law foldr_map_sym

bend-mathlib@0.8.1.0 · list.bend:2688

import Base

2688# A right fold over a map folds with the mapped function: foldr g z (map f xs) = foldr (g . f) z xs, reversed to rewrite toward the simple side.
2689law foldr_map_sym:
2690  for ~A: Type
2691  for ~B: Type
2692  for ~C: Type
2693  for ~f: A -> B
2694  for ~g: B -> C -> C
2695  for xs: List<A>
2696  for -z: C
2697  {List.foldr(~&1, ~A, ~C, ~(x => y => g(f(x), y)), xs, z) == List.foldr(~&1, ~B, ~C, ~g, List.map(~A, ~B, ~f, xs), z) : C}