ProofFind.find_pair_t: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_find.bend as ProofFind
Lines 135-141 of lawful-bytes@0.1.1.0/proof_find.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_find.bend&start_line=135&end_line=141

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 find_pair_t:
  for +len: U32
  for +t: P.Tree<U32>
  for +from: U32
  for +to: U32
  for +c: U32
  {B.find(C.BT(len, t), from, to, c) == (C.BT(len, t), Pair.snd(D.Bytes, U32, B.find(C.BT(len, t), from, to, c))) : D.Bytes & U32}

Uses (19):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_eq
  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-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=find
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=find.go
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=find.start
  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
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_find.bend&name=fgo_pair