ProofFastFind.run_skip: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_fast_find.bend as ProofFastFind
Lines 185-195 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=185&end_line=195

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

# No c in xs, and n reaches past it: the search goes on in ys.
law run_skip:
  for +xs: List<&2, U32>
  for +ys: List<&2, U32>
  for +n: Nat
  for +c: U32
  for +b: Bool
  for +hb: {hd_eq(xs, c) == b : Bool}
  for +h: {D.run_len(xs, c) == List.length(&2, U32, xs) : Nat}
  for +hn: {Nat.is_le(List.length(&2, U32, xs), n) == True{} : Bool}
  {D.run_len(List.take(&2, U32, List.append(&2, U32, xs, ys), n), c) == Nat.add(List.length(&2, U32, xs), D.run_len(List.take(&2, U32, ys, Nat.sub(n, List.length(&2, U32, xs))), c)) : Nat}

Uses (20):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  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_le
  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=lawful-arrays@0.1.0.0/proof_base.bend&name=false_ne_true
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  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/proof_fast_find.bend&name=hd_eq
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=sub_zero
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=succ_inj
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=zero_ne_succ