law all_eq_not_any_not

bend-mathlib@0.8.1.0 · list.bend:2041

import Base

2041# All elements satisfy f exactly when no element fails it.
2042law all_eq_not_any_not:
2043  for ~a: Quant
2044  for ~A: Kind(a)
2045  for ~f: A -> Bool
2046  for xs: List<a, A>
2047  {List.all(~a, ~A, ~f, xs) == Bool.not(List.any(~a, ~A, ~(x => Bool.not(f(x))), xs)) : Bool}