List.update_append_right: 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 90-98 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=90&end_line=98

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
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 update_append_right(-A: Data, +xs: List<&2, A>, +ys: List<&2, A>, +i: Nat, +v: A, +h: {Nat.is_le(SC.length(A, xs), i) == True{} : Bool}) -> {SC.update(A, SC.append(A, xs, ys), i, v) == SC.append(A, xs, SC.update(A, ys, Nat.sub(i, SC.length(A, xs)), v)) : List<&2, A>}:
  match xs i:
    case Nil{} _:
      %Equal.sym(Nat, Nat.sub(i, 0n), i, N.sub_zero(i)) : {SC.update(A, ys, i, v) == SC.update(A, ys, _, v) : List<&2, A>}
      {==}
    case Con{h1, t} 0n:
      Empty.absurd({SC.update(A, SC.append(A, Con{h1, t}, ys), 0n, v) == SC.append(A, Con{h1, t}, SC.update(A, ys, Nat.sub(0n, 1n+SC.length(A, t)), v)) : List<&2, A>}, L.false_true(h))
    case Con{+h1, t} 1n+p:
      cons_cong(A, h1, SC.update(A, SC.append(A, t, ys), p, v), SC.append(A, t, SC.update(A, ys, Nat.sub(p, SC.length(A, t)), v)), update_append_right(A, t, ys, p, v, h))

Uses (13):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/list.bend&name=cons_cong
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=false_true
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend&name=sub_zero
  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
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=update