ProofSame.at2_eq: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_same.bend as ProofSame
Lines 571-576 of lawful-bytes@0.1.1.0/proof_same.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_same.bend&start_line=571&end_line=576

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-bytes@0.1.1.0/bytes.bend as B
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-arrays@0.1.0.0/proof_tree.bend as P

law at2_eq:
  for +len: U32
  for +t: P.Tree<U32>
  for +i: U32
  for +j: U32
  {B.at2(C.BT(len, t), i, j) == (C.BT(len, t), (C.AT(len, t, i), C.AT(len, t, j))) : D.Bytes & (U32 & U32)}

Uses (13):
  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=Sigma
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  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-bytes@0.1.1.0/bytes.bend&name=at
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=at2
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=at2.fin
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=at2.fin2
  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=BT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=at_pair_t