law any_filter

bend-mathlib@0.8.1.0 · list.bend:1475

import Base

1475# Any over a filter looks for q only where p holds: any q (filter p xs) = any (p and q) xs.
1476law any_filter:
1477  for ~A: Data
1478  for ~p: A -> Bool
1479  for ~q: A -> Bool
1480  for xs: List<&2, A>
1481  {List.any(~&2, ~A, ~q, List.filter(~A, ~p, xs)) == List.any(~&2, ~A, ~(+x => Bool.and(p(x), q(x))), xs) : Bool}