BackwardLAWS.lookup_exact: law of bendtorch-core@0.1.0.0
Import: import bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend as BackwardLAWS
Lines 317-324 of bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend: https://jend.leeeet.dev/read.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_LAWS.bend&start_line=317&end_line=324

import Base
import bendtorch-core@0.1.0.0/src/autograd/backward.bend as Backward

# Ids (C2): id k reads exactly the element with k older elements, and an id
# the list does not hold reads None, never another element.
law lookup_exact:
  for -A: Data
  for +newer: List<&2, A>
  for +item: A
  for +rest: List<&2, A>
  {Backward.lookup(A, List.append(&2, A, newer, item <> rest), List.length(&2, A, rest)) == Some{item} : Maybe<&2, A>}

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=find
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=lookup
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward.bend&name=picked
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&name=append_ne
  https://jend.leeeet.dev/definition.txt?path=bendtorch-core@0.1.0.0/src/autograd/backward_PROOF.bend&name=eq_refl