PROOF.q_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 1174-1178 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=1174&end_line=1178

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

def q_take_app_le(+n: Nat, +xs: List<&2, B.OctByte>, +ys: List<&2, B.OctByte>, h: {Nat.is_le(n, List.length(&2, B.OctByte, xs)) == True{} : Bool}) -> {B.Octets{B.w8s.take.fast(n, B.w8s.append.fast(xs, ys))} == B.Octets{B.w8s.take.fast(n, xs)} : B.Octets}:
  %F_app(xs, ys) : {B.Octets{B.w8s.take.fast(n, _)} == B.Octets{B.w8s.take.fast(n, xs)} : B.Octets}
  %F_take(n, List.append(&2, B.OctByte, xs, ys)) : {B.Octets{_} == B.Octets{B.w8s.take.fast(n, xs)} : B.Octets}
  %F_take(n, xs) : {B.Octets{B.w8s.take(n, List.append(&2, B.OctByte, xs, ys))} == B.Octets{_} : B.Octets}
  Equal.cong(List<&2, B.OctByte>, B.Octets, l => B.Octets{l}, B.w8s.take(n, List.append(&2, B.OctByte, xs, ys)), B.w8s.take(n, xs), off.take_app_le(n, xs, ys, h))

Uses (15):
  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=F_app
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=F_take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=off.take_app_le
  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=Octets
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=w8s.append.fast
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=w8s.take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=w8s.take.fast