Perm.internal_swap_at_length: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/perm.bend as Perm
Lines 316-326 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=316&end_line=326

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

def internal_swap_at_length(-A: Data, +i: Nat, +xs: List<&2, A>) -> {List.length(&2, A, K.swap_at(A, i, xs)) == List.length(&2, A, xs) : Nat}:
  match i:
    case 0n:
      internal_swap_head_length(A, xs)
    case 1n+p:
      match xs:
        case Nil{}:
          {==}
        case +x <> t:
          %Equal.sym(Nat, List.length(&2, A, K.swap_at(A, p, t)), List.length(&2, A, t), internal_swap_at_length(A, p, t)) : {1n+_ == 1n+List.length(&2, A, t) : Nat}
          {==}

Uses (6):
  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.length
  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_swap_head_length
  https://jend.leeeet.dev/definition.txt?path=bendlib-kernel-list@1.0.0.0/list.bend&name=swap_at