TensorVjpLAWS.tn_reads_transpose: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend as TensorVjpLAWS
Lines 470-494 of bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend&start_line=470&end_line=494

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/LAWS.bend as StorageLaws
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/dot_fold.bend as DotFold
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Contracts

# matmul_tn likewise: for a left operand of dimensions [inner, rows], the
# pairs of a product of two `Swapped` operands (`matmul_tn`), left[k, row] and
# right[k, column], are the pairs `left_transposed_factors` reads through
# `permute_source` on left^T, the pairs `tensor_matmul_vjp_values` states for
# x^T @ g.
law tn_reads_transpose:
  for +row: Nat
  for +column: Nat
  for +columns: Nat
  for +left: Shape.Shape
  for +left_fill: F32
  for +left_ops: List<&2, StorageLaws.Op>
  for +right: Shape.Shape
  for +right_fill: F32
  for +right_ops: List<&2, StorageLaws.Op>
  for +inner: U32
  for +rows: U32
  for matrix: {Shape.dimensions(left) == [inner, rows] : List<&2, U32>}
  for row_below: {Nat.is_lt(row, U32.to_nat(rows)) == True{} : Bool}
  for +count: Nat
  for room: {Nat.is_le(count, U32.to_nat(inner)) == True{} : Bool}
  {Contracts.product_factors(row, column, Matrix.Swapped{}, Matrix.Swapped{}, U32.to_nat(inner), U32.to_nat(rows), columns,
    left, left_fill, left_ops, right, right_fill, right_ops, count) ==
    left_transposed_factors(row, column, U32.to_nat(inner), columns, left, left_fill, left_ops, swapped(left),
      right, right_fill, right_ops, count) : List<&2, DotFold.Factors>}

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  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_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  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/autograd/tensor_vjp_LAWS.bend&name=left_transposed_factors
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_LAWS.bend&name=swapped
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/tensor_vjp_PROOF.bend&name=tn_factors
  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/storage/LAWS.bend&name=Op
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=product_factors
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/dot_fold.bend&name=Factors
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Order