PROOF.AP.set_length: def of bend-osdev-array@0.1.0.1
Import: import bend-osdev-array@0.1.0.1/PROOF.bend as PROOF
Lines 1475-1482 of bend-osdev-array@0.1.0.1/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&start_line=1475&end_line=1482

import Base

def AP.set_length(-T: Data, xs: List<&2, T>, k: Nat, -v: T) -> {List.length(&2, T, List.set(&2, T, xs, k, v)) == List.length(&2, T, xs) : Nat}:
  match xs k:
    case Nil{} _:
      {==}
    case Con{x, t} 0n:
      {==}
    case Con{x, t} 1n+p:
      AP.succ_cong(List.length(&2, T, List.set(&2, T, t, p, v)), List.length(&2, T, t), AP.set_length(T, 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=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.set
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-array@0.1.0.1/PROOF.bend&name=AP.succ_cong