List.all_eq_not_any_not_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 3110-3116 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=3110&end_line=3116

import Base

# All elements satisfy f exactly when no element fails it, reversed to rewrite toward the simple side.
law all_eq_not_any_not_sym:
  for ~a: Quant
  for ~A: Kind(a)
  for ~f: A -> Bool
  for xs: List<a, A>
  {Bool.not(List.any(~a, ~A, ~(x => Bool.not(f(x))), xs)) == List.all(~a, ~A, ~f, 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=Bool.not
  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.any
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=all_eq_not_any_not