BinaryProofs.words_cells: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/binary_proofs.bend as BinaryProofs
Lines 280-296 of bendtorch-core@0.1.0.0/src/tensor/contracts/binary_proofs.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_proofs.bend&start_line=280&end_line=296

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/elementwise.bend as Elementwise
import bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend as Conversion
import bendtorch-core@0.1.0.0/src/tensor/contracts/replayed.bend as Replayed
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend as Pointwise
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend as PointwiseProof
import bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend as Broadcast
import bendtorch-core@0.1.0.0/src/tensor/contracts/LAWS.bend as Contracts
import bendtorch-core@0.1.0.0/src/tensor/contracts/binary_LAWS.bend as Laws

# The words of the family history are `cells`.
def words_cells(+operation: Elementwise.Operation, +plan: Shape.BroadcastPlan, +left: Shape.Shape, +left_fill: F32, +left_ops: List<&2, StorageLaws.Op>, +right: Shape.Shape, +right_fill: F32, +right_ops: List<&2, StorageLaws.Op>, +count: Nat, +room: {Nat.is_le(count, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan)))) == True{} : Bool}) ->
  {Contracts.words(Shape.output_shape(plan), 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), count) == Laws.cells(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, count) : List<&2, F32>}:
  match count:
    case 0n:
      {==}
    case 1n+previous:
      +output = Shape.output_shape(plan)
      +total = Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan)))
      +below = Conversion.le_successor_lt(previous, total, room)
      +position = U32.from_nat(previous)
      cells_snoc(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous, Contracts.words(output, 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), previous), Replayed.value(output, 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), position),
        cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous), words_cells(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous, Conversion.le_predecessor(previous, total, room)),
        Equal.trans(F32, Replayed.value(output, 0.0, Pointwise.writes(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan))), operation, plan, left, left_fill, left_ops, right, right_fill, right_ops), position), cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, U32.to_nat(position)), cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, previous),
          PointwiseProof.writes_value(~Elementwise.Operation, ~Elementwise.scalar, ~Shape.BroadcastPlan, ~Broadcast.left_map, ~Broadcast.right_map, total, operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, output, position,
            PointwiseProof.word_inside(previous, output, below), Conversion.le_reflexive(total)),
          Equal.cong(Nat, F32, number => cell(operation, plan, left, left_fill, left_ops, right, right_fill, right_ops, number), U32.to_nat(position), previous, PointwiseProof.word_exact(previous, output, below))))

Uses (31):
  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.trans
  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=U32.from_nat
  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=BroadcastPlan
  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/shape/core.bend&name=output_shape
  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=words
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_LAWS.bend&name=cells
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_proofs.bend&name=cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/binary_proofs.bend&name=cells_snoc
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend&name=left_map
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast.bend&name=right_map
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend&name=writes
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=word_exact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=word_inside
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise_proof.bend&name=writes_value
  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/elementwise.bend&name=Operation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise.bend&name=scalar
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend&name=le_predecessor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend&name=le_reflexive
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend&name=le_successor_lt