ProofCore.at_val: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_core.bend as ProofCore
Lines 57-61 of lawful-bytes@0.1.1.0/proof_core.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&start_line=57&end_line=61

import Base
import lawful-words@0.1.0.0/defs.bend as W
import lawful-arrays@0.1.0.0/proof_tree.bend as P

law at_val:
  for +len: U32
  for +t: P.Tree<U32>
  for +i: U32
  {AT(len, t, i) == W.byte(WD(t, (i >> 2n : U32)), U32.to_nat((i .&. 3 : U32))) : U32}

Uses (18):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Array.get
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Pair.snd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=fromT
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=get_pair_t
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=at.fin
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=Bytes
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=AT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=WD
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=byte