Add more Z.modulo lemmas

After    | File Name                                       | Before   || Change
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1m46.85s | Total                                           | 1m47.35s || -0m00.49s
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0m16.06s | ModularArithmetic/ModularBaseSystemProofs       | 0m15.05s || +0m01.00s
0m33.23s | Specific/GF25519                                | 0m32.88s || +0m00.34s
0m11.78s | Experiments/SpecEd25519                         | 0m11.50s || +0m00.27s
0m07.61s | Specific/GF1305                                 | 0m07.36s || +0m00.25s
0m04.57s | ModularArithmetic/Tutorial                      | 0m04.04s || +0m00.53s
0m04.12s | ModularArithmetic/Pow2BaseProofs                | 0m04.82s || -0m00.70s
0m03.93s | BaseSystemProofs                                | 0m03.73s || +0m00.20s
0m03.19s | ModularArithmetic/ModularBaseSystemOpt          | 0m03.25s || -0m00.06s
0m02.75s | Util/ZUtil                                      | 0m02.64s || +0m00.10s
0m01.70s | ModularArithmetic/PrimeFieldTheorems            | 0m01.56s || +0m00.13s
0m01.59s | ModularArithmetic/ModularArithmeticTheorems     | 0m01.65s || -0m00.05s
0m01.58s | Encoding/PointEncodingPre                       | 0m02.25s || -0m00.67s
0m01.21s | BaseSystem                                      | 0m01.39s || -0m00.17s
0m01.07s | ModularArithmetic/ExtendedBaseVector            | 0m01.34s || -0m00.27s
0m01.01s | Experiments/DerivationsOptionRectLetInEncoding  | 0m01.31s || -0m00.30s
0m00.97s | Util/NumTheoryUtil                              | 0m00.89s || +0m00.07s
0m00.91s | ModularArithmetic/BarrettReduction/Z            | 0m01.16s || -0m00.24s
0m00.89s | ModularArithmetic/ModularBaseSystemField        | 0m00.87s || +0m00.02s
0m00.86s | ModularArithmetic/ModularBaseSystemListProofs   | 0m00.80s || +0m00.05s
0m00.78s | ModularArithmetic/PseudoMersenneBaseParamProofs | 0m00.61s || +0m00.17s
0m00.72s | Encoding/ModularWordEncodingTheorems            | 0m01.02s || -0m00.30s
0m00.71s | Experiments/SpecificCurve25519                  | 0m00.72s || -0m00.01s
0m00.67s | Testbit                                         | 0m00.89s || -0m00.21s
0m00.66s | ModularArithmetic/ExtPow2BaseMulProofs          | 0m00.66s || +0m00.00s
0m00.62s | Encoding/ModularWordEncodingPre                 | 0m00.65s || -0m00.03s
0m00.60s | ModularArithmetic/ModularBaseSystem             | 0m00.61s || -0m00.01s
0m00.60s | Spec/ModularWordEncoding                        | 0m00.64s || -0m00.04s
0m00.58s | ModularArithmetic/ModularBaseSystemList         | 0m00.89s || -0m00.31s
0m00.58s | ModularArithmetic/Pow2Base                      | 0m00.68s || -0m00.10s
0m00.54s | ModularArithmetic/Pre                           | 0m00.48s || +0m00.06s
0m00.44s | ModularArithmetic/PseudoMersenneBaseParams      | 0m00.60s || -0m00.15s
0m00.33s | Spec/ModularArithmetic                          | 0m00.41s || -0m00.07s

1 files changed, 36 insertions, 1 deletions

diff --git a/src/Util/ZUtil.v b/src/Util/ZUtil.v
index b7abb2023..319e018a9 100644
--- a/src/Util/ZUtil.v
+++ b/src/Util/ZUtil.v
@@ -55,7 +55,8 @@ Hint Rewrite Z.pow_sub_r Z.pow_div_l Z.pow_twice_r Z.pow_mul_l Z.pow_add_r using
 Hint Rewrite <- Z.pow_sub_r Z.pow_div_l Z.pow_mul_l Z.pow_add_r Z.pow_twice_r using lia : pull_Zpow.
 Hint Rewrite Z.mul_add_distr_l Z.mul_add_distr_r Z.mul_sub_distr_l Z.mul_sub_distr_r : push_Zmul.
 Hint Rewrite <- Z.mul_add_distr_l Z.mul_add_distr_r Z.mul_sub_distr_l Z.mul_sub_distr_r : pull_Zmul.
-Hint Rewrite <- Z.mul_mod Z.add_mod using lia : pull_Zmod.
+Hint Rewrite <- Z.mul_mod Z.add_mod Zminus_mod using lia : pull_Zmod.
+Hint Rewrite Zminus_mod_idemp_l Zminus_mod_idemp_r : pull_Zmod.
 
 (** For the occasional lemma that can remove the use of [Z.div] *)
 Create HintDb zstrip_div.
@@ -1160,6 +1161,20 @@ Module Z.
   Qed.
   Hint Rewrite <- mul_mod_r using lia : pull_Zmod.
 
+  Lemma add_mod_l a b n : n <> 0 -> (a + b) mod n = ((a mod n) + b) mod n.
+  Proof.
+    intros; rewrite (Z.add_mod a b), (Z.add_mod (a mod n) b) by lia.
+    autorewrite with zsimplify; reflexivity.
+  Qed.
+  Hint Rewrite <- add_mod_l using lia : pull_Zmod.
+
+  Lemma add_mod_r a b n : n <> 0 -> (a + b) mod n = (a + (b mod n)) mod n.
+  Proof.
+    intros; rewrite (Z.add_mod a b), (Z.add_mod a (b mod n)) by lia.
+    autorewrite with zsimplify; reflexivity.
+  Qed.
+  Hint Rewrite <- add_mod_r using lia : pull_Zmod.
+
   Definition NoZMod (x : Z) := True.
   Ltac NoZMod :=
     lazymatch goal with
@@ -1183,6 +1198,26 @@ Module Z.
   Proof. intros; apply mul_mod_r; assumption. Qed.
   Hint Rewrite mul_mod_r_push using solve [ NoZMod | lia ] : push_Zmod.
 
+  Lemma add_mod_l_push a b n : n <> 0 -> NoZMod a -> (a + b) mod n = ((a mod n) + b) mod n.
+  Proof. intros; apply add_mod_l; assumption. Qed.
+  Hint Rewrite add_mod_l_push using solve [ NoZMod | lia ] : push_Zmod.
+
+  Lemma add_mod_r_push a b n : n <> 0 -> NoZMod b -> (a + b) mod n = (a + (b mod n)) mod n.
+  Proof. intros; apply add_mod_r; assumption. Qed.
+  Hint Rewrite add_mod_r_push using solve [ NoZMod | lia ] : push_Zmod.
+
+  Lemma sub_mod_push a b n : n <> 0 -> NoZMod a -> NoZMod b -> (a - b) mod n = ((a mod n) - (b mod n)) mod n.
+  Proof. intros; apply Zminus_mod; assumption. Qed.
+  Hint Rewrite sub_mod_push using solve [ NoZMod | lia ] : push_Zmod.
+
+  Lemma sub_mod_l_push a b n : n <> 0 -> NoZMod a -> (a - b) mod n = ((a mod n) - b) mod n.
+  Proof. intros; symmetry; apply Zminus_mod_idemp_l; assumption. Qed.
+  Hint Rewrite sub_mod_l_push using solve [ NoZMod | lia ] : push_Zmod.
+
+  Lemma sub_mod_r_push a b n : n <> 0 -> NoZMod b -> (a - b) mod n = (a - (b mod n)) mod n.
+  Proof. intros; symmetry; apply Zminus_mod_idemp_r; assumption. Qed.
+  Hint Rewrite sub_mod_r_push using solve [ NoZMod | lia ] : push_Zmod.
+
   Section equiv_modulo.
     Context (N : Z).
     Definition equiv_modulo x y := x mod N = y mod N.