PROOFChecksum.ckp.split: def of bend-osdev-acpi@0.1.2.0
Import: import bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend as PROOFChecksum
Lines 217-226 of bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend: https://jend.leeeet.dev/read.txt?path=bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend&start_line=217&end_line=226

import Base
import bend-osdev-bytes@0.1.1.1/bytes.bend as B
import bend-osdev-bytes@0.1.1.1/LAWS.bend as BL
import bend-osdev-u32@0.1.0.0/LAWS.bend as UL

def ckp.split(+i: Nat, +o: B.Octets, +h: {Nat.is_lt(i, B.Octets.len(o)) == True{} : Bool}) -> {ckp.ns(B.Octets.to_list(o)) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}:
  %BL.octets_take_drop(i, o) : {ckp.ns(B.Octets.to_list(_)) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  %Equal.sym(List<&2, U32>, B.Octets.to_list(B.Octets.append(B.Octets.take(i, o), B.Octets.drop(i, o))), B.append(B.Octets.to_list(B.Octets.take(i, o)), B.Octets.to_list(B.Octets.drop(i, o))), BL.octets_append_list(B.Octets.take(i, o), B.Octets.drop(i, o))) : {ckp.ns(_) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  %Equal.sym(Nat, ckp.ns(B.append(B.Octets.to_list(B.Octets.take(i, o)), B.Octets.to_list(B.Octets.drop(i, o)))), Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), ckp.ns(B.Octets.to_list(B.Octets.drop(i, o)))), ckp.nsapp(B.Octets.to_list(B.Octets.take(i, o)), B.Octets.to_list(B.Octets.drop(i, o)))) : {_ == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  %Equal.sym(Nat, ckp.ns(B.Octets.to_list(B.Octets.drop(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(B.Octets.drop(i, o), 0n), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, B.Octets.drop(i, o))))), ckp.head(B.Octets.drop(i, o), ckp.hdd(i, o, h))) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), _) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  %Equal.sym(Maybe<&2, U32>, B.Octets.at(B.Octets.drop(i, o), 0n), B.Octets.at(o, Nat.add(i, 0n)), BL.octets_at_drop(i, o, 0n)) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, _, 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, B.Octets.drop(i, o)))))) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  %Equal.sym(Nat, Nat.add(i, 0n), i, UL.nat_add_zero(i)) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, _), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, B.Octets.drop(i, o)))))) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  %Equal.sym(B.Octets, B.Octets.drop(1n, B.Octets.drop(i, o)), B.Octets.drop(Nat.add(i, 1n), o), BL.octets_drop_drop(i, 1n, o)) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(_)))) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  %UL.nat_add_comm(1n, i) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(_, o))))) == Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(i, o))), Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(o, i), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n+i, o))))) : Nat}
  {==}

Uses (29):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Maybe.default
  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_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend&name=ckp.hdd
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend&name=ckp.head
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend&name=ckp.ns
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-acpi@0.1.2.0/PROOF_checksum.bend&name=ckp.nsapp
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/LAWS.bend&name=octets_append_list
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/LAWS.bend&name=octets_at_drop
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/LAWS.bend&name=octets_drop_drop
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/LAWS.bend&name=octets_take_drop
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=Octets
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=Octets.append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=Octets.at
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=Octets.drop
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=Octets.len
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=Octets.take
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=Octets.to_list
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-bytes@0.1.1.1/bytes.bend&name=append
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_comm
  https://jend.leeeet.dev/definition.txt?path=bend-osdev-u32@0.1.0.0/LAWS.bend&name=nat_add_zero