List.length_append: def of bend-collections-laws-math@1.0.0.0
Import: import bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend as List
Lines 25-30 of bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&start_line=25&end_line=30

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC

def length_append(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>) -> {SC.length(A, SC.append(A, xs, ys)) == Nat.add(SC.length(A, xs), SC.length(A, ys)) : Nat}:
  match xs:
    case Nil{}:
      {==}
    case Con{+h, +t}:
      N.succ_cong(SC.length(A, SC.append(A, t, ys)), Nat.add(SC.length(A, t), SC.length(A, ys)), length_append(A, t, ys))

Uses (6):
  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=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=succ_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=append
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=length