/- ──────────────────────────────────────────────────────────────────────────────
   gen/SlhVerify/FunsExternal.lean — hand-maintained external functions.

   TWO CLASSES of external, per honesty invariants H4/H5:

   (1) THE CRYPTOGRAPHIC BOUNDARY — the deliberate opaque axioms.
       The five SLH-DSA-SHA2-128s hash primitives, reached by name from the
       monomorphic verify path (verify_mono::oracle):
         · verify_mono.oracle.f      — F  (chain / FORS leaf)
         · verify_mono.oracle.h      — H  (Merkle node)
         · verify_mono.oracle.t_l    — T_len (WOTS+ pk compression)
         · verify_mono.oracle.t_len  — T_k   (FORS root compression)
         · verify_mono.oracle.h_msg  — H_msg (message digest)
       These are SHA-256-based; their correctness against FIPS 180-4 is the
       standing hash-oracle boundary (see TRUSTED-BASE.md). The apex
       certificate carries EXACTLY these five beyond Lean's three kernel
       axioms — nothing else.
       NOTE, so a future reader is not misled: these are five AXIOMS but only
       FOUR distinct Rust primitives. `oracle.t_l` and `oracle.t_len` both
       delegate to `crate::hashers::sha2_cat_1::t_l` (src/verify_mono.rs) —
       modelling them as two INDEPENDENT axioms is deliberately conservative
       (a theorem proved for unrelated oracles also holds when they coincide),
       but the model cannot express that they agree. Note also the naming
       inversion against FIPS 205: `oracle.t_l` models T_len (WOTS+ pk
       compression) and `oracle.t_len` models T_k (FORS root compression).

   (2) TRANSPILER PLUMBING — core-library externals Aeneas emits for this
       extraction config. These carry NO cryptographic content. The u32
       range Step machinery is DISCHARGED below with real definitions
       (2026-07-22). The try_from / is_err / &u32-Sub / wots-Take /
       Debug-fmt axioms were ELIMINATED at source level by the
       fips205-source de-plumbing patch (8 sites, semantics identical,
       differential-test-validated) and their declarations deleted here
       (dead-stub rule, 2026-07-23). De-plumbing round 2 (2026-07-24) then
       removed the LAST iterator adapters: helpers::to_int's Take and base_2b's
       IterMut became index loops, so the Take::next axiom was deleted too.
       Remaining as axioms on the whole model: the FIVE SHA-2 verify-path
       oracles and three zeroize blanket impls (never on the verify path) —
       nothing else. The in-Lean audit (Proofs/Audit.lean, `collectAxioms`,
       round 5) confirms only the five oracles + the kernel three appear in any
       certificate cone, and that no other declaration in the audited modules
       reaches outside that boundary. The zeroize axioms are deliberately
       absent from the audit's `allowedBoundary`, so if one ever reached a cone
       the build would fail. THIS FILE is hand-maintained (Aeneas does not
       regenerate it) and its bytes are sha256-pinned by check.sh Phase 0.
   ────────────────────────────────────────────────────────────────────────────── -/
import Aeneas
import SlhVerify.Types
open Aeneas Aeneas.Std Result ControlFlow Error
set_option linter.dupNamespace false
set_option linter.hashCommand false
set_option linter.unusedVariables false

/- You can set the `maxHeartbeats` value with the `-max-heartbeats` CLI option -/
set_option maxHeartbeats 1000000

/- You can set the `maxRecDepth` value with the `-max-recdepth` CLI option -/
set_option maxRecDepth 2048
open fips205

-- (the core::iter::adapters::take::Take::next axiom was here; DELETED
-- 2026-07-24 after de-plumbing round 2 removed the last Take iterator on the
-- verify path — to_int/base_2b now index-loop. dead-stub hygiene rule.)

/-- [core::iter::range::{impl core::iter::range::Step for u32}::backward_checked]:
    Source: '/rustc/library/core/src/iter/range.rs', lines 290:16-290:74
    Name pattern: [core::iter::range::{core::iter::range::Step<u32>}::backward_checked]
    Visibility: public -/
-- DISCHARGED (2026-07-22, proof phase): Aeneas.Std ships a real `Step`
-- instance only for `usize` (StepUsize); u32 ranges therefore extracted as
-- opaque axioms. These are the FAITHFUL models of Rust's `impl Step for u32`
-- (core/src/iter/range.rs), mirroring StepUsize: forward/backward via
-- u32::try_from(n)-then-checked_{add,sub}; steps_between = saturating
-- difference. Real defs, axiom-clean — so the range-loop cones (chain, and
-- every layer above) carry no plumbing axiom, only the kernel three + the
-- five hash oracles. NOT the deployed hash boundary; ordinary loop control.
@[rust_fun
  "core::iter::range::{core::iter::range::Step<u32>}::backward_checked"]
def U32.Insts.CoreIterRangeStep.backward_checked
  : Std.U32 → Std.Usize → Result (Option Std.U32) :=
  fun start n =>
    if h : n.val < 2 ^ 32 then
      ok (Std.U32.checked_sub start (Std.U32.ofNatCore n.val (by omega)))
    else ok none

/-- [core::iter::range::{impl core::iter::range::Step for u32}::forward_checked]:
    Source: '/rustc/library/core/src/iter/range.rs', lines 282:16-282:73
    Name pattern: [core::iter::range::{core::iter::range::Step<u32>}::forward_checked]
    Visibility: public -/
@[rust_fun
  "core::iter::range::{core::iter::range::Step<u32>}::forward_checked"]
def U32.Insts.CoreIterRangeStep.forward_checked
  : Std.U32 → Std.Usize → Result (Option Std.U32) :=
  fun start n =>
    if h : n.val < 2 ^ 32 then
      ok (Std.U32.checked_add start (Std.U32.ofNatCore n.val (by omega)))
    else ok none

/-- [core::iter::range::{impl core::iter::range::Step for u32}::steps_between]:
    Source: '/rustc/library/core/src/iter/range.rs', lines 271:16-271:84
    Name pattern: [core::iter::range::{core::iter::range::Step<u32>}::steps_between]
    Visibility: public -/
@[rust_fun "core::iter::range::{core::iter::range::Step<u32>}::steps_between"]
def U32.Insts.CoreIterRangeStep.steps_between
  : Std.U32 → Std.U32 → Result (Std.Usize × (Option Std.Usize)) :=
  fun start end_ =>
    if h : start.val > end_.val then ok (0#usize, none)
    else
      let steps := Std.Usize.ofNatCore (end_.val - start.val) (by scalar_tac)
      ok (steps, some steps)

/-- [zeroize::{impl zeroize::Zeroize for Z}::zeroize]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/zeroize-1.9.0/src/lib.rs', lines 274:4-274:25
    Name pattern: [zeroize::{zeroize::Zeroize<@Z>}::zeroize]
    Visibility: public -/
@[rust_fun "zeroize::{zeroize::Zeroize<@Z>}::zeroize"]
axiom zeroize.Zeroize.Blanket.zeroize
  {Z : Type} (DefaultIsZeroesInst : zeroize.DefaultIsZeroes Z) : Z → Result Z

/-- [zeroize::{impl zeroize::Zeroize for [Z; N]}::zeroize]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/zeroize-1.9.0/src/lib.rs', lines 346:4-346:25
    Name pattern: [zeroize::{zeroize::Zeroize<[@Z; @N]>}::zeroize]
    Visibility: public -/
@[rust_fun "zeroize::{zeroize::Zeroize<[@Z; @N]>}::zeroize"]
axiom Array.Insts.ZeroizeZeroize.zeroize
  {Z : Type} {N : Std.Usize} (ZeroizeInst : zeroize.Zeroize Z) :
  Array Z N → Result (Array Z N)

/-- [zeroize::__internal::{impl zeroize::__internal::AssertZeroize for T}::zeroize_or_on_drop]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/zeroize-1.9.0/src/lib.rs', lines 846:8-846:40
    Name pattern: [zeroize::__internal::{zeroize::__internal::AssertZeroize<@T>}::zeroize_or_on_drop]
    Visibility: public -/
@[rust_fun
  "zeroize::__internal::{zeroize::__internal::AssertZeroize<@T>}::zeroize_or_on_drop"]
axiom zeroize.__internal.AssertZeroize.Blanket.zeroize_or_on_drop
  {T : Type} (ZeroizeInst : zeroize.Zeroize T) : T → Result T

/-- [fips205::verify_mono::oracle::f]:
    Source: 'src/verify_mono.rs', lines 49:4-51:5 -/
axiom verify_mono.oracle.f
  (N : Std.Usize) :
  Slice Std.U8 → types.Adrs → Slice Std.U8 → Result (Array Std.U8 N)

/-- [fips205::verify_mono::oracle::h]:
    Source: 'src/verify_mono.rs', lines 54:4-56:5 -/
axiom verify_mono.oracle.h
  (N : Std.Usize) :
  Slice Std.U8 → types.Adrs → Slice Std.U8 → Slice Std.U8 → Result
    (Array Std.U8 N)

/-- [fips205::verify_mono::oracle::t_l]:
    Source: 'src/verify_mono.rs', lines 60:4-64:5 -/
axiom verify_mono.oracle.t_l
  {X : Std.Usize} {N : Std.Usize} :
  Slice Std.U8 → types.Adrs → Array (Array Std.U8 N) X → Result (Array
    Std.U8 N)

/-- [fips205::verify_mono::oracle::t_len]:
    Source: 'src/verify_mono.rs', lines 69:4-73:5 -/
axiom verify_mono.oracle.t_len
  {X : Std.Usize} {N : Std.Usize} :
  Slice Std.U8 → types.Adrs → Array (Array Std.U8 N) X → Result (Array
    Std.U8 N)

/-- [fips205::verify_mono::oracle::h_msg]:
    Source: 'src/verify_mono.rs', lines 81:4-85:5 -/
axiom verify_mono.oracle.h_msg
  (M : Std.Usize) :
  Slice Std.U8 → Slice Std.U8 → Slice Std.U8 → Slice Std.U8 → Result
    (Array Std.U8 M)