ReducePROOF.natural_presence: def of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend as ReducePROOF
Lines 579-585 of bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend&start_line=579&end_line=585

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/word_conversion.bend as Conversion
import bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend as Laws

def natural_presence(+shape: Shape.Shape, tensor: Core.Tensor<shape>, +values: List<&2, F32>,
  -listed: Laws.Listed(Core.Packed{shape, tensor}, values), +position: Nat, -within: Shape.LE(position, 1048576n)) ->
  Holds<{Nat.is_lt(position, List.length(&2, F32, values)) == Nat.is_lt(position, Shape.logical_numel(Shape.dimensions(shape))) : Bool}>:
  Holds{
    %Conversion.capacity_natural_word_exact(position, within) : {Nat.is_lt(_, List.length(&2, F32, values)) == Nat.is_lt(_, Shape.logical_numel(Shape.dimensions(shape))) : Bool}
    {\{Holds: proof => proof} : Holds<{Nat.is_lt(U32.to_nat(U32.from_nat(position)), List.length(&2, F32, values)) == Nat.is_lt(U32.to_nat(U32.from_nat(position)), Shape.logical_numel(Shape.dimensions(shape))) : Bool}> -> {Nat.is_lt(U32.to_nat(U32.from_nat(position)), List.length(&2, F32, values)) == Nat.is_lt(U32.to_nat(U32.from_nat(position)), Shape.logical_numel(Shape.dimensions(shape))) : Bool}}(
      same_presence(shape, tensor, values, listed, U32.from_nat(position)))}

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=List.length
  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_lt
  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/autograd/reduce_LAWS.bend&name=Listed
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend&name=Holds
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend&name=same_presence
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/shape/core.bend&name=LE
  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=logical_numel
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=Dynamic
  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/word_conversion.bend&name=capacity_natural_word_exact