law all_eq_not_any_not_sym

bend-mathlib@0.8.1.0 · list.bend:3110

import Base

3110# All elements satisfy f exactly when no element fails it, reversed to rewrite toward the simple side.
3111law all_eq_not_any_not_sym:
3112  for ~a: Quant
3113  for ~A: Kind(a)
3114  for ~f: A -> Bool
3115  for xs: List<a, A>
3116  {Bool.not(List.any(~a, ~A, ~(x => Bool.not(f(x))), xs)) == List.all(~a, ~A, ~f, xs) : Bool}