PROOF.p_take_append_add: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 1185-1193 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=1185&end_line=1193

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

def p_take_append_add(+a: B.Octets, +n: Nat, +b: B.Octets) -> {B.Octets.take(Nat.add(B.Octets.len(a), n), B.Octets.append(a, b)) == B.Octets.append(a, B.Octets.take(n, b)) : B.Octets}:
  match a b:
    case B.Octets{+xs} B.Octets{+ys}:
      %F_app(xs, ys) : {B.Octets{B.w8s.take.fast(Nat.add(B.w8s.len.fast(xs), n), _)} == B.Octets{B.w8s.append.fast(xs, B.w8s.take.fast(n, ys))} : B.Octets}
      %F_len(xs) : {B.Octets{B.w8s.take.fast(Nat.add(_, n), List.append(&2, B.OctByte, xs, ys))} == B.Octets{B.w8s.append.fast(xs, B.w8s.take.fast(n, ys))} : B.Octets}
      %F_take(Nat.add(List.length(&2, B.OctByte, xs), n), List.append(&2, B.OctByte, xs, ys)) : {B.Octets{_} == B.Octets{B.w8s.append.fast(xs, B.w8s.take.fast(n, ys))} : B.Octets}
      %F_take(n, ys) : {B.Octets{B.w8s.take(Nat.add(List.length(&2, B.OctByte, xs), n), List.append(&2, B.OctByte, xs, ys))} == B.Octets{B.w8s.append.fast(xs, _)} : B.Octets}
      %F_app(xs, B.w8s.take(n, ys)) : {B.Octets{B.w8s.take(Nat.add(List.length(&2, B.OctByte, xs), 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(Nat.add(List.length(&2, B.OctByte, xs), n), List.append(&2, B.OctByte, xs, ys)), List.append(&2, B.OctByte, xs, B.w8s.take(n, ys)), off.take_app_add(xs, n, ys))

Uses (19):
  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.add
  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_len
  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_add
  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=Octets.append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.take
  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.len.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