-- THIS FILE WAS AUTOMATICALLY GENERATED BY AENEAS
-- [curve25519_dalek]: external functions.
-- This is a template file: rename it to "FunsExternal.lean" and fill the holes.
import Aeneas
import CurveField.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 curve25519_dalek

/-- [core::array::{impl core::hash::Hash for [T; N]}::hash]:
    Source: '/rustc/library/core/src/array/mod.rs', lines 349:4-349:50
    Name pattern: [core::array::{core::hash::Hash<[@T; @N]>}::hash]
    Visibility: public -/
@[rust_fun "core::array::{core::hash::Hash<[@T; @N]>}::hash"]
axiom Array.Insts.CoreHashHash.hash
  {T : Type} {H : Type} {N : Std.Usize} (hashHashInst : core.hash.Hash T)
  (hashHasherInst : core.hash.Hasher H) :
  Array T N → H → Result H

/-- [core::fmt::{impl core::fmt::Debug for [T]}::fmt]:
    Source: '/rustc/library/core/src/fmt/mod.rs', lines 3122:4-3122:50
    Name pattern: [core::fmt::{core::fmt::Debug<[@T]>}::fmt]
    Visibility: public -/
@[rust_fun "core::fmt::{core::fmt::Debug<[@T]>}::fmt"]
axiom Slice.Insts.CoreFmtDebug.fmt
  {T : Type} (DebugInst : core.fmt.Debug T) :
  Slice T → core.fmt.Formatter → Result ((core.result.Result Unit
    core.fmt.Error) × core.fmt.Formatter)

/-- [core::hash::impls::{impl core::hash::Hash for u8}::hash]:
    Source: '/rustc/library/core/src/hash/mod.rs', lines 812:16-812:56
    Name pattern: [core::hash::impls::{core::hash::Hash<u8>}::hash]
    Visibility: public -/
@[rust_fun "core::hash::impls::{core::hash::Hash<u8>}::hash"]
axiom U8.Insts.CoreHashHash.hash
  {H : Type} (HasherInst : core.hash.Hasher H) : Std.U8 → H → Result H

/-- [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 -/
@[rust_fun
  "core::iter::range::{core::iter::range::Step<u32>}::backward_checked"]
axiom U32.Insts.CoreIterRangeStep.backward_checked
  : Std.U32 → Std.Usize → Result (Option Std.U32)

/-- [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"]
axiom U32.Insts.CoreIterRangeStep.forward_checked
  : Std.U32 → Std.Usize → Result (Option Std.U32)

/-- [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"]
axiom U32.Insts.CoreIterRangeStep.steps_between
  : Std.U32 → Std.U32 → Result (Std.Usize × (Option Std.Usize))

/-- [core::slice::index::{impl core::slice::index::SliceIndex<[T], [T]> for core::ops::range::RangeFull}::index_mut]:
    Source: '/rustc/library/core/src/slice/index.rs', lines 660:4-660:51
    Name pattern: [core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::index_mut]
    Visibility: public -/
@[rust_fun
  "core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::index_mut"]
axiom
  core.ops.range.RangeFull.Insts.CoreSliceIndexSliceIndexSliceSlice.index_mut
  {T : Type} :
  core.ops.range.RangeFull → Slice T → Result ((Slice T) × (Slice T →
    Slice T))

/-- [core::slice::index::{impl core::slice::index::SliceIndex<[T], [T]> for core::ops::range::RangeFull}::index]:
    Source: '/rustc/library/core/src/slice/index.rs', lines 655:4-655:39
    Name pattern: [core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::index]
    Visibility: public -/
@[rust_fun
  "core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::index"]
axiom core.ops.range.RangeFull.Insts.CoreSliceIndexSliceIndexSliceSlice.index
  {T : Type} : core.ops.range.RangeFull → Slice T → Result (Slice T)

/-- [core::slice::index::{impl core::slice::index::SliceIndex<[T], [T]> for core::ops::range::RangeFull}::get_unchecked_mut]:
    Source: '/rustc/library/core/src/slice/index.rs', lines 650:4-650:66
    Name pattern: [core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get_unchecked_mut]
    Visibility: public -/
@[rust_fun
  "core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get_unchecked_mut"]
axiom
  core.ops.range.RangeFull.Insts.CoreSliceIndexSliceIndexSliceSlice.get_unchecked_mut
  {T : Type} :
  core.ops.range.RangeFull → MutRawPtr (Slice T) → Result (MutRawPtr (Slice
    T))

/-- [core::slice::index::{impl core::slice::index::SliceIndex<[T], [T]> for core::ops::range::RangeFull}::get_unchecked]:
    Source: '/rustc/library/core/src/slice/index.rs', lines 645:4-645:66
    Name pattern: [core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get_unchecked]
    Visibility: public -/
@[rust_fun
  "core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get_unchecked"]
axiom
  core.ops.range.RangeFull.Insts.CoreSliceIndexSliceIndexSliceSlice.get_unchecked
  {T : Type} :
  core.ops.range.RangeFull → ConstRawPtr (Slice T) → Result (ConstRawPtr
    (Slice T))

/-- [core::slice::index::{impl core::slice::index::SliceIndex<[T], [T]> for core::ops::range::RangeFull}::get_mut]:
    Source: '/rustc/library/core/src/slice/index.rs', lines 640:4-640:57
    Name pattern: [core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get_mut]
    Visibility: public -/
@[rust_fun
  "core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get_mut"]
axiom core.ops.range.RangeFull.Insts.CoreSliceIndexSliceIndexSliceSlice.get_mut
  {T : Type} :
  core.ops.range.RangeFull → Slice T → Result ((Option (Slice T)) ×
    (Option (Slice T) → Slice T))

/-- [core::slice::index::{impl core::slice::index::SliceIndex<[T], [T]> for core::ops::range::RangeFull}::get]:
    Source: '/rustc/library/core/src/slice/index.rs', lines 635:4-635:45
    Name pattern: [core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get]
    Visibility: public -/
@[rust_fun
  "core::slice::index::{core::slice::index::SliceIndex<core::ops::range::RangeFull, [@T], [@T]>}::get"]
axiom core.ops.range.RangeFull.Insts.CoreSliceIndexSliceIndexSliceSlice.get
  {T : Type} :
  core.ops.range.RangeFull → Slice T → Result (Option (Slice T))

/-- [subtle::{subtle::Choice}::unwrap_u8]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 133:4-133:33
    Name pattern: [subtle::{subtle::Choice}::unwrap_u8]
    Visibility: public -/
@[rust_fun "subtle::{subtle::Choice}::unwrap_u8"]
axiom subtle.Choice.unwrap_u8 : subtle.Choice → Result Std.U8

/-- [subtle::{impl core::convert::From<subtle::Choice> for bool}::from]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 153:4-153:35
    Name pattern: [subtle::{core::convert::From<bool, subtle::Choice>}::from]
    Visibility: public -/
@[rust_fun "subtle::{core::convert::From<bool, subtle::Choice>}::from"]
axiom Bool.Insts.CoreConvertFromChoice.from : subtle.Choice → Result Bool

/-- [subtle::{impl core::ops::bit::BitAnd<subtle::Choice, subtle::Choice> for subtle::Choice}::bitand]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 162:4-162:42
    Name pattern: [subtle::{core::ops::bit::BitAnd<subtle::Choice, subtle::Choice, subtle::Choice>}::bitand]
    Visibility: public -/
@[rust_fun
  "subtle::{core::ops::bit::BitAnd<subtle::Choice, subtle::Choice, subtle::Choice>}::bitand"]
axiom subtle.Choice.Insts.CoreOpsBitBitAndChoiceChoice.bitand
  : subtle.Choice → subtle.Choice → Result subtle.Choice

/-- [subtle::{impl core::ops::bit::BitOr<subtle::Choice, subtle::Choice> for subtle::Choice}::bitor]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 177:4-177:41
    Name pattern: [subtle::{core::ops::bit::BitOr<subtle::Choice, subtle::Choice, subtle::Choice>}::bitor]
    Visibility: public -/
@[rust_fun
  "subtle::{core::ops::bit::BitOr<subtle::Choice, subtle::Choice, subtle::Choice>}::bitor"]
axiom subtle.Choice.Insts.CoreOpsBitBitOrChoiceChoice.bitor
  : subtle.Choice → subtle.Choice → Result subtle.Choice

/-- [subtle::{impl core::convert::From<u8> for subtle::Choice}::from]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 238:4-238:32
    Name pattern: [subtle::{core::convert::From<subtle::Choice, u8>}::from]
    Visibility: public -/
@[rust_fun "subtle::{core::convert::From<subtle::Choice, u8>}::from"]
axiom subtle.Choice.Insts.CoreConvertFromU8.from
  : Std.U8 → Result subtle.Choice

/-- [subtle::{impl subtle::ConstantTimeEq for [T]}::ct_eq]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 313:4-313:41
    Name pattern: [subtle::{subtle::ConstantTimeEq<[@T]>}::ct_eq]
    Visibility: public -/
@[rust_fun "subtle::{subtle::ConstantTimeEq<[@T]>}::ct_eq"]
axiom Slice.Insts.SubtleConstantTimeEq.ct_eq
  {T : Type} (ConstantTimeEqInst : subtle.ConstantTimeEq T) :
  Slice T → Slice T → Result subtle.Choice

/-- [subtle::{impl subtle::ConstantTimeEq for u8}::ct_eq]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 348:12-348:51
    Name pattern: [subtle::{subtle::ConstantTimeEq<u8>}::ct_eq]
    Visibility: public -/
@[rust_fun "subtle::{subtle::ConstantTimeEq<u8>}::ct_eq"]
axiom U8.Insts.SubtleConstantTimeEq.ct_eq
  : Std.U8 → Std.U8 → Result subtle.Choice

/-- [subtle::ConditionallySelectable::conditional_assign]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 442:4-442:66
    Name pattern: [subtle::ConditionallySelectable::conditional_assign]
    Visibility: public -/
@[rust_fun "subtle::ConditionallySelectable::conditional_assign"]
axiom subtle.ConditionallySelectable.conditional_assign.default
  {Self : Type} (ConditionallySelectableInst : subtle.ConditionallySelectable
  Self) :
  Self → Self → subtle.Choice → Result Self

/-- [subtle::ConditionallySelectable::conditional_swap]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 469:4-469:67
    Name pattern: [subtle::ConditionallySelectable::conditional_swap]
    Visibility: public -/
@[rust_fun "subtle::ConditionallySelectable::conditional_swap"]
axiom subtle.ConditionallySelectable.conditional_swap.default
  {Self : Type} (ConditionallySelectableInst : subtle.ConditionallySelectable
  Self) :
  Self → Self → subtle.Choice → Result (Self × Self)

/-- [subtle::{impl subtle::ConditionallySelectable for u64}::conditional_select]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 513:12-513:77
    Name pattern: [subtle::{subtle::ConditionallySelectable<u64>}::conditional_select]
    Visibility: public -/
@[rust_fun
  "subtle::{subtle::ConditionallySelectable<u64>}::conditional_select"]
axiom U64.Insts.SubtleConditionallySelectable.conditional_select
  : Std.U64 → Std.U64 → subtle.Choice → Result Std.U64

/-- [subtle::{impl subtle::ConditionallySelectable for u64}::conditional_assign]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 521:12-521:74
    Name pattern: [subtle::{subtle::ConditionallySelectable<u64>}::conditional_assign]
    Visibility: public -/
@[rust_fun
  "subtle::{subtle::ConditionallySelectable<u64>}::conditional_assign"]
axiom U64.Insts.SubtleConditionallySelectable.conditional_assign
  : Std.U64 → Std.U64 → subtle.Choice → Result Std.U64

/-- [subtle::{impl subtle::ConditionallySelectable for u64}::conditional_swap]:
    Source: '/cargo/registry/src/index.crates.io-1949cf8c6b5b557f/subtle-2.6.1/src/lib.rs', lines 529:12-529:75
    Name pattern: [subtle::{subtle::ConditionallySelectable<u64>}::conditional_swap]
    Visibility: public -/
@[rust_fun "subtle::{subtle::ConditionallySelectable<u64>}::conditional_swap"]
axiom U64.Insts.SubtleConditionallySelectable.conditional_swap
  : Std.U64 → Std.U64 → subtle.Choice → Result (Std.U64 × Std.U64)

/-- [curve25519_dalek::backend::get_selected_backend]:
    Source: 'curve25519-dalek/src/backend/mod.rs', lines 55:0-75:1 -/
axiom backend.get_selected_backend : Result backend.BackendKind

/-- [curve25519_dalek::backend::vector::scalar_mul::variable_base::spec_avx512ifma_avx512vl::mul]:
    Source: 'curve25519-dalek/src/backend/vector/scalar_mul/variable_base.rs', lines 3:0-6:2
    Visibility: public -/
axiom backend.vector.scalar_mul.variable_base.spec_avx512ifma_avx512vl.mul
  : edwards.EdwardsPoint → scalar.Scalar → Result edwards.EdwardsPoint

/-- [curve25519_dalek::backend::vector::scalar_mul::variable_base::spec_avx2::mul]:
    Source: 'curve25519-dalek/src/backend/vector/scalar_mul/variable_base.rs', lines 3:0-6:2
    Visibility: public -/
axiom backend.vector.scalar_mul.variable_base.spec_avx2.mul
  : edwards.EdwardsPoint → scalar.Scalar → Result edwards.EdwardsPoint

/-- [curve25519_dalek::backend::serial::scalar_mul::variable_base::mul]:
    Source: 'curve25519-dalek/src/backend/serial/scalar_mul/variable_base.rs', lines 11:0-48:1 -/
axiom backend.serial.scalar_mul.variable_base.mul
  : edwards.EdwardsPoint → scalar.Scalar → Result edwards.EdwardsPoint

/-- [curve25519_dalek::backend::vector::scalar_mul::vartime_double_base::spec_avx512ifma_avx512vl::mul]:
    Source: 'curve25519-dalek/src/backend/vector/scalar_mul/vartime_double_base.rs', lines 14:0-17:2
    Visibility: public -/
axiom
  backend.vector.scalar_mul.vartime_double_base.spec_avx512ifma_avx512vl.mul
  :
  scalar.Scalar → edwards.EdwardsPoint → scalar.Scalar → Result
    edwards.EdwardsPoint

/-- [curve25519_dalek::backend::vector::scalar_mul::vartime_double_base::spec_avx2::mul]:
    Source: 'curve25519-dalek/src/backend/vector/scalar_mul/vartime_double_base.rs', lines 14:0-17:2
    Visibility: public -/
axiom backend.vector.scalar_mul.vartime_double_base.spec_avx2.mul
  :
  scalar.Scalar → edwards.EdwardsPoint → scalar.Scalar → Result
    edwards.EdwardsPoint

/-- [curve25519_dalek::backend::serial::curve_models::{impl subtle::ConditionallySelectable for curve25519_dalek::backend::serial::curve_models::ProjectiveNielsPoint}::conditional_swap]:
    Source: 'curve25519-dalek/src/backend/serial/curve_models/mod.rs', lines 295:0-311:1
    Visibility: public -/
axiom
  backend.serial.curve_models.ProjectiveNielsPoint.Insts.SubtleConditionallySelectable.conditional_swap
  :
  backend.serial.curve_models.ProjectiveNielsPoint →
    backend.serial.curve_models.ProjectiveNielsPoint → subtle.Choice →
    Result (backend.serial.curve_models.ProjectiveNielsPoint ×
    backend.serial.curve_models.ProjectiveNielsPoint)

/-- [curve25519_dalek::backend::serial::curve_models::{impl subtle::ConditionallySelectable for curve25519_dalek::backend::serial::curve_models::AffineNielsPoint}::conditional_swap]:
    Source: 'curve25519-dalek/src/backend/serial/curve_models/mod.rs', lines 313:0-327:1
    Visibility: public -/
axiom
  backend.serial.curve_models.AffineNielsPoint.Insts.SubtleConditionallySelectable.conditional_swap
  :
  backend.serial.curve_models.AffineNielsPoint →
    backend.serial.curve_models.AffineNielsPoint → subtle.Choice → Result
    (backend.serial.curve_models.AffineNielsPoint ×
    backend.serial.curve_models.AffineNielsPoint)

/-- [curve25519_dalek::edwards::decompress::step_2]:
    Source: 'curve25519-dalek/src/edwards.rs', lines 223:4-240:5 -/
axiom edwards.decompress.step_2
  :
  edwards.CompressedEdwardsY → backend.serial.u64.field.FieldElement51 →
    backend.serial.u64.field.FieldElement51 →
    backend.serial.u64.field.FieldElement51 → Result edwards.EdwardsPoint

/-- [curve25519_dalek::edwards::decompress::step_1]:
    Source: 'curve25519-dalek/src/edwards.rs', lines 209:4-220:5 -/
axiom edwards.decompress.step_1
  :
  edwards.CompressedEdwardsY → Result (subtle.Choice ×
    backend.serial.u64.field.FieldElement51 ×
    backend.serial.u64.field.FieldElement51 ×
    backend.serial.u64.field.FieldElement51)

/-- [curve25519_dalek::edwards::{curve25519_dalek::edwards::CompressedEdwardsY}::from_slice]:
    Source: 'curve25519-dalek/src/edwards.rs', lines 404:4-406:5
    Visibility: public -/
axiom edwards.CompressedEdwardsY.from_slice
  :
  Slice Std.U8 → Result (core.result.Result edwards.CompressedEdwardsY
    core.array.TryFromSliceError)

/-- [curve25519_dalek::edwards::{impl subtle::ConditionallySelectable for curve25519_dalek::edwards::EdwardsPoint}::conditional_swap]:
    Source: 'curve25519-dalek/src/edwards.rs', lines 467:0-476:1
    Visibility: public -/
axiom edwards.EdwardsPoint.Insts.SubtleConditionallySelectable.conditional_swap
  :
  edwards.EdwardsPoint → edwards.EdwardsPoint → subtle.Choice → Result
    (edwards.EdwardsPoint × edwards.EdwardsPoint)

/-- [curve25519_dalek::edwards::{impl subtle::ConditionallySelectable for curve25519_dalek::edwards::EdwardsPoint}::conditional_assign]:
    Source: 'curve25519-dalek/src/edwards.rs', lines 467:0-476:1
    Visibility: public -/
axiom
  edwards.EdwardsPoint.Insts.SubtleConditionallySelectable.conditional_assign
  :
  edwards.EdwardsPoint → edwards.EdwardsPoint → subtle.Choice → Result
    edwards.EdwardsPoint

/-- [curve25519_dalek::edwards::{impl core::cmp::Eq for curve25519_dalek::edwards::EdwardsPoint}::assert_fields_are_eq]:
    Source: 'curve25519-dalek/src/edwards.rs', lines 501:0-501:27
    Visibility: public -/
axiom edwards.EdwardsPoint.Insts.CoreCmpEq.assert_fields_are_eq
  : edwards.EdwardsPoint → Result Unit

/-- [curve25519_dalek::edwards::{impl core::iter::traits::accum::Sum<T> for curve25519_dalek::edwards::EdwardsPoint}::sum]:
    Source: 'curve25519-dalek/src/edwards.rs', lines 671:4-676:5
    Visibility: public -/
axiom edwards.EdwardsPoint.Insts.CoreIterTraitsAccumSum.sum
  {T : Type} {I : Type} (coreborrowBorrowTEdwardsPointInst : core.borrow.Borrow
  T edwards.EdwardsPoint) (coreitertraitsiteratorIteratorInst :
  core.iter.traits.iterator.Iterator I T) :
  I → Result edwards.EdwardsPoint

/-- [curve25519_dalek::field::{impl core::cmp::Eq for curve25519_dalek::backend::serial::u64::field::FieldElement51}::assert_fields_are_eq]:
    Source: 'curve25519-dalek/src/field.rs', lines 84:0-84:27
    Visibility: public -/
axiom
  backend.serial.u64.field.FieldElement51.Insts.CoreCmpEq.assert_fields_are_eq
  : backend.serial.u64.field.FieldElement51 → Result Unit