LAWS.product_replayed: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as LAWS
Lines 313-334 of bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&start_line=313&end_line=334

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/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend as Lifecycle
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed

# product_ordered in transport form, as matmul_replayed states matmul: for
# every P, if P holds for every result that hands back both inputs with
# their words and gives an output of the plan's shape whose cells hold the
# ordered totals, then P holds for the product. The output is a replayed
# tensor, so a later family law applies to it.
law product_replayed:
  for +lo: Matrix.Order
  for +ro: Matrix.Order
  for +left: Shape.Shape
  for +right: Shape.Shape
  for +plan: Matrix.Product<lo, ro, left, right>
  for planned: {Matrix.product_plan(lo, ro, left, right) == Done{plan} : Result<&2, &2, Matrix.Error, Matrix.Product<lo, ro, left, right>>}
  for +left_fill: F32
  for +left_ops: List<&2, StorageLaws.Op>
  for -left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_ops)) == Shape.logical_numel(Shape.dimensions(left)) : Nat}
  for +right_fill: F32
  for +right_ops: List<&2, StorageLaws.Op>
  for -right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_ops)) == Shape.logical_numel(Shape.dimensions(right)) : Nat}
  for -P: Result<&2, &1, Matrix.Error, Core.Dynamic & Core.Dynamic & Core.Dynamic> -> Type
  for h: ProductWith(lo, ro, left, right, plan, left_fill, left_ops, right_fill, right_ops, P)
  P(Matrix.product(lo, ro, Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_ops), left_fits}},
    Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_ops), right_fits}}))

Uses (20):
  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=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Result
  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=logical_numel
  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=ProductWith
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/product_proof.bend&name=product_replayed
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend&name=storage
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Dynamic
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/lifecycle.bend&name=logical_length
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Error
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Order
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=Product
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=product
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=product_plan