LAWS.array_find_list: law of bend-osdev-algo@0.1.0.0
Import: import bend-osdev-algo@0.1.0.0/LAWS.bend as LAWS
Lines 299-308 of bend-osdev-algo@0.1.0.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-algo@0.1.0.0/LAWS.bend&start_line=299&end_line=308

import Base
import bend-osdev-array@0.1.0.0/array.bend as AR
import bend-osdev-algo@0.1.0.0/bsearch.bend as S

law array_find_list:
  for +d: Nat
  for a: Array<U32>
  for hp: {AR.Arrays.is_perfect(U32, d, a) == True{} : Bool}
  for hd: {Nat.is_lt(d, 32n) == True{} : Bool}
  for n: U32
  for hn: {Nat.is_le(U32.to_nat(n), AR.Arrays.slots(d)) == True{} : Bool}
  for key: U32
  for hs: {S.bsearch.sorted(List.take(&2, U32, AR.Arrays.leaves(U32, a), U32.to_nat(n))) == True{} : Bool}
  {algo_index_nat(Pair.snd(Array<U32>, Maybe<&2, U32>, S.bsearch.array_find(a, n, key))) == S.bsearch.find(List.take(&2, U32, AR.Arrays.leaves(U32, a), U32.to_nat(n)), key) : Maybe<&2, Nat>}

Uses (19):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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=Pair.snd
  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=bend-osdev-algo@0.1.0.0/LAWS.bend&name=algo_index_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/PROOF.bend&name=ba.fl.ref
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.array_find
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.find
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-algo@0.1.0.0/bsearch.bend&name=bsearch.sorted
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/LAWS.bend&name=reflect
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.is_perfect
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.leaves
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/array.bend&name=Arrays.slots