ProofFastFind.fast_eq: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_find.bend as ProofFastFind
Lines 64-71 of lawful-bytes@0.1.1.0/proof_fast_find.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&start_line=64&end_line=71

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

# fast find on the mirror: the same Bytes, and the min of the loop's answer with to.
law fast_eq:
  for +len: U32
  for +t: P.Tree<U32>
  for +from: U32
  for +to: U32
  for +c: U32
  {FA.find(C.BT(len, t), from, to, c) == (C.BT(len, t), U32.min(FG(FA.words(from, to), U32.is_zero(M0(t, from, FA.rep(c))), (from >> 2n : U32), M0(t, from, FA.rep(c)), FA.rep(c), t), to)) : D.Bytes & U32}

Uses (26):
  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=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_zero
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.min
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shrn
  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/defs.bend&name=Bytes
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=find
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=find.fin
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=find.go
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=find.k
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=find.start
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=rep
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=words
  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=WD
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=FG
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=M0
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=fg_eq