List.foldl_map_sym: law of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/list.bend as List
Lines 2702-2711 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=2702&end_line=2711

import Base

# A left fold over a map folds with the mapped function: foldl g z (map f xs) = foldl (fun acc x => g acc (f x)) z xs, reversed to rewrite toward the simple side.
law foldl_map_sym:
  for ~A: Type
  for ~B: Type
  for ~C: Type
  for ~f: A -> B
  for ~g: C -> B -> C
  for xs: List<A>
  for -z: C
  {List.foldl(~&1, ~A, ~C, ~(x => y => g(x, f(y))), xs, z) == List.foldl(~&1, ~B, ~C, ~g, List.map(~A, ~B, ~f, xs), z) : C}

Uses (5):
  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.foldl
  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=foldl_map