1 files changed, 4 insertions, 77 deletions

diff --git a/src/Util/IterAssocOp.v b/src/Util/IterAssocOp.v
index d630698e7..85868f33f 100644
--- a/src/Util/IterAssocOp.v
+++ b/src/Util/IterAssocOp.v
@@ -1,8 +1,8 @@
 Require Import Coq.Setoids.Setoid Coq.Classes.Morphisms Coq.Classes.Equivalence.
 Require Import Coq.NArith.NArith Coq.PArith.BinPosDef.
 Require Import Coq.Numbers.Natural.Peano.NPeano.
-Require Import Crypto.Algebra.
-Import Monoid.
+Require Import Crypto.Algebra. Import Monoid.
+Require Import Crypto.Util.NUtil.
 
 Local Open Scope equiv_scope.
 
@@ -64,56 +64,6 @@ Section IterAssocOp.
   Definition test_and_op_inv a (s : nat * T) :=
     snd s === nat_iter_op (N.to_nat (N.shiftr_nat x (fst s))) a.
 
-  Hint Rewrite
-    N.succ_double_spec
-    N.add_1_r
-    Nat2N.inj_succ
-    Nat2N.inj_mul
-    N2Nat.id: N_nat_conv
- .
-
-  Lemma Nsucc_double_to_nat : forall n,
-    N.succ_double n = N.of_nat (S (2 * N.to_nat n)).
-  Proof.
-    intros.
-    replace 2 with (N.to_nat 2) by auto.
-    autorewrite with N_nat_conv.
-    reflexivity.
-  Qed.
-
-  Lemma Ndouble_to_nat : forall n,
-    N.double n = N.of_nat (2 * N.to_nat n).
-  Proof.
-    intros.
-    replace 2 with (N.to_nat 2) by auto.
-    autorewrite with N_nat_conv.
-    reflexivity.
-  Qed.
-
-  Lemma Nshiftr_succ : forall n i,
-    N.to_nat (N.shiftr_nat n i) =
-    if N.testbit_nat n i
-    then S (2 * N.to_nat (N.shiftr_nat n (S i)))
-    else (2 * N.to_nat (N.shiftr_nat n (S i))).
-  Proof.
-    intros.
-    rewrite Nshiftr_nat_S.
-    case_eq (N.testbit_nat n i); intro testbit_i;
-      pose proof (Nshiftr_nat_spec n i 0) as shiftr_n_odd;
-      rewrite Nbit0_correct in shiftr_n_odd; simpl in shiftr_n_odd;
-      rewrite testbit_i in shiftr_n_odd.
-    + pose proof (Ndiv2_double_plus_one (N.shiftr_nat n i) shiftr_n_odd) as Nsucc_double_shift.
-      rewrite Nsucc_double_to_nat in Nsucc_double_shift.
-      apply Nat2N.inj.
-      rewrite Nsucc_double_shift.
-      apply N2Nat.id.
-    + pose proof (Ndiv2_double (N.shiftr_nat n i) shiftr_n_odd) as Nsucc_double_shift.
-      rewrite Ndouble_to_nat in Nsucc_double_shift.
-      apply Nat2N.inj.
-      rewrite Nsucc_double_shift.
-      apply N2Nat.id.
-  Qed.
-
   Lemma test_and_op_inv_step : forall a s,
     test_and_op_inv a s ->
     test_and_op_inv a (test_and_op a s).
@@ -122,7 +72,7 @@ Section IterAssocOp.
     unfold test_and_op_inv, test_and_op; simpl; intro Hpre.
     destruct i; [ apply Hpre | ].
     simpl.
-    rewrite Nshiftr_succ.
+    rewrite N.shiftr_succ.
     rewrite sel_correct.
     case_eq (testbit i); intro testbit_eq; simpl;
       rewrite testbit_correct in testbit_eq; rewrite testbit_eq;
@@ -157,29 +107,6 @@ Section IterAssocOp.
     reflexivity.
   Qed.
 
-  Lemma Nsize_nat_equiv : forall n, N.size_nat n = N.to_nat (N.size n).
-  Proof.
-    destruct n; auto; simpl; induction p; simpl; auto; rewrite IHp, Pnat.Pos2Nat.inj_succ; reflexivity.
-  Qed.
-
-  Lemma Nshiftr_size : forall n bound, N.size_nat n <= bound ->
-    N.shiftr_nat n bound = 0%N.
-  Proof.
-    intros.
-    rewrite <- (Nat2N.id bound).
-    rewrite Nshiftr_nat_equiv.
-    destruct (N.eq_dec n 0); subst; [apply N.shiftr_0_l|].
-    apply N.shiftr_eq_0.
-    rewrite Nsize_nat_equiv in *.
-    rewrite N.size_log2 in * by auto.
-    apply N.le_succ_l.
-    rewrite <- N.compare_le_iff.
-    rewrite N2Nat.inj_compare.
-    rewrite <- Compare_dec.nat_compare_le.
-    rewrite Nat2N.id.
-    auto.
-  Qed.
-
   Lemma iter_op_correct : forall a bound, N.size_nat x <= bound ->
     iter_op bound a === nat_iter_op (N.to_nat x) a.
   Proof.
@@ -188,7 +115,7 @@ Section IterAssocOp.
     apply test_and_op_inv_holds.
     unfold test_and_op_inv.
     simpl.
-    rewrite Nshiftr_size by auto.
+    rewrite N.shiftr_size by auto.
     reflexivity.
   Qed.
 End IterAssocOp.