TensorVjpLAWS.nt_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 442-468 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=442&end_line=468

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_nt reads what matmul reads from the transposed copy: for a right
# operand of dimensions [columns, inner], the factor pairs of cell
# (row, column) of a product of two `Kept` operands (`matmul_nt`), left[row,
# k] and right[column, k], are the pairs `right_transposed_factors` reads
# through `permute_source` on right^T, the pairs `tensor_matmul_vjp_values`
# states for g @ y^T. Both fold the same words in the same order, so
# `matmul_nt(g, y)` and `matmul(g, transpose_copy(y))` agree word for word.
law nt_reads_transpose:
  for +row: Nat
  for +column: Nat
  for +rows: 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 +columns: U32
  for +inner: U32
  for matrix: {Shape.dimensions(right) == [columns, inner] : List<&2, U32>}
  for column_below: {Nat.is_lt(column, U32.to_nat(columns)) == True{} : Bool}
  for +count: Nat
  for room: {Nat.is_le(count, U32.to_nat(inner)) == True{} : Bool}
  {Contracts.product_factors(row, column, Matrix.Kept{}, Matrix.Kept{}, U32.to_nat(inner), rows, U32.to_nat(columns),
    left, left_fill, left_ops, right, right_fill, right_ops, count) ==
    right_transposed_factors(row, column, U32.to_nat(inner), U32.to_nat(columns), left, left_fill, left_ops,
      right, right_fill, right_ops, swapped(right), 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=right_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=nt_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