MatmulParallelProof.cell_keeps: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_parallel_proof.bend as MatmulParallelProof
Lines 188-214 of bendtorch-core@0.1.0.0/src/tensor/matmul_parallel_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_parallel_proof.bend&start_line=188&end_line=214

import Base
import bendtorch-core@0.1.0.0/src/storage/model.bend as Model
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend as Parallel

# Every cell hands both input arrays back.
def cell_keeps(+dl: Nat, +dr: Nat, A: Array<F32>, B: Array<F32>, +inner: Nat, +columns: Nat, +position: Nat, inside: Bool,
  -left_valid: Model.Balanced(F32, dl, A), -right_valid: Model.Balanced(F32, dr, B)) ->
  Parallel.Fact<{Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, inside)) == (A, B) : Array<F32> & Array<F32>}>:
  match inside:
    case False{}:
      Parallel.Fact{{==}}
    case True{}:
      Parallel.Fact{{\{DotRun: values => logical => fold => left_kept => right_kept =>
        Equal.trans(Array<F32> & Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, True{})),
          (Pair.fst(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, True{}))),
            Pair.snd(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, True{})))),
          (A, B),
          eta(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, True{}))),
          Parallel.pair_equal(Pair.fst(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, True{}))),
            Pair.snd(Array<F32>, Array<F32>, Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, True{}))),
            A, B, left_kept, right_kept))} :
        DotRun<inner, dl, dr, A, B, inner, columns, Matrix.row_of(columns, position), Matrix.column_of(columns, position), 0n, 0.0,
          cell_of(inner, columns, position, A, B, True{})> ->
        {Pair.snd(F32, Array<F32> & Array<F32>, cell_of(inner, columns, position, A, B, True{})) == (A, B) : Array<F32> & Array<F32>}}(
        {\{Parallel.Fact: p => p} :
          Parallel.Fact<DotRun<inner, dl, dr, A, B, inner, columns, Matrix.row_of(columns, position), Matrix.column_of(columns, position), 0n, 0.0,
            cell_of(inner, columns, position, A, B, True{})>> ->
          DotRun<inner, dl, dr, A, B, inner, columns, Matrix.row_of(columns, position), Matrix.column_of(columns, position), 0n, 0.0,
            cell_of(inner, columns, position, A, B, True{})>}(
          dot_run(inner, dl, dr, A, B, inner, columns, Matrix.row_of(columns, position), Matrix.column_of(columns, position), 0n, 0.0, A, B,
            {==}, {==}, left_valid, right_valid)))}

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.fst
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/storage/model.bend&name=Balanced
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend&name=Fact
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/elementwise_parallel_proof.bend&name=pair_equal
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=column_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=row_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_parallel_proof.bend&name=DotRun
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_parallel_proof.bend&name=cell_of
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_parallel_proof.bend&name=dot_run
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_parallel_proof.bend&name=eta