List.nth_update_other: 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 162-173 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=162&end_line=173

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/spec/lib/common.bend as SC

def nth_update_other(-A: Data, +xs: List<&2, A>, +i: Nat, +j: Nat, +v: A, +ne: {Nat.is_eq(i, j) == False{} : Bool}) -> {SC.nth(A, SC.update(A, xs, i, v), j) == SC.nth(A, xs, j) : Maybe<&2, A>}:
  match xs i j:
    case Nil{} _ _:
      {==}
    case Con{h, t} 0n 0n:
      Empty.absurd({Some{v} == Some{h} : Maybe<&2, A>}, L.true_false(ne))
    case Con{h, t} 0n 1n+q:
      {==}
    case Con{h, t} 1n+p 0n:
      {==}
    case Con{h, +t} 1n+p 1n+q:
      nth_update_other(A, t, p, q, v, ne)

Uses (9):
  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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  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_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend&name=true_false
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=nth
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-math@1.0.0.0/spec/lib/common.bend&name=update