ReduceLAWS.reduce_empty_zeros: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend as ReduceLAWS
Lines 144-150 of bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend&start_line=144&end_line=150

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/elementwise_totality.bend as Totality
import bendtorch-core@0.1.0.0/src/autograd/reduce.bend as Reduce

# Reducing an empty contribution gives zeros at every target position, not an
# empty tensor: for example [0, 3] reduced to [1, 3] is three zeros.
law reduce_empty_zeros:
  for input: Core.Dynamic
  for +target: Shape.Shape
  for empty: {Shape.logical_numel(Totality.dimensions(input)) == 0n : Nat}
  Zeros<target, Reduce.reduce_to(input, target)>

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce.bend&name=reduce_to
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_LAWS.bend&name=Zeros
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/reduce_PROOF.bend&name=planned_zeros
  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=broadcast_checked
  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/plan_proofs.bend&name=broadcast_checked_plan
  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/elementwise_totality.bend&name=dimensions