DotProof.left_inside: 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 85-104 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=85&end_line=104

import Base
import bendtorch-core@0.1.0.0/src/shape/core.bend as Shape
import bendtorch-core@0.1.0.0/src/tensor/word_conversion.bend as Conversion
import bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend as Pointwise
import bendtorch-core@0.1.0.0/src/tensor/contracts/dot.bend as Dot

def left_inside(+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>}, +count: Nat,
  +room: {Nat.is_le(count, inner) == True{} : Bool}) ->
  {Pointwise.inside(~Dot.Cell, ~Dot.left_index, Dot.Cell{row, column, inner, columns}, count, Shape.logical_numel(Shape.dimensions(left))) == True{} : Bool}:
  match count:
    case 0n:
      {==}
    case 1n+previous:
      +cell : Dot.Cell = Dot.Cell{row, column, inner, columns}
      +bound = Shape.logical_numel(Shape.dimensions(left))
      %Equal.sym(Bool, Pointwise.inside(~Dot.Cell, ~Dot.left_index, cell, previous, bound), True{},
        left_inside(rows, inner, columns, row, column, row_below, left, left_extents, previous,
          Conversion.le_predecessor(previous, inner, room))) :
        {Bool.and(_, Nat.is_lt(Dot.left_index(cell, previous), bound)) == True{} : Bool}
      %Equal.sym(Bool, Nat.is_lt(Dot.left_index(cell, previous), bound), True{},
        left_below(rows, inner, columns, row, column, row_below, left, left_extents, previous,
          Conversion.le_successor_lt(previous, inner, room))) :
        {Bool.and(True{}, _) == True{} : Bool}
      {==}

Uses (17):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  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/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=left_below
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/pointwise.bend&name=inside
  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_successor_lt