PROOF.p_len_slice: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 1110-1113 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=1110&end_line=1113

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

def p_len_slice(+i: Nat, +n: Nat, +o: B.Octets) -> {B.Octets.len(B.Octets.slice(i, n, o)) == Nat.min(n, Nat.sub(B.Octets.len(o), i)) : Nat}:
  Equal.trans(Nat, B.Octets.len(B.Octets.take(n, B.Octets.drop(i, o))), Nat.min(n, B.Octets.len(B.Octets.drop(i, o))), Nat.min(n, Nat.sub(B.Octets.len(o), i)),
    p_len_take(n, B.Octets.drop(i, o)),
    Equal.cong(Nat, Nat, k => Nat.min(n, k), B.Octets.len(B.Octets.drop(i, o)), Nat.sub(B.Octets.len(o), i), p_len_drop(i, o)))

Uses (12):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  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=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=p_len_drop
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=p_len_take
  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.len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.slice
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.take