ReduceFoldPROOF.source_inside: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_fold_PROOF.bend as ReduceFoldPROOF
Lines 186-203 of bendtorch-core@0.1.0.0/src/autograd/reduce_fold_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fold_PROOF.bend&start_line=186&end_line=203

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/broadcast_proof.bend as BroadcastProof
import bendtorch-core@0.1.0.0/src/autograd/reduce_fold.bend as ReduceFold

def source_inside(+plan: Shape.BroadcastPlan, +index: U32, +count: Nat,
  +room: {Nat.is_le(count, Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan)))) == True{} : Bool}) ->
  {Pointwise.inside(~ReduceFold.Cell, ~ReduceFold.source, ReduceFold.Cell{plan, index}, count,
    Shape.logical_numel(Shape.dimensions(Shape.right_shape(plan)))) == True{} : Bool}:
  match count:
    case 0n:
      {==}
    case 1n+previous:
      +cell : ReduceFold.Cell = ReduceFold.Cell{plan, index}
      +limit = Shape.logical_numel(Shape.dimensions(Shape.output_shape(plan)))
      +bound = Shape.logical_numel(Shape.dimensions(Shape.right_shape(plan)))
      %Equal.sym(Bool, Pointwise.inside(~ReduceFold.Cell, ~ReduceFold.source, cell, previous, bound), True{},
        source_inside(plan, index, previous, Conversion.le_predecessor(previous, limit, room))) :
        {Bool.and(_, Nat.is_lt(ReduceFold.source(cell, previous), bound)) == True{} : Bool}
      %Equal.sym(Bool, Nat.is_lt(ReduceFold.source(cell, previous), bound), True{},
        BroadcastProof.right_walk_bound(plan, Shape.index_map(plan), previous, Conversion.le_successor_lt(previous, limit, room))) :
        {Bool.and(True{}, _) == True{} : Bool}
      {==}

Uses (19):
  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=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=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fold.bend&name=Cell
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_fold.bend&name=source
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=BroadcastPlan
  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=index_map
  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=output_shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=right_shape
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/contracts/broadcast_proof.bend&name=right_walk_bound
  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