MatmulProof.ParallelFinal: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_proof.bend as MatmulProof
Lines 183-202 of bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_proof.bend&start_line=183&end_line=202

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/storage/main.bend as Storage
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
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Laws
import bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend as Par

# The parallel product over replayed inputs, in transport form: P holds for
# the product if it holds for both inputs replayed with histories that keep
# their words, next to the output replayed with the writes of every cell.
def ParallelFinal(+left: Shape.Shape, +right: Shape.Shape, +output: Shape.Shape, +inner: U32, +columns: U32,
  +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>,
  -s: Storage.Storage, -P: Result<&2, &1, Matrix.Error, Core.Dynamic & Core.Dynamic & Core.Dynamic> -> Type) -> Type:
  @+left_kept: List<&2, StorageLaws.Op> ->
  @left_values: (@+other: U32 -> {Replayed.value(left, left_fill, left_kept, other) == Replayed.value(left, left_fill, left_ops, other) : F32}) ->
  @left_words: {Laws.words(left, left_fill, left_kept, Shape.logical_numel(Shape.dimensions(left))) ==
    Laws.words(left, left_fill, left_ops, Shape.logical_numel(Shape.dimensions(left))) : List<&2, F32>} ->
  @-left_fits: {Lifecycle.logical_length(Replayed.storage(left, left_fill, left_kept)) == Shape.logical_numel(Shape.dimensions(left)) : Nat} ->
  @+right_kept: List<&2, StorageLaws.Op> ->
  @right_values: (@+other: U32 -> {Replayed.value(right, right_fill, right_kept, other) == Replayed.value(right, right_fill, right_ops, other) : F32}) ->
  @right_words: {Laws.words(right, right_fill, right_kept, Shape.logical_numel(Shape.dimensions(right))) ==
    Laws.words(right, right_fill, right_ops, Shape.logical_numel(Shape.dimensions(right))) : List<&2, F32>} ->
  @-right_fits: {Lifecycle.logical_length(Replayed.storage(right, right_fill, right_kept)) == Shape.logical_numel(Shape.dimensions(right)) : Nat} ->
  @-output_fits: {Lifecycle.logical_length(StorageLaws.replay(Par.writes(U32.to_nat(inner), U32.to_nat(columns), left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(Shape.count(output))), s)) == Shape.logical_numel(Shape.dimensions(output)) : Nat} ->
    P(Done{(Core.Packed{left, Core.TTensor{Replayed.storage(left, left_fill, left_kept), left_fits}},
      Core.Packed{right, Core.TTensor{Replayed.storage(right, right_fill, right_kept), right_fits}},
      Core.Packed{output, Core.TTensor{StorageLaws.replay(Par.writes(U32.to_nat(inner), U32.to_nat(columns), left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(Shape.count(output))), s), output_fits}})})

Uses (23):
  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=Base/base.bend&name=Sigma
  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/shape/core.bend&name=Shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=count
  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/storage/LAWS.bend&name=replay
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/main.bend&name=Storage
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend&name=words
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/matmul_parallel_proof.bend&name=writes
  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/contracts/replayed.bend&name=value
  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