List.sc_drop_take: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend as List
Lines 368-380 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend&start_line=368&end_line=380

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

# drop l (take n xs) == take (n - l) (drop l xs)
def sc_drop_take(-A: Data, +xs: List<&2, A>, +n: Nat, +l: Nat) -> {SC.drop(A, SC.take(A, xs, n), l) == SC.take(A, SC.drop(A, xs, l), Nat.sub(n, l)) : List<&2, A>}:
  match xs n l:
    case Nil{} _ _:
      {==}
    case Con{a, t} 0n 0n:
      {==}
    case Con{a, t} 0n 1n+k:
      Equal.sym(List<&2, A>, SC.take(A, SC.drop(A, t, k), 0n), Nil{}, sc_take_zero(A, SC.drop(A, t, k)))
    case Con{a, t} 1n+m 0n:
      {==}
    case Con{a, t} 1n+m 1n+k:
      sc_drop_take(A, t, m, k)

Uses (7):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend&name=sc_take_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=take