PROOF.off.take_take: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 874-883 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=874&end_line=883

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

def off.take_take(+i: Nat, +j: Nat, ws: List<&2, B.OctByte>) -> {B.w8s.take(i, B.w8s.take(j, ws)) == B.w8s.take(Nat.min(i, j), ws) : List<&2, B.OctByte>}:
  match i j ws:
    case 0n _ _:
      {==}
    case 1n+p 0n _:
      {==}
    case 1n+p 1n+q Nil{}:
      {==}
    case 1n+p 1n+q Con{x, t}:
      Equal.cong(List<&2, B.OctByte>, List<&2, B.OctByte>, l => Con{x, l}, B.w8s.take(p, B.w8s.take(q, t)), B.w8s.take(Nat.min(p, q), t), off.take_take(p, q, t))

Uses (6):
  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.min
  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