PROOF.p_slice_take: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 1228-1233 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=1228&end_line=1233

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

def p_slice_take(+m: Nat, +i: Nat, +n: Nat, +o: B.Octets, +h: {Nat.is_le(Nat.add(i, n), m) == True{} : Bool}) -> {B.Octets.slice(i, n, B.Octets.take(m, o)) == B.Octets.slice(i, n, o) : B.Octets}:
  Equal.trans(B.Octets, B.Octets.take(n, B.Octets.drop(i, B.Octets.take(m, o))), B.Octets.take(n, B.Octets.take(Nat.sub(m, i), B.Octets.drop(i, o))), B.Octets.take(n, B.Octets.drop(i, o)),
    Equal.cong(B.Octets, B.Octets, x => B.Octets.take(n, x), B.Octets.drop(i, B.Octets.take(m, o)), B.Octets.take(Nat.sub(m, i), B.Octets.drop(i, o)), p_drop_take(i, m, o)),
    Equal.trans(B.Octets, B.Octets.take(n, B.Octets.take(Nat.sub(m, i), B.Octets.drop(i, o))), B.Octets.take(Nat.min(n, Nat.sub(m, i)), B.Octets.drop(i, o)), B.Octets.take(n, B.Octets.drop(i, o)),
      p_take_take(n, Nat.sub(m, i), B.Octets.drop(i, o)),
      Equal.cong(Nat, B.Octets, k => B.Octets.take(k, B.Octets.drop(i, o)), Nat.min(n, Nat.sub(m, i)), n, off.min_le(n, Nat.sub(m, i), off.le_sub(i, n, m, h)))))

Uses (16):
  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=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.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  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=off.le_sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=off.min_le
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=p_drop_take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=p_take_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.slice
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/bytes.bend&name=Octets.take