PROOF.off.take_app_le: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 847-854 of bend-osdev-bytes@0.1.1.0/PROOF.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&start_line=847&end_line=854

import Base
import bend-osdev-bytes@0.1.1.0/bytes.bend as B

def off.take_app_le(+n: Nat, xs: List<&2, B.OctByte>, +ys: List<&2, B.OctByte>) -> {Nat.is_le(n, List.length(&2, B.OctByte, xs)) == True{} : Bool} -> {B.w8s.take(n, List.append(&2, B.OctByte, xs, ys)) == B.w8s.take(n, xs) : List<&2, B.OctByte>}:
  match n xs:
    case 0n _:
      h => {==}
    case 1n+p Nil{}:
      h => off.no({B.w8s.take(1n+p, ys) == Nil{} : List<&2, B.OctByte>}, h)
    case 1n+p Con{x, t}:
      h => Equal.cong(List<&2, B.OctByte>, List<&2, B.OctByte>, l => Con{x, l}, B.w8s.take(p, List.append(&2, B.OctByte, t, ys)), B.w8s.take(p, t), off.take_app_le(p, t, ys, h))

Uses (10):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  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=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=off.no
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=OctByte
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=w8s.take