List.length_set_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 2948-2955 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=2948&end_line=2955

import Base

# Setting an element does not change the length, reversed to rewrite toward the simple side.
law length_set_sym:
  for -a: Quant
  for -A: Kind(a)
  for xs: List<a, A>
  for n: Nat
  for -x: A
  {List.length(a, A, xs) == List.length(a, A, List.set(a, A, xs, n, x)) : Nat}

Uses (6):
  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.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.set
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=length_set