def ckp.head

bend-osdev-acpi@0.1.2.0 · PROOF_checksum.bend:189

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

189def ckp.head(+d: B.Octets, +hd: {Nat.is_le(1n, B.Octets.len(d)) == True{} : Bool}) -> {ckp.ns(B.Octets.to_list(d)) == Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(d, 0n), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) : Nat}:
190  %BL.octets_take_drop(1n, d) : {ckp.ns(B.Octets.to_list(_)) == Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(d, 0n), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) : Nat}
191  %Equal.sym(List<&2, U32>, B.Octets.to_list(B.Octets.append(B.Octets.take(1n, d), B.Octets.drop(1n, d))), B.append(B.Octets.to_list(B.Octets.take(1n, d)), B.Octets.to_list(B.Octets.drop(1n, d))), BL.octets_append_list(B.Octets.take(1n, d), B.Octets.drop(1n, d))) : {ckp.ns(_) == Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(d, 0n), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) : Nat}
192  %Equal.sym(Nat, ckp.ns(B.append(B.Octets.to_list(B.Octets.take(1n, d)), B.Octets.to_list(B.Octets.drop(1n, d)))), Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(1n, d))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))), ckp.nsapp(B.Octets.to_list(B.Octets.take(1n, d)), B.Octets.to_list(B.Octets.drop(1n, d)))) : {_ == Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, B.Octets.at(d, 0n), 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) : Nat}
193  %BL.octets_at_take(1n, d, 0n, {==}) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(1n, d))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) == Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, _, 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) : Nat}
194  %Equal.sym(Maybe<&2, U32>, B.Octets.at(B.Octets.take(1n, d), 0n), B.at(B.Octets.to_list(B.Octets.take(1n, d)), 0n), BL.octets_at_list(B.Octets.take(1n, d), 0n)) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(1n, d))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) == Nat.add(U32.to_nat(U32.and(255, Maybe.default(&2, U32, _, 0))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) : Nat}
195  %ckp.one(B.Octets.to_list(B.Octets.take(1n, d)), Equal.trans(Nat, B.len(B.Octets.to_list(B.Octets.take(1n, d))), B.Octets.len(B.Octets.take(1n, d)), 1n, Equal.sym(Nat, B.Octets.len(B.Octets.take(1n, d)), B.len(B.Octets.to_list(B.Octets.take(1n, d))), BL.octets_len_list(B.Octets.take(1n, d))), BL.octets_len_take_le(1n, d, hd))) : {Nat.add(ckp.ns(B.Octets.to_list(B.Octets.take(1n, d))), ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) == Nat.add(_, ckp.ns(B.Octets.to_list(B.Octets.drop(1n, d)))) : Nat}
196  {==}