law any_filter_sym

bend-mathlib@0.8.1.0 · list.bend:2777

import Base

2777# Any over a filter looks for q only where p holds: any q (filter p xs) = any (p and q) xs, reversed to rewrite toward the simple side.
2778law any_filter_sym:
2779  for ~A: Data
2780  for ~p: A -> Bool
2781  for ~q: A -> Bool
2782  for xs: List<&2, A>
2783  {List.any(~&2, ~A, ~(+x => Bool.and(p(x), q(x))), xs) == List.any(~&2, ~A, ~q, List.filter(~A, ~p, xs)) : Bool}