Perm.internal_apply_shift: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/perm.bend as Perm
Lines 20-25 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=20&end_line=25

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

def internal_apply_shift(-A: Data, +s: List<&2, Nat>, +x: A, +xs: List<&2, A>) -> {K.apply(A, internal_shift(s), x <> xs) == x <> K.apply(A, s, xs) : List<&2, A>}:
  match s:
    case Nil{}:
      {==}
    case +i <> rest:
      internal_apply_shift(A, rest, x, 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=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=internal_shift
  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