ProofFastFind.nohit_run: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_find.bend as ProofFastFind
Lines 570-579 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=570&end_line=579

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_fast_word.bend as FW
import lawful-arrays@0.1.0.0/proof_tree.bend as P

# An unflagged word has no c from the start on.
law nohit_run:
  for +t: P.Tree<U32>
  for +wi: U32
  for +o: Nat
  for +v: U32
  for +c: U32
  for +hv: {FW.P0(v) == Nat.add(o, D.run_len(AW(t, wi, o), c)) : Nat}
  for +hz: {U32.is_zero(FA.zb(v)) == True{} : Bool}
  {D.run_len(AW(t, wi, o), c) == List.length(&2, U32, AW(t, wi, o)) : Nat}

Uses (19):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.is_zero
  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/defs.bend&name=run_len
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/fast.bend&name=zb
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=AW
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_find.bend&name=awl
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_word.bend&name=P0
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_fast_word.bend&name=zb_none
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=eq_sound
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=sub_add_l