MatmulPROOF.advance_prefix: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 341-365 of bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&start_line=341&end_line=365

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/core.bend as Core
import bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend as Laws

def advance_prefix(+inner: U32, +left: Shape.Shape, +right: Shape.Shape, -a: Core.Tensor<left>, -b: Core.Tensor<right>,
  -before_a: Core.Tensor<left>, -before_b: Core.Tensor<right>, -after_a: Core.Tensor<left>, -after_b: Core.Tensor<right>,
  +output: Shape.Shape, -before: Core.Tensor<output>, -after: Core.Tensor<output>, +cursor: Nat,
  +row: U32, +column: U32, +coordinate: Shape.CheckedCoordinate<output>, +value: F32,
  -decoded: {Shape.unflatten_checked(output, U32.from_nat(cursor)) == Done{coordinate} : Result<&2, &2, Shape.Error, Shape.CheckedCoordinate<output>>},
  -coordinates: {Shape.coordinate_values(output, coordinate) == [row, column] : List<&2, U32>},
  -word_exact: {U32.to_nat(U32.from_nat(cursor)) == cursor : Nat},
  prefix: Laws.ProductPrefix<inner, left, right, a, b, output, before_a, before_b, before, cursor>,
  dot: Laws.DotMeaning<U32.to_nat(inner), left, right, before_a, before_b, row, column, 0n, 0.0, after_a, after_b, value>,
  update: Core.CheckedUpdateMeaning(output, before, U32.from_nat(cursor), value, (after, Done{Unit{}}))) ->
  Laws.ProductPrefix<inner, left, right, a, b, output, after_a, after_b, after, 1n+cursor>:
  Laws.ProductPrefix{left_prior, right_prior, cells} = prefix
  Laws.DotMeaning{factors, logical, fold, left_kept, right_kept} = dot
  (checked, pair) = update
  (observed, frame) = pair
  Laws.ProductPrefix{other => Equal.trans(Maybe<&2, F32>, Core.checked_observe(left, after_a, other),
      Core.checked_observe(left, before_a, other), Core.checked_observe(left, a, other), left_kept(other), left_prior(other)),
    other => Equal.trans(Maybe<&2, F32>, Core.checked_observe(right, after_b, other),
      Core.checked_observe(right, before_b, other), Core.checked_observe(right, b, other), right_kept(other), right_prior(other)),
    position => earlier => prefix_cell_case(inner, left, right, a, b, output, after, cursor, position,
      Laws.ProductCell{row, column, coordinate, decoded, coordinates, word_exact, factors,
        logical_dot_original(U32.to_nat(inner), left, right, a, b, before_a, before_b, row, column, 0n, factors, logical, left_prior, right_prior),
        value, fold, checked, observed},
      position => earlier => frame_cell(inner, left, right, a, b, output, before, after, cursor, position, cells(position, earlier), word_exact, earlier, frame),
      earlier_split(position, cursor, earlier))}

Uses (26):
  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=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.from_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Unit
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=CheckedCoordinate
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=Error
  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=coordinate_values
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=unflatten_checked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=CheckedUpdateMeaning
  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/core.bend&name=checked_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=DotMeaning
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=ProductCell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_LAWS.bend&name=ProductPrefix
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=earlier_split
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=frame_cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=logical_dot_original
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend&name=prefix_cell_case