PROOF.p_slice_append_le: def of bend-osdev-bytes@0.1.1.0
Import: import bend-osdev-bytes@0.1.1.0/PROOF.bend as PROOF
Lines 1217-1223 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=1217&end_line=1223

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

def p_slice_append_le(+i: Nat, +n: Nat, +a: B.Octets, +b: B.Octets, +h: {Nat.is_le(Nat.add(i, n), B.Octets.len(a)) == True{} : Bool}) -> {B.Octets.slice(i, n, B.Octets.append(a, b)) == B.Octets.slice(i, n, a) : B.Octets}:
  Equal.trans(B.Octets, B.Octets.take(n, B.Octets.drop(i, B.Octets.append(a, b))), B.Octets.take(n, B.Octets.append(B.Octets.drop(i, a), b)), B.Octets.take(n, B.Octets.drop(i, a)),
    Equal.cong(B.Octets, B.Octets, x => B.Octets.take(n, x), B.Octets.drop(i, B.Octets.append(a, b)), B.Octets.append(B.Octets.drop(i, a), b), p_drop_append_le(i, a, b, off.le_add_l(i, n, B.Octets.len(a), h))),
    p_take_append_le(n, B.Octets.drop(i, a), b,
      Equal.trans(Bool, Nat.is_le(n, B.Octets.len(B.Octets.drop(i, a))), Nat.is_le(n, Nat.sub(B.Octets.len(a), i)), True{},
        Equal.cong(Nat, Bool, k => Nat.is_le(n, k), B.Octets.len(B.Octets.drop(i, a)), Nat.sub(B.Octets.len(a), i), p_len_drop(i, a)),
        off.le_sub(i, n, B.Octets.len(a), h))))

Uses (18):
  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.sub
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.0/PROOF.bend&name=off.le_add_l
  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=p_drop_append_le
  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_take_append_le
  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.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