Perm.internal_apply_app: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/perm.bend as Perm
Lines 13-18 of bend-mathlib@0.8.1.0/perm.bend: https://jend.leeeet.dev/read.txt?path=bend-mathlib@0.8.1.0/perm.bend&start_line=13&end_line=18

import Base
import bendlib-kernel-list@1.0.0.0/list.bend as K

def internal_apply_app(-A: Data, +s1: List<&2, Nat>, +s2: List<&2, Nat>, +xs: List<&2, A>) -> {K.apply(A, List.append(&2, Nat, s1, s2), xs) == K.apply(A, s2, K.apply(A, s1, xs)) : List<&2, A>}:
  match s1:
    case Nil{}:
      {==}
    case +i <> rest:
      internal_apply_app(A, rest, s2, K.swap_at(A, i, xs))

Uses (5):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bendlib-kernel-list@1.0.0.0/list.bend&name=apply
  https://jend.leeeet.dev/definition.txt?path=bendlib-kernel-list@1.0.0.0/list.bend&name=swap_at