List.is_empty_iff_length_eq_zero_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 3003-3008 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=3003&end_line=3008

import Base

# A list is empty exactly when its length is zero, reversed to rewrite toward the simple side.
law is_empty_iff_length_eq_zero_sym:
  for -a: Quant
  for -A: Kind(a)
  for xs: List<a, A>
  {Nat.is_eq(List.length(a, A, xs), 0n) == List.is_empty(a, A, xs) : 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=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.is_empty
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_eq
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=is_empty_iff_length_eq_zero