ProofList.first2_miss: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_list.bend as ProofList
Lines 502-511 of lawful-bytes@0.1.1.0/proof_list.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_list.bend&start_line=502&end_line=511

import Base
import lawful-bytes@0.1.1.0/defs.bend as D

law first2_miss:
  for +xs: List<&2, U32>
  for +from: Nat
  for +to: Nat
  for +c1: U32
  for +c2: U32
  for +k: Nat
  for +hk1: {Nat.is_le(from, k) == True{} : Bool}
  for +hk2: {Nat.is_lt(k, D.first2(xs, from, to, c1, c2)) == True{} : Bool}
  {D.has2(xs, k, c1, c2) == False{} : Bool}

Uses (11):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=first2
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=has2
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_list.bend&name=pl_ft
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_list.bend&name=pl_r2_miss