ProofList.pl_r2_miss_step: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_list.bend as ProofList
Lines 398-409 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=398&end_line=409

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

law pl_r2_miss_step:
  for +x: U32
  for +t: List<&2, U32>
  for +c1: U32
  for +c2: U32
  for +r: Nat
  for +z: Bool
  for +k: Nat
  for +hz: {(U32.is_eq(x, c1) || U32.is_eq(x, c2)) == z : Bool}
  for +hk: {Nat.is_lt(k, Bool.pick(Nat, z, 0n, 1n+r)) == True{} : Bool}
  for ih: @k2: Nat -> {Nat.is_lt(k2, r) == True{} : Bool} -> {D.has2(t, k2, c1, c2) == False{} : Bool}
  {D.has2(Con{x, t}, 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=Bool.or
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.pick
  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_lt
  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_eq
  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_lt0