List.length_update: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend as List
Lines 100-107 of bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/list.bend&start_line=100&end_line=107

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

def length_update(-A: Data, +xs: List<&2, A>, +i: Nat, +v: A) -> {SC.length(A, SC.update(A, xs, i, v)) == SC.length(A, xs) : Nat}:
  match xs i:
    case Nil{} _:
      {==}
    case Con{h1, t} 0n:
      {==}
    case Con{h1, t} 1n+p:
      N.succ_cong(SC.length(A, SC.update(A, t, p, v)), SC.length(A, t), length_update(A, t, p, v))

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-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=update