def take_drop

bend-collections-laws-math@1.0.0.0 · proofs/lib/two_list.bend:17

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

17def 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>}:
18  match xs k:
19    case Nil{} _:
20      {==}
21    case Con{h, t} 0n:
22      {==}
23    case Con{h, t} 1n+p:
24      LL.cons_cong(T, h, SC.append(T, SC.take(T, t, p), SC.drop(T, t, p)), t, take_drop(T, t, p))