TwoList.take_drop: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/two_list.bend as TwoList
Lines 17-24 of bend-collections-laws-math@1.0.0.0/proofs/lib/two_list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/two_list.bend&start_line=17&end_line=24

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend as LL
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def take_drop(-T: Data, +xs: List<&2, T>, +k: Nat) -> {SC.append(T, SC.take(T, xs, k), SC.drop(T, xs, k)) == xs : List<&2, T>}:
  match xs k:
    case Nil{} _:
      {==}
    case Con{h, t} 0n:
      {==}
    case Con{h, t} 1n+p:
      LL.cons_cong(T, h, SC.append(T, SC.take(T, t, p), SC.drop(T, t, p)), t, take_drop(T, t, p))

Uses (6):
  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=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&name=cons_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=append
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=take