List.all_append_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 2494-2501 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=2494&end_line=2501

import Base

# All over an append is all over each part, joined by and, reversed to rewrite toward the simple side.
law all_append_sym:
  for ~a: Quant
  for ~A: Kind(a)
  for ~f: A -> Bool
  for xs: List<a, A>
  for -ys: List<a, A>
  {Bool.and(List.all(~a, ~A, ~f, xs), List.all(~a, ~A, ~f, ys)) == List.all(~a, ~A, ~f, List.append(a, A, xs, ys)) : Bool}

Uses (7):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  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.all
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=all_append