nat, +columns: Nat,
  +extents: {Shape.extents(output) == [rows, columns] : List<&2, Nat>}, +position: Nat,
  +below: {Nat.is_lt(position, Shape.logical_numel(Shape.dimensions(output))) == True{} : Bool}) ->
  {Shape.fit([rows, columns], [Matrix.row_of(columns, position), Matrix.column_of(columns, position)]) == True{} : Bool}:
  +bound = Shape.numel(Shape.extents(output))
  +fits = Equal.sym(Bool, Nat.is_lt(position, bound), True{}, below)
  +coordinate = Shape.unflatten(Shape.extents(output), Coordinates.fin_from(bound, position, fits))
  +digits : List<&2, Nat> = [Matrix.row_of(columns, position), Matrix.column_of(columns, position)]
  Equal.sym(Bool, True{}, Shape.fit([rows, columns], digits),
    Equal.trans(Bool, True{}, Shape.fit(Shape.extents(output), Shape.indices(Shape.extents(output), coordinate)), Shape.fit([rows, columns], digits),
      Coordinates.fit_indices(Shape.extents(output), coordinate),
      Equal.trans(Bool, Shape.fit(Shape.extents(output), Shape.indices(Shape.extents(output), coordinate)),
        Shape.fit(Shape.extents(output), digits), Shape.fit([rows, columns], digits),
        Equal.cong(List<&2, Nat>, Bool, values => Shape.fit(Shape.extents(output), values),
          Shape.indices(Shape.extents(output), coordinate), digits, position_digits(output, rows, columns, extents, position, fits)),
        Equal.cong(List<&2, Nat>, Bool, dims => Shape.fit(dims, digits), Shape.extents(output), [rows, columns], extents))))

Uses (20):
  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.sym
  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=fin_from
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/coordinate_proofs.bend&name=fit_indices
  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=extents
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=fit
  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=logical_numel
  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
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=position_digits