Fewer side-conditions on zsimplify

After    | File Name                                       | Before   || Change
----------------------------------------------------------------------------------
3m23.91s | Total                                           | 3m03.61s || +0m20.30s
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0m52.44s | ModularArithmetic/Pow2BaseProofs                | 0m38.87s || +0m13.57s
0m18.83s | ModularArithmetic/ModularBaseSystemProofs       | 0m27.00s || -0m08.17s
0m13.77s | ModularArithmetic/Montgomery/ZProofs            | 0m09.31s || +0m04.45s
0m16.91s | Experiments/SpecEd25519                         | 0m14.02s || +0m02.89s
0m05.95s | ModularArithmetic/BarrettReduction/ZHandbook    | 0m03.94s || +0m02.01s
0m15.10s | Specific/GF25519                                | 0m16.29s || -0m01.18s
0m09.03s | Specific/GF1305                                 | 0m10.27s || -0m01.24s
0m05.09s | ModularArithmetic/Tutorial                      | 0m03.68s || +0m01.40s
0m03.78s | ModularArithmetic/ModularArithmeticTheorems     | 0m02.61s || +0m01.16s
0m12.20s | Util/ZUtil                                      | 0m11.39s || +0m00.80s
0m10.50s | Testbit                                         | 0m10.45s || +0m00.05s
0m04.99s | BaseSystemProofs                                | 0m04.22s || +0m00.77s
0m04.01s | ModularArithmetic/BarrettReduction/ZGeneralized | 0m03.05s || +0m00.96s
0m03.42s | Experiments/SpecificCurve25519                  | 0m03.52s || -0m00.10s
0m02.87s | ModularArithmetic/BarrettReduction/ZBounded     | 0m02.38s || +0m00.49s
0m02.55s | ModularArithmetic/ModularBaseSystemOpt          | 0m03.43s || -0m00.88s
0m02.14s | ModularArithmetic/BarrettReduction/Z            | 0m01.55s || +0m00.59s
0m01.77s | Encoding/PointEncodingPre                       | 0m01.57s || +0m00.19s
0m01.68s | BaseSystem                                      | 0m01.65s || +0m00.03s
0m01.51s | ModularArithmetic/PrimeFieldTheorems            | 0m01.09s || +0m00.41s
0m01.37s | ModularArithmetic/ModularBaseSystemListProofs   | 0m00.86s || +0m00.51s
0m01.31s | ModularArithmetic/ExtendedBaseVector            | 0m01.17s || +0m00.14s
0m01.16s | Experiments/DerivationsOptionRectLetInEncoding  | 0m01.30s || -0m00.14s
0m01.15s | Util/NumTheoryUtil                              | 0m01.33s || -0m00.18s
0m01.07s | Encoding/ModularWordEncodingTheorems            | 0m01.02s || +0m00.05s
0m00.98s | Encoding/ModularWordEncodingPre                 | 0m00.92s || +0m00.05s
0m00.97s | ModularArithmetic/ExtPow2BaseMulProofs          | 0m00.64s || +0m00.32s
0m00.85s | ModularArithmetic/Montgomery/ZBounded           | 0m00.97s || -0m00.12s
0m00.79s | ModularArithmetic/PseudoMersenneBaseParamProofs | 0m00.69s || +0m00.10s
0m00.76s | ModularArithmetic/Pre                           | 0m00.48s || +0m00.28s
0m00.73s | ModularArithmetic/ModularBaseSystemList         | 0m00.66s || +0m00.06s
0m00.71s | Spec/ModularWordEncoding                        | 0m00.58s || +0m00.13s
0m00.68s | ModularArithmetic/Pow2Base                      | 0m00.41s || +0m00.27s
0m00.67s | ModularArithmetic/ZBounded                      | 0m00.48s || +0m00.19s
0m00.66s | ModularArithmetic/PseudoMersenneBaseParams      | 0m00.43s || +0m00.23s
0m00.66s | ModularArithmetic/ModularBaseSystem             | 0m00.62s || +0m00.04s
0m00.45s | ModularArithmetic/Montgomery/Z                  | 0m00.40s || +0m00.04s
0m00.41s | Spec/ModularArithmetic                          | 0m00.36s || +0m00.04s

1 files changed, 14 insertions, 2 deletions

diff --git a/src/Util/ZUtil.v b/src/Util/ZUtil.v
index d06477d3c..35aa20dc4 100644
--- a/src/Util/ZUtil.v
+++ b/src/Util/ZUtil.v
@@ -324,15 +324,27 @@ Module Z.
 
   Hint Resolve elim_mod : zarith.
 
+  Lemma mod_add_full : forall a b c, (a + b * c) mod c = a mod c.
+  Proof. intros; destruct (Z_zerop c); try subst; autorewrite with zsimplify; reflexivity. Qed.
+  Hint Rewrite mod_add_full : zsimplify.
+
+  Lemma mod_add_l_full : forall a b c, (a * b + c) mod b = c mod b.
+  Proof. intros; rewrite (Z.add_comm _ c); autorewrite with zsimplify; reflexivity. Qed.
+  Hint Rewrite mod_add_l_full : zsimplify.
+
+  Lemma mod_add'_full : forall a b c, (a + b * c) mod b = a mod b.
+  Proof. intros; rewrite (Z.mul_comm _ c); autorewrite with zsimplify; reflexivity. Qed.
+  Lemma mod_add_l'_full : forall a b c, (a * b + c) mod a = c mod a.
+  Proof. intros; rewrite (Z.mul_comm _ b); autorewrite with zsimplify; reflexivity. Qed.
+  Hint Rewrite mod_add'_full mod_add_l'_full : zsimplify.
+
   Lemma mod_add_l : forall a b c, b <> 0 -> (a * b + c) mod b = c mod b.
   Proof. intros; rewrite (Z.add_comm _ c); autorewrite with zsimplify; reflexivity. Qed.
-  Hint Rewrite mod_add_l using zutil_arith : zsimplify.
 
   Lemma mod_add' : forall a b c, b <> 0 -> (a + b * c) mod b = a mod b.
   Proof. intros; rewrite (Z.mul_comm _ c); autorewrite with zsimplify; reflexivity. Qed.
   Lemma mod_add_l' : forall a b c, a <> 0 -> (a * b + c) mod a = c mod a.
   Proof. intros; rewrite (Z.mul_comm _ b); autorewrite with zsimplify; reflexivity. Qed.
-  Hint Rewrite mod_add' mod_add_l' using zutil_arith : zsimplify.
 
   Lemma pos_pow_nat_pos : forall x n,
     Z.pos x ^ Z.of_nat n > 0.