LAWS.first_miss: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/LAWS.bend as LAWS
Lines 355-364 of lawful-bytes@0.1.1.0/LAWS.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/LAWS.bend&start_line=355&end_line=364

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

# No index from from up to the answer holds c.
law first_miss:
  for xs: List<&2, U32>
  for from: Nat
  for to: Nat
  for c: U32
  for k: Nat
  for hk1: {Nat.is_le(from, k) == True{} : Bool}
  for hk2: {Nat.is_lt(k, D.first(xs, from, to, c)) == True{} : Bool}
  {D.has(xs, k, c) == False{} : Bool}

Uses (9):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=first
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=has
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_list.bend&name=first_miss