PROOF.p_take_drop: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 1152-1157 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=1152&end_line=1157

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

def p_take_drop(+i: Nat, +j: Nat, +o: B.Octets) -> {B.Octets.take(i, B.Octets.drop(j, o)) == B.Octets.drop(j, B.Octets.take(Nat.add(j, i), o)) : B.Octets}:
  match o:
    case B.Octets{+ws}:
      %F_take(i, B.w8s.drop(j, ws)) : {B.Octets{_} == B.Octets{B.w8s.drop(j, B.w8s.take.fast(Nat.add(j, i), ws))} : B.Octets}
      %F_take(Nat.add(j, i), ws) : {B.Octets{B.w8s.take(i, B.w8s.drop(j, ws))} == B.Octets{B.w8s.drop(j, _)} : B.Octets}
      Equal.cong(List<&2, B.OctByte>, B.Octets, l => B.Octets{l}, B.w8s.take(i, B.w8s.drop(j, ws)), B.w8s.drop(j, B.w8s.take(Nat.add(j, i), ws)), off.take_drop(i, j, ws))

Uses (13):
  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=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_take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=off.take_drop
  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.drop
  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.drop
  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