law all_filter

bend-mathlib@0.8.1.0 · list.bend:1450

import Base

1450# All over a filter checks q only where p holds: all q (filter p xs) = all (not p or q) xs.
1451law all_filter:
1452  for ~A: Data
1453  for ~p: A -> Bool
1454  for ~q: A -> Bool
1455  for xs: List<&2, A>
1456  {List.all(~&2, ~A, ~q, List.filter(~A, ~p, xs)) == List.all(~&2, ~A, ~(+x => Bool.or(Bool.not(p(x)), q(x))), xs) : Bool}