DotProof.left_below: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/tensor/contracts/dot_proof.bend as DotProof
Lines 65-73 of bendtorch-core@0.1.0.0/src/tensor/contracts/dot_proof.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/dot_proof.bend&start_line=65&end_line=73

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend as Nats
import bendtorch-core@0.1.0.0/src/tensor/contracts/dot.bend as Dot

def left_below(+rows: Nat, +inner: Nat, +columns: Nat, +row: Nat, +column: Nat,
  row_below: {Nat.is_lt(row, rows) == True{} : Bool}, +left: Shape.Shape,
  left_extents: {Shape.extents(left) == [rows, inner] : List<&2, Nat>}, +k: Nat, below: {Nat.is_lt(k, inner) == True{} : Bool}) ->
  {Nat.is_lt(Dot.left_index(Dot.Cell{row, column, inner, columns}, k), Shape.logical_numel(Shape.dimensions(left))) == True{} : Bool}:
  %Equal.sym(List<&2, Nat>, Shape.extents(left), [rows, inner], left_extents) :
    {Nat.is_lt(Nat.add(Nat.mul(row, inner), k), Shape.numel(_)) == True{} : Bool}
  %Equal.sym(Nat, Nat.mul(inner, 1n), inner, Nats.mul_one_right(inner)) :
    {Nat.is_lt(Nat.add(Nat.mul(row, inner), k), Nat.mul(rows, _)) == True{} : Bool}
  lt_mul_add(row, rows, k, inner, row_below, below)

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  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.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=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=extents
  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=numel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/nat_proofs.bend&name=mul_one_right
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/dot.bend&name=Cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/dot.bend&name=left_index
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/dot_proof.bend&name=lt_mul_add