val va_quick_ReduceLast (h_BE y_prev: quad32) (data: (seq quad32))
    : (va_quickCode unit (va_code_ReduceLast ()))
let va_quick_ReduceLast (h_BE:quad32) (y_prev:quad32) (data:(seq quad32)) : (va_quickCode unit
  (va_code_ReduceLast ())) =
  (va_QProc (va_code_ReduceLast ()) ([va_Mod_vec 10; va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 4;
    va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec 0]) (va_wp_ReduceLast h_BE y_prev data)
    (va_wpProof_ReduceLast h_BE y_prev data))
val va_quick_ReduceLast (h_BE y_prev: quad32) (data: (seq quad32))
    : (va_quickCode unit (va_code_ReduceLast ()))
let va_quick_ReduceLast (h_BE y_prev: quad32) (data: (seq quad32))
    : (va_quickCode unit (va_code_ReduceLast ())) =
(va_QProc (va_code_ReduceLast ())
    ([
        va_Mod_vec 10;
        va_Mod_vec 9;
        va_Mod_vec 8;
        va_Mod_vec 4;
        va_Mod_vec 3;
        va_Mod_vec 2;
        va_Mod_vec 1;
        va_Mod_vec 0
      ])
    (va_wp_ReduceLast h_BE y_prev data)
    (va_wpProof_ReduceLast h_BE y_prev data))
Vale.AES.PPC64LE.GHash.fsti.checked
Vale.PPC64LE.State.fsti.checked Vale.PPC64LE.QuickCodes.fsti.checked Vale.PPC64LE.QuickCode.fst.checked Vale.PPC64LE.Memory.fsti.checked Vale.PPC64LE.Machine_s.fst.checked Vale.PPC64LE.InsVector.fsti.checked Vale.PPC64LE.InsMem.fsti.checked Vale.PPC64LE.InsBasic.fsti.checked Vale.PPC64LE.Decls.fsti.checked Vale.Poly1305.Math.fsti.checked Vale.Math.Poly2_s.fsti.checked Vale.Math.Poly2.Lemmas.fsti.checked Vale.Math.Poly2.Bits_s.fsti.checked Vale.Math.Poly2.Bits.fsti.checked Vale.Math.Poly2.fsti.checked Vale.Def.Words_s.fsti.checked Vale.Def.Types_s.fst.checked Vale.Def.Prop_s.fst.checked Vale.Def.Opaque_s.fsti.checked Vale.Arch.TypesNative.fsti.checked Vale.Arch.Types.fsti.checked Vale.Arch.HeapImpl.fsti.checked Vale.AES.PPC64LE.PolyOps.fsti.checked Vale.AES.PPC64LE.GF128_Mul.fsti.checked Vale.AES.GHash_BE.fsti.checked Vale.AES.GF128_s.fsti.checked Vale.AES.GF128.fsti.checked Vale.AES.GCTR_BE_s.fst.checked Vale.AES.GCTR_BE.fsti.checked Vale.AES.GCM_helpers_BE.fsti.checked Vale.AES.AES_helpers.fsti.checked Vale.AES.AES_BE_s.fst.checked prims.fst.checked FStar.Seq.Base.fsti.checked FStar.Seq.fst.checked FStar.Pervasives.Native.fst.checked FStar.Pervasives.fsti.checked
Vale.AES.PPC64LE.GHash.fsti
Vale.PPC64LE.Memory.quad32 FStar.Seq.Base.seq Vale.PPC64LE.QuickCode.va_QProc Prims.unit Vale.AES.PPC64LE.GHash.va_code_ReduceLast Prims.Cons Vale.PPC64LE.QuickCode.mod_t Vale.PPC64LE.QuickCode.va_Mod_vec Prims.Nil Vale.AES.PPC64LE.GHash.va_wp_ReduceLast Vale.AES.PPC64LE.GHash.va_wpProof_ReduceLast Vale.PPC64LE.QuickCode.va_quickCode
module Vale.AES.PPC64LE.GHash
open Vale.Def.Prop_s
open Vale.Def.Opaque_s
open Vale.Def.Words_s
open Vale.Def.Types_s
open FStar.Seq
open Vale.Arch.Types
open Vale.Arch.HeapImpl
open Vale.AES.AES_BE_s
open Vale.PPC64LE.Machine_s
open Vale.PPC64LE.Memory
open Vale.PPC64LE.State
open Vale.PPC64LE.Decls
open Vale.PPC64LE.InsBasic
open Vale.PPC64LE.InsMem
open Vale.PPC64LE.InsVector
open Vale.PPC64LE.QuickCode
open Vale.PPC64LE.QuickCodes
open Vale.AES.AES_helpers
open Vale.Poly1305.Math    // For lemma_poly_bits64()
open Vale.AES.GCM_helpers_BE
open Vale.AES.GCTR_BE_s
open Vale.AES.GCTR_BE
open Vale.Arch.TypesNative
open Vale.AES.PPC64LE.PolyOps
open Vale.AES.PPC64LE.GF128_Mul
open Vale.Math.Poly2_s
open Vale.Math.Poly2
open Vale.Math.Poly2.Bits_s
open Vale.Math.Poly2.Bits
open Vale.Math.Poly2.Lemmas
open Vale.AES.GF128_s
open Vale.AES.GF128
open Vale.AES.GHash_BE
#reset-options "--z3rlimit 50"

unfold let va_subscript_FStar__Seq__Base__seq = Seq.index

let hkeys_b_powers (hkeys_b:buffer128) (heap0:vale_heap) (layout:vale_heap_layout) (ptr:int) (h:poly) =
  validSrcAddrs128 heap0 ptr hkeys_b 3 layout Secret /\
  of_quad32 (reverse_bytes_quad32 (buffer128_read hkeys_b 0 heap0)) == gf128_power h 1 /\
  of_quad32 (reverse_bytes_quad32 (buffer128_read hkeys_b 1 heap0)) == gf128_power h 2

let in_b_blocks
    (in_b:buffer128) (in_index count:int) (heap_s:vale_heap) (layout:vale_heap_layout) (ptr:int) (data:seq quad32)
  =
  validSrcAddrsOffset128 heap_s ptr in_b in_index count layout Secret /\
  (forall (i:nat).{:pattern (index data i)}
    i < count /\ i < length data ==>
      reverse_bytes_quad32 (buffer128_read in_b (in_index + i) heap_s) == index data i)
//-- ReduceLast

val va_code_ReduceLast : va_dummy:unit -> Tot va_code

val va_codegen_success_ReduceLast : va_dummy:unit -> Tot va_pbool

val va_lemma_ReduceLast : va_b0:va_code -> va_s0:va_state -> h_BE:quad32 -> y_prev:quad32 ->
  data:(seq quad32)
  -> Ghost (va_state & va_fuel)
  (requires (va_require_total va_b0 (va_code_ReduceLast ()) va_s0 /\ va_get_ok va_s0 /\ (let
    (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 h_BE in let
    (prev:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 y_prev in let
    (pdata:(Prims.int -> Vale.AES.GHash_BE.poly128)) = Vale.AES.GHash_BE.fun_seq_quad32_BE_poly128
    data in let (n:Prims.nat) = FStar.Seq.Base.length #quad32 data in va_get_vec 8 va_s0 ==
    Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 3254779904 0 0 /\ n > 0 /\ add (add
    (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s0)) (Vale.Math.Poly2_s.shift
    (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0)) 64)) (Vale.Math.Poly2_s.shift
    (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0)) 128) ==
    Vale.AES.GHash_BE.ghash_unroll_back h prev pdata 0 n (n - 1))))
  (ensures (fun (va_sM, va_fM) -> va_ensure_total va_b0 va_s0 va_sM va_fM /\ va_get_ok va_sM /\
    (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 h_BE in let
    (prev:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 y_prev in let
    (pdata:(Prims.int -> Vale.AES.GHash_BE.poly128)) = Vale.AES.GHash_BE.fun_seq_quad32_BE_poly128
    data in let (n:Prims.nat) = FStar.Seq.Base.length #quad32 data in let xi =
    Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) in Vale.Math.Poly2.Bits_s.to_quad32 xi ==
    Vale.AES.GHash_BE.ghash_incremental h_BE y_prev data /\ xi == Vale.Math.Poly2.Bits_s.of_quad32
    (Vale.Math.Poly2.Bits_s.to_quad32 xi)) /\ va_state_eq va_sM (va_update_vec 10 va_sM
    (va_update_vec 9 va_sM (va_update_vec 8 va_sM (va_update_vec 4 va_sM (va_update_vec 3 va_sM
    (va_update_vec 2 va_sM (va_update_vec 1 va_sM (va_update_vec 0 va_sM (va_update_ok va_sM
    va_s0)))))))))))
[@ va_qattr]
let va_wp_ReduceLast (h_BE:quad32) (y_prev:quad32) (data:(seq quad32)) (va_s0:va_state)
  (va_k:(va_state -> unit -> Type0)) : Type0 =
  (va_get_ok va_s0 /\ (let (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 h_BE in
    let (prev:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 y_prev in let
    (pdata:(Prims.int -> Vale.AES.GHash_BE.poly128)) = Vale.AES.GHash_BE.fun_seq_quad32_BE_poly128
    data in let (n:Prims.nat) = FStar.Seq.Base.length #quad32 data in va_get_vec 8 va_s0 ==
    Vale.Def.Words_s.Mkfour #Vale.Def.Types_s.nat32 0 3254779904 0 0 /\ n > 0 /\ add (add
    (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 2 va_s0)) (Vale.Math.Poly2_s.shift
    (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 3 va_s0)) 64)) (Vale.Math.Poly2_s.shift
    (Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 4 va_s0)) 128) ==
    Vale.AES.GHash_BE.ghash_unroll_back h prev pdata 0 n (n - 1)) /\ (forall (va_x_v0:quad32)
    (va_x_v1:quad32) (va_x_v2:quad32) (va_x_v3:quad32) (va_x_v4:quad32) (va_x_v8:quad32)
    (va_x_v9:quad32) (va_x_v10:quad32) . let va_sM = va_upd_vec 10 va_x_v10 (va_upd_vec 9 va_x_v9
    (va_upd_vec 8 va_x_v8 (va_upd_vec 4 va_x_v4 (va_upd_vec 3 va_x_v3 (va_upd_vec 2 va_x_v2
    (va_upd_vec 1 va_x_v1 (va_upd_vec 0 va_x_v0 va_s0))))))) in va_get_ok va_sM /\ (let
    (h:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 h_BE in let
    (prev:Vale.Math.Poly2_s.poly) = Vale.Math.Poly2.Bits_s.of_quad32 y_prev in let
    (pdata:(Prims.int -> Vale.AES.GHash_BE.poly128)) = Vale.AES.GHash_BE.fun_seq_quad32_BE_poly128
    data in let (n:Prims.nat) = FStar.Seq.Base.length #quad32 data in let xi =
    Vale.Math.Poly2.Bits_s.of_quad32 (va_get_vec 1 va_sM) in Vale.Math.Poly2.Bits_s.to_quad32 xi ==
    Vale.AES.GHash_BE.ghash_incremental h_BE y_prev data /\ xi == Vale.Math.Poly2.Bits_s.of_quad32
    (Vale.Math.Poly2.Bits_s.to_quad32 xi)) ==> va_k va_sM (())))

val va_wpProof_ReduceLast : h_BE:quad32 -> y_prev:quad32 -> data:(seq quad32) -> va_s0:va_state ->
  va_k:(va_state -> unit -> Type0)
  -> Ghost (va_state & va_fuel & unit)
  (requires (va_t_require va_s0 /\ va_wp_ReduceLast h_BE y_prev data va_s0 va_k))
  (ensures (fun (va_sM, va_f0, va_g) -> va_t_ensure (va_code_ReduceLast ()) ([va_Mod_vec 10;
    va_Mod_vec 9; va_Mod_vec 8; va_Mod_vec 4; va_Mod_vec 3; va_Mod_vec 2; va_Mod_vec 1; va_Mod_vec
    0]) va_s0 va_k ((va_sM, va_f0, va_g))))
[@ "opaque_to_smt" va_qattr]
let va_quick_ReduceLast (h_BE:quad32) (y_prev:quad32) (data:(seq quad32)) : (va_quickCode unit
val va_quick_ReduceLast (h_BE y_prev: quad32) (data: (seq quad32))
    : (va_quickCode unit (va_code_ReduceLast ()))

    h_BE: Vale.PPC64LE.Memory.quad32 ->
    y_prev: Vale.PPC64LE.Memory.quad32 ->
    data: FStar.Seq.Base.seq Vale.PPC64LE.Memory.quad32
  -> Vale.PPC64LE.QuickCode.va_quickCode Prims.unit (Vale.AES.PPC64LE.GHash.va_code_ReduceLast ())