List.all_map_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 2788-2795 of bend-mathlib@0.8.1.0/list.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/list.bend&start_line=2788&end_line=2795

import Base

# All over a map checks the composed predicate: all p (map f xs) = all (p . f) xs, reversed to rewrite toward the simple side.
law all_map_sym:
  for ~A: Type
  for ~B: Type
  for ~f: A -> B
  for ~p: B -> Bool
  for xs: List<A>
  {List.all(~&1, ~A, ~(x => p(f(x))), xs) == List.all(~&1, ~B, ~p, List.map(~A, ~B, ~f, xs)) : Bool}

Uses (6):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.all
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.map
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/list.bend&name=all_map