List.take_append_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 2573-2580 of bend-mathlib@0.8.1.0/list.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/list.bend&start_line=2573&end_line=2580

import Base

# Taking past the first part of an append keeps it and takes the rest from the second part, reversed to rewrite toward the simple side.
law take_append_sym:
  for -a: Quant
  for -A: Kind(a)
  for xs: List<a, A>
  for -ys: List<a, A>
  for -n: Nat
  {List.append(a, A, xs, List.take(a, A, ys, n)) == List.take(a, A, List.append(a, A, xs, ys), Nat.add(List.length(a, A, xs), n)) : List<a, A>}

Uses (8):
  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=bend-mathlib@0.8.1.0/list.bend&name=take_append