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-rw-r--r--theories/Numbers/Cyclic/Int31/Cyclic31.v1
-rw-r--r--theories/Numbers/Cyclic/Int63/Int63.v1
-rw-r--r--theories/Numbers/Cyclic/ZModulo/ZModulo.v3
-rw-r--r--theories/Numbers/Natural/Abstract/NDefOps.v1
4 files changed, 6 insertions, 0 deletions
diff --git a/theories/Numbers/Cyclic/Int31/Cyclic31.v b/theories/Numbers/Cyclic/Int31/Cyclic31.v
index f6b2544b6e..c5c75fc17a 100644
--- a/theories/Numbers/Cyclic/Int31/Cyclic31.v
+++ b/theories/Numbers/Cyclic/Int31/Cyclic31.v
@@ -467,6 +467,7 @@ Section Basics.
apply phibis_aux_pos.
Qed.
+ #[local]
Hint Resolve phi_nonneg : zarith.
Lemma phi_bounded : forall x, (0 <= phi x < 2 ^ (Z.of_nat size))%Z.
diff --git a/theories/Numbers/Cyclic/Int63/Int63.v b/theories/Numbers/Cyclic/Int63/Int63.v
index 383c0aff3a..dbca2f0947 100644
--- a/theories/Numbers/Cyclic/Int63/Int63.v
+++ b/theories/Numbers/Cyclic/Int63/Int63.v
@@ -290,6 +290,7 @@ Proof. intros h; apply Z.lt_gt, Zpower_gt_0; lia. Qed.
Lemma pow2_nz n : 0 <= n → 2 ^ n ≠ 0.
Proof. intros h; generalize (pow2_pos _ h); lia. Qed.
+#[global]
Hint Resolve pow2_pos pow2_nz : zarith.
(* =================================================== *)
diff --git a/theories/Numbers/Cyclic/ZModulo/ZModulo.v b/theories/Numbers/Cyclic/ZModulo/ZModulo.v
index 5e486333b2..6aad65899a 100644
--- a/theories/Numbers/Cyclic/ZModulo/ZModulo.v
+++ b/theories/Numbers/Cyclic/ZModulo/ZModulo.v
@@ -61,6 +61,7 @@ Section ZModulo.
apply Z.lt_gt.
unfold wB, base; auto with zarith.
Qed.
+ #[local]
Hint Resolve wB_pos : core.
Lemma spec_to_Z_1 : forall x, 0 <= [|x|].
@@ -72,6 +73,7 @@ Section ZModulo.
Proof.
unfold to_Z; intros; destruct (Z_mod_lt x wB wB_pos); auto.
Qed.
+ #[local]
Hint Resolve spec_to_Z_1 spec_to_Z_2 : core.
Lemma spec_to_Z : forall x, 0 <= [|x|] < wB.
@@ -706,6 +708,7 @@ Section ZModulo.
Proof.
induction p; simpl; auto with zarith.
Qed.
+ #[local]
Hint Resolve Ptail_pos : core.
Lemma Ptail_bounded : forall p d, Zpos p < 2^(Zpos d) -> Ptail p < Zpos d.
diff --git a/theories/Numbers/Natural/Abstract/NDefOps.v b/theories/Numbers/Natural/Abstract/NDefOps.v
index 019b138b4d..2f8fcc7290 100644
--- a/theories/Numbers/Natural/Abstract/NDefOps.v
+++ b/theories/Numbers/Natural/Abstract/NDefOps.v
@@ -383,6 +383,7 @@ f_equiv. apply E, half_decrease.
rewrite two_succ, <- not_true_iff_false, ltb_lt, nlt_ge, le_succ_l in H.
order'.
Qed.
+#[global]
Hint Resolve log_good_step : core.
Theorem log_init : forall n, n < 2 -> log n == 0.