val lemma_poly_multiply_canon : n: Prims.int ->
    p: _ ->
    r: _ ->
    h: _ ->
    r0: Prims.int ->
    r1: Prims.int ->
    h0: Prims.int ->
    h1: Prims.int ->
    h2: Prims.int ->
    s1: _ ->
    d0: _ ->
    d1: _ ->
    d2: _ ->
    hh: _
  -> Prims.unit
let lemma_poly_multiply_canon n p r h r0 r1 h0 h1 h2 s1 d0 d1 d2 hh =
  let r1_4 = r1 / 4 in
  let h_r_expand = (h2 * (n * n) + h1 * n + h0) * ((r1_4 * 4) * n + r0) in
  let hh_expand = (h2 * r0) * (n * n) + (h0 * (r1_4 * 4) + h1 * r0 + h2 * (5 * r1_4)) * n
    + (h0 * r0 + h1 * (5 * r1_4)) in
  let b = ((h2 * n + h1) * r1_4) in
  assert (h_r_expand == hh_expand + b * (n * n * 4 + (-5)))
  by (int_semiring ())
(*
   Copyright 2008-2018 Microsoft Research

   Licensed under the Apache License, Version 2.0 (the "License");
   you may not use this file except in compliance with the License.
   You may obtain a copy of the License at

       http://www.apache.org/licenses/LICENSE-2.0

   Unless required by applicable law or agreed to in writing, software
   distributed under the License is distributed on an "AS IS" BASIS,
   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   See the License for the specific language governing permissions and
   limitations under the License.
*)
module Poly

open FStar.Tactics.CanonCommSemiring
open FStar.Mul

#set-options "--no_smt --tactics_info"
/
prims.fst.checked FStar.Tactics.Effect.fsti.checked FStar.Tactics.CanonCommSemiring.fst.checked FStar.Pervasives.fsti.checked FStar.Mul.fst.checked
Poly.fst

    n: Prims.int ->
    p: _ ->
    r: _ ->
    h: _ ->
    r0: Prims.int ->
    r1: Prims.int ->
    h0: Prims.int ->
    h1: Prims.int ->
    h2: Prims.int ->
    s1: _ ->
    d0: _ ->
    d1: _ ->
    d2: _ ->
    hh: _
  -> Prims.unit
Prims.int FStar.Tactics.Effect.assert_by_tactic Prims.eq2 Prims.op_Addition FStar.Mul.op_Star Prims.op_Minus Prims.unit FStar.Tactics.CanonCommSemiring.int_semiring Prims.op_Division
let lemma_poly_multiply_canon n p r h r0 r1 h0 h1 h2 s1 d0 d1 d2 hh =
  
let r1_4 = r1 / 4 in
let h_r_expand = (h2 * (n * n) + h1 * n + h0) * ((r1_4 * 4) * n + r0) in
let hh_expand =
  (h2 * r0) * (n * n) + (h0 * (r1_4 * 4) + h1 * r0 + h2 * (5 * r1_4)) * n +
  (h0 * r0 + h1 * (5 * r1_4))
in
let b = ((h2 * n + h1) * r1_4) in
FStar.Tactics.Effect.assert_by_tactic (h_r_expand == hh_expand + b * ((n * n) * 4 + (- 5)))
  (fun _ ->
      ();
      (int_semiring ()))