Perm.perm_append_comm: def of bend-mathlib@0.8.1.0
Import: import bend-mathlib@0.8.1.0/perm.bend as Perm
Lines 169-175 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=169&end_line=175

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

# Appending commutes up to permutation (derived without symmetry).
def perm_append_comm(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>) -> K.perm(A, List.append(&2, A, xs, ys), List.append(&2, A, ys, xs)):
  match xs:
    case Nil{}:
      (Nil{}, Equal.sym(List<&2, A>, List.append(&2, A, ys, Nil{}), ys, internal_append_nil(A, ys)))
    case +x <> r:
      perm_trans(A, x <> List.append(&2, A, r, ys), x <> List.append(&2, A, ys, r), List.append(&2, A, ys, x <> r), perm_cons(A, x, List.append(&2, A, r, ys), List.append(&2, A, ys, r), perm_append_comm(A, r, ys)), perm_move_rev(A, ys, x, r))

Uses (9):
  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.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Sigma
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=internal_append_nil
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=perm_cons
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=perm_move_rev
  https://jend.leeeet.dev/definition.txt?path=bend-mathlib@0.8.1.0/perm.bend&name=perm_trans
  https://jend.leeeet.dev/definition.txt?path=bendlib-kernel-list@1.0.0.0/list.bend&name=perm