ReducePROOF.observed_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 551-563 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=551&end_line=563

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/transform_PROOF.bend as TransformProof

def observed_presence(+shape: Shape.Shape, tensor: Core.Tensor<shape>, +source: U32, +inside: Bool,
  -decision: {inside == Nat.is_lt(U32.to_nat(source), Shape.logical_numel(Shape.dimensions(shape))) : Bool}) ->
  Holds<{TransformProof.maybe_present(Core.checked_observe(shape, tensor, source)) == inside : Bool}>:
  match inside:
    case False{}:
      Holds{Equal.cong(Maybe<&2, F32>, Bool, TransformProof.maybe_present, Core.checked_observe(shape, tensor, source), None{},
        {\{Holds: proof => proof} : Holds<{Core.checked_observe(shape, tensor, source) == None{} : Maybe<&2, F32>}> -> {Core.checked_observe(shape, tensor, source) == None{} : Maybe<&2, F32>}}(
          absent_observation(shape, tensor, source, Equal.sym(Bool, False{}, Nat.is_lt(U32.to_nat(source), Shape.logical_numel(Shape.dimensions(shape))), decision))))}
    case True{}:
      Holds{{\{TransformProof.PresentObservation: value => equal =>
        Equal.cong(Maybe<&2, F32>, Bool, TransformProof.maybe_present, Core.checked_observe(shape, tensor, source), Some{value}, equal)} :
        TransformProof.PresentObservation<shape, tensor, source> -> {TransformProof.maybe_present(Core.checked_observe(shape, tensor, source)) == True{} : Bool}}(
        TransformProof.present_observation(shape, tensor, source, Equal.sym(Bool, True{}, Nat.is_lt(U32.to_nat(source), Shape.logical_numel(Shape.dimensions(shape))), decision)))}

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=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=F32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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=Base/base.bend&name=U32.to_nat
  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=absent_observation
  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=Tensor
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/core.bend&name=checked_observe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=PresentObservation
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=maybe_present
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/tensor/transform_PROOF.bend&name=present_observation