MatmulPROOF.left_flat: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/matmul_PROOF.bend as MatmulPROOF
Lines 1336-1349 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=1336&end_line=1349

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/matmul.bend as Matrix
import bendtorch-core@0.1.0.0/src/shape/LAWS.bend as ShapeLaws
import bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend as MatrixIndex

def left_flat(+left: Shape.Shape, +rows: U32, +inner: U32, +row: Nat, +k: Nat,
  +le: {Shape.dimensions(left) == [rows, inner] : List<&2, U32>},
  +row_below: {Nat.is_lt(row, U32.to_nat(rows)) == True{} : Bool}, +below: {Nat.is_lt(k, U32.to_nat(inner)) == True{} : Bool}) ->
  {ShapeLaws.index_result(left, Shape.flatten_checked(left, [U32.from_nat(row), U32.from_nat(k)])) ==
    Some{Matrix.left_index(U32.to_nat(inner), row, k)} : Maybe<&2, U32>}:
  +k_exact = MatrixIndex.word_below(k, inner, below)
  +row_exact = MatrixIndex.word_below(row, rows, row_below)
  Equal.trans(Maybe<&2, U32>, ShapeLaws.index_result(left, Shape.flatten_checked(left, [U32.from_nat(row), U32.from_nat(k)])),
    Some{U32.from_nat(Nat.add(Nat.mul(U32.to_nat(U32.from_nat(row)), U32.to_nat(inner)), U32.to_nat(U32.from_nat(k))))},
    Some{U32.from_nat(Nat.add(Nat.mul(row, U32.to_nat(inner)), k))},
    MatrixIndex.flat_pair(left, rows, inner, U32.from_nat(row), U32.from_nat(k), le,
      MatrixIndex.lt_same(U32.to_nat(U32.from_nat(row)), row, U32.to_nat(rows), row_exact, row_below),
      MatrixIndex.lt_same(U32.to_nat(U32.from_nat(k)), k, U32.to_nat(inner), k_exact, below)),
    MatrixIndex.index_same(U32.to_nat(U32.from_nat(row)), U32.to_nat(U32.from_nat(k)), row, k, U32.to_nat(inner), row_exact, k_exact))

Uses (20):
  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=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=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  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=bendtorch-core@0.1.0.0/src/shape/LAWS.bend&name=index_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=flatten_checked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matmul.bend&name=left_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=flat_pair
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=index_same
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=lt_same
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/matrix_index_proof.bend&name=word_below