Merge branch 'kvx-work' into BTL

33 files changed, 1365 insertions, 1327 deletions

diff --git a/lib/Axioms.v b/lib/Axioms.v
index fdc89920..d7b3d036 100644
--- a/lib/Axioms.v
+++ b/lib/Axioms.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/BoolEqual.v b/lib/BoolEqual.v
index e8c1d831..6479c1ee 100644
--- a/lib/BoolEqual.v
+++ b/lib/BoolEqual.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Camlcoq.ml b/lib/Camlcoq.ml
index af65b28e..8ad1ed39 100644
--- a/lib/Camlcoq.ml
+++ b/lib/Camlcoq.ml
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Commandline.ml b/lib/Commandline.ml
index 672ed834..2f0d7cc1 100644
--- a/lib/Commandline.ml
+++ b/lib/Commandline.ml
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Commandline.mli b/lib/Commandline.mli
index 8bb6f18f..cb9a7513 100644
--- a/lib/Commandline.mli
+++ b/lib/Commandline.mli
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Coqlib.v b/lib/Coqlib.v
index 7a7261a3..eda3862f 100644
--- a/lib/Coqlib.v
+++ b/lib/Coqlib.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -22,6 +23,7 @@ Require Export ZArith.
 Require Export Znumtheory.
 Require Export List.
 Require Export Bool.
+Require Export Lia.
 
 Global Set Asymmetric Patterns.
 
@@ -45,11 +47,7 @@ Ltac decEq :=
       cut (A <> B); [intro; congruence | try discriminate]
   end.
 
-Ltac byContradiction :=
-  cut False; [contradiction|idtac].
-
-Ltac omegaContradiction :=
-  cut False; [contradiction|omega].
+Ltac byContradiction := exfalso.
 
 Lemma modusponens: forall (P Q: Prop), P -> (P -> Q) -> Q.
 Proof. auto. Qed.
@@ -119,7 +117,7 @@ Lemma Plt_ne:
 Proof.
   unfold Plt; intros. red; intro. subst y. eelim Pos.lt_irrefl; eauto.
 Qed.
-Hint Resolve Plt_ne: coqlib.
+Global Hint Resolve Plt_ne: coqlib.
 
 Lemma Plt_trans:
   forall (x y z: positive), Plt x y -> Plt y z -> Plt x z.
@@ -130,14 +128,14 @@ Lemma Plt_succ:
 Proof.
   unfold Plt; intros. apply Pos.lt_succ_r. apply Pos.le_refl.
 Qed.
-Hint Resolve Plt_succ: coqlib.
+Global Hint Resolve Plt_succ: coqlib.
 
 Lemma Plt_trans_succ:
   forall (x y: positive), Plt x y -> Plt x (Pos.succ y).
 Proof.
   intros. apply Plt_trans with y. assumption. apply Plt_succ.
 Qed.
-Hint Resolve Plt_succ: coqlib.
+Global Hint Resolve Plt_succ: coqlib.
 
 Lemma Plt_succ_inv:
   forall (x y: positive), Plt x (Pos.succ y) -> Plt x y \/ x = y.
@@ -178,10 +176,9 @@ Proof (Pos.lt_le_trans).
 Lemma Plt_strict: forall p, ~ Plt p p.
 Proof (Pos.lt_irrefl).
 
-Hint Resolve Ple_refl Plt_Ple Ple_succ Plt_strict: coqlib.
+Global Hint Resolve Ple_refl Plt_Ple Ple_succ Plt_strict: coqlib.
 
-Ltac xomega := unfold Plt, Ple in *; zify; omega.
-Ltac xomegaContradiction := exfalso; xomega.
+Ltac extlia := unfold Plt, Ple in *; lia.
 
 (** Peano recursion over positive numbers. *)
 
@@ -284,7 +281,7 @@ Lemma zlt_true:
 Proof.
   intros. case (zlt x y); intros.
   auto.
-  omegaContradiction.
+  extlia.
 Qed.
 
 Lemma zlt_false:
@@ -292,7 +289,7 @@ Lemma zlt_false:
   x >= y -> (if zlt x y then a else b) = b.
 Proof.
   intros. case (zlt x y); intros.
-  omegaContradiction.
+  extlia.
   auto.
 Qed.
 
@@ -304,7 +301,7 @@ Lemma zle_true:
 Proof.
   intros. case (zle x y); intros.
   auto.
-  omegaContradiction.
+  extlia.
 Qed.
 
 Lemma zle_false:
@@ -312,7 +309,7 @@ Lemma zle_false:
   x > y -> (if zle x y then a else b) = b.
 Proof.
   intros. case (zle x y); intros.
-  omegaContradiction.
+  extlia.
   auto.
 Qed.
 
@@ -323,54 +320,54 @@ Proof. reflexivity. Qed.
 
 Lemma two_power_nat_pos : forall n : nat, two_power_nat n > 0.
 Proof.
-  induction n. rewrite two_power_nat_O. omega.
-  rewrite two_power_nat_S. omega.
+  induction n. rewrite two_power_nat_O. lia.
+  rewrite two_power_nat_S. lia.
 Qed.
 
 Lemma two_power_nat_two_p:
   forall x, two_power_nat x = two_p (Z.of_nat x).
 Proof.
   induction x. auto.
-  rewrite two_power_nat_S. rewrite Nat2Z.inj_succ. rewrite two_p_S. omega. omega.
+  rewrite two_power_nat_S. rewrite Nat2Z.inj_succ. rewrite two_p_S. lia. lia.
 Qed.
 
 Lemma two_p_monotone:
   forall x y, 0 <= x <= y -> two_p x <= two_p y.
 Proof.
   intros.
-  replace (two_p x) with (two_p x * 1) by omega.
-  replace y with (x + (y - x)) by omega.
-  rewrite two_p_is_exp; try omega.
+  replace (two_p x) with (two_p x * 1) by lia.
+  replace y with (x + (y - x)) by lia.
+  rewrite two_p_is_exp; try lia.
   apply Zmult_le_compat_l.
-  assert (two_p (y - x) > 0). apply two_p_gt_ZERO. omega. omega.
-  assert (two_p x > 0). apply two_p_gt_ZERO. omega. omega.
+  assert (two_p (y - x) > 0). apply two_p_gt_ZERO. lia. lia.
+  assert (two_p x > 0). apply two_p_gt_ZERO. lia. lia.
 Qed.
 
 Lemma two_p_monotone_strict:
   forall x y, 0 <= x < y -> two_p x < two_p y.
 Proof.
-  intros. assert (two_p x <= two_p (y - 1)). apply two_p_monotone; omega.
-  assert (two_p (y - 1) > 0). apply two_p_gt_ZERO. omega.
-  replace y with (Z.succ (y - 1)) by omega. rewrite two_p_S. omega. omega.
+  intros. assert (two_p x <= two_p (y - 1)). apply two_p_monotone; lia.
+  assert (two_p (y - 1) > 0). apply two_p_gt_ZERO. lia.
+  replace y with (Z.succ (y - 1)) by lia. rewrite two_p_S. lia. lia.
 Qed.
 
 Lemma two_p_strict:
   forall x, x >= 0 -> x < two_p x.
 Proof.
   intros x0 GT. pattern x0. apply natlike_ind.
-  simpl. omega.
-  intros. rewrite two_p_S; auto. generalize (two_p_gt_ZERO x H). omega.
-  omega.
+  simpl. lia.
+  intros. rewrite two_p_S; auto. generalize (two_p_gt_ZERO x H). lia.
+  lia.
 Qed.
 
 Lemma two_p_strict_2:
   forall x, x >= 0 -> 2 * x - 1 < two_p x.
 Proof.
-  intros. assert (x = 0 \/ x - 1 >= 0) by omega. destruct H0.
+  intros. assert (x = 0 \/ x - 1 >= 0) by lia. destruct H0.
   subst. vm_compute. auto.
   replace (two_p x) with (2 * two_p (x - 1)).
-  generalize (two_p_strict _ H0). omega.
-  rewrite <- two_p_S. decEq. omega. omega.
+  generalize (two_p_strict _ H0). lia.
+  rewrite <- two_p_S. decEq. lia. lia.
 Qed.
 
 (** Properties of [Zmin] and [Zmax] *)
@@ -401,12 +398,12 @@ Qed.
 Lemma Zmax_bound_l:
   forall x y z, x <= y -> x <= Z.max y z.
 Proof.
-  intros. generalize (Z.le_max_l y z). omega.
+  intros. generalize (Z.le_max_l y z). lia.
 Qed.
 Lemma Zmax_bound_r:
   forall x y z, x <= z -> x <= Z.max y z.
 Proof.
-  intros. generalize (Z.le_max_r y z). omega.
+  intros. generalize (Z.le_max_r y z). lia.
 Qed.
 
 (** Properties of Euclidean division and modulus. *)
@@ -416,7 +413,7 @@ Lemma Zmod_unique:
   x = a * y + b -> 0 <= b < y -> x mod y = b.
 Proof.
   intros. subst x. rewrite Z.add_comm.
-  rewrite Z_mod_plus. apply Z.mod_small. auto. omega.
+  rewrite Z_mod_plus. apply Z.mod_small. auto. lia.
 Qed.
 
 Lemma Zdiv_unique:
@@ -424,14 +421,14 @@ Lemma Zdiv_unique:
   x = a * y + b -> 0 <= b < y -> x / y = a.
 Proof.
   intros. subst x. rewrite Z.add_comm.
-  rewrite Z_div_plus. rewrite (Zdiv_small b y H0). omega. omega.
+  rewrite Z_div_plus. rewrite (Zdiv_small b y H0). lia. lia.
 Qed.
 
 Lemma Zdiv_Zdiv:
   forall a b c,
   b > 0 -> c > 0 -> (a / b) / c = a / (b * c).
 Proof.
-  intros. apply Z.div_div; omega.
+  intros. apply Z.div_div; lia.
 Qed.
 
 Lemma Zdiv_interval_1:
@@ -445,14 +442,14 @@ Proof.
   set (q := a/b) in *. set (r := a mod b) in *.
   split.
   assert (lo < (q + 1)).
-  apply Zmult_lt_reg_r with b. omega.
-  apply Z.le_lt_trans with a. omega.
+  apply Zmult_lt_reg_r with b. lia.
+  apply Z.le_lt_trans with a. lia.
   replace ((q + 1) * b) with (b * q + b) by ring.
-  omega.
-  omega.
-  apply Zmult_lt_reg_r with b. omega.
+  lia.
+  lia.
+  apply Zmult_lt_reg_r with b. lia.
   replace (q * b) with (b * q) by ring.
-  omega.
+  lia.
 Qed.
 
 Lemma Zdiv_interval_2:
@@ -462,13 +459,13 @@ Lemma Zdiv_interval_2:
 Proof.
   intros.
   assert (lo <= a / b < hi+1).
-  apply Zdiv_interval_1. omega. omega. auto.
-  assert (lo * b <= lo * 1) by (apply Z.mul_le_mono_nonpos_l; omega).
+  apply Zdiv_interval_1. lia. lia. auto.
+  assert (lo * b <= lo * 1) by (apply Z.mul_le_mono_nonpos_l; lia).
   replace (lo * 1) with lo in H3 by ring.
-  assert ((hi + 1) * 1 <= (hi + 1) * b) by (apply Z.mul_le_mono_nonneg_l; omega).
+  assert ((hi + 1) * 1 <= (hi + 1) * b) by (apply Z.mul_le_mono_nonneg_l; lia).
   replace ((hi + 1) * 1) with (hi + 1) in H4 by ring.
-  omega.
-  omega.
+  lia.
+  lia.
 Qed.
 
 Lemma Zmod_recombine:
@@ -476,7 +473,7 @@ Lemma Zmod_recombine:
   a > 0 -> b > 0 ->
   x mod (a * b) = ((x/b) mod a) * b + (x mod b).
 Proof.
-  intros. rewrite (Z.mul_comm a b). rewrite Z.rem_mul_r by omega. ring. 
+  intros. rewrite (Z.mul_comm a b). rewrite Z.rem_mul_r by lia. ring. 
 Qed.
 
 (** Properties of divisibility. *)
@@ -486,9 +483,9 @@ Lemma Zdivide_interval:
   0 < c -> 0 <= a < b -> (c | a) -> (c | b) -> 0 <= a <= b - c.
 Proof.
   intros. destruct H1 as [x EQ1]. destruct H2 as [y EQ2]. subst. destruct H0.
-  split. omega. exploit Zmult_lt_reg_r; eauto. intros.
+  split. lia. exploit Zmult_lt_reg_r; eauto. intros.
   replace (y * c - c) with ((y - 1) * c) by ring.
-  apply Zmult_le_compat_r; omega.
+  apply Zmult_le_compat_r; lia.
 Qed.
 
 (** Conversion from [Z] to [nat]. *)
@@ -503,8 +500,8 @@ Lemma Z_to_nat_max:
   forall z, Z.of_nat (Z.to_nat z) = Z.max z 0.
 Proof.
   intros. destruct (zle 0 z).
-- rewrite Z2Nat.id by auto. xomega.
-- rewrite Z_to_nat_neg by omega. xomega.
+- rewrite Z2Nat.id by auto. extlia.
+- rewrite Z_to_nat_neg by lia. extlia.
 Qed.
 
 (** Alignment: [align n amount] returns the smallest multiple of [amount]
@@ -519,8 +516,8 @@ Proof.
   generalize (Z_div_mod_eq (x + y - 1) y H). intro.
   replace ((x + y - 1) / y * y)
      with ((x + y - 1) - (x + y - 1) mod y).
-  generalize (Z_mod_lt (x + y - 1) y H). omega.
-  rewrite Z.mul_comm. omega.
+  generalize (Z_mod_lt (x + y - 1) y H). lia.
+  rewrite Z.mul_comm. lia.
 Qed.
 
 Lemma align_divides: forall x y, y > 0 -> (y | align x y).
@@ -563,7 +560,7 @@ Definition sum_left_map (A B C: Type) (f: A -> B) (x: A + C) : B + C :=
 
 (** Properties of [List.nth] (n-th element of a list). *)
 
-Hint Resolve in_eq in_cons: coqlib.
+Global Hint Resolve in_eq in_cons: coqlib.
 
 Lemma nth_error_in:
   forall (A: Type) (n: nat) (l: list A) (x: A),
@@ -577,14 +574,14 @@ Proof.
     discriminate.
     apply in_cons. auto.
 Qed.
-Hint Resolve nth_error_in: coqlib.
+Global Hint Resolve nth_error_in: coqlib.
 
 Lemma nth_error_nil:
   forall (A: Type) (idx: nat), nth_error (@nil A) idx = None.
 Proof.
   induction idx; simpl; intros; reflexivity.
 Qed.
-Hint Resolve nth_error_nil: coqlib.
+Global Hint Resolve nth_error_nil: coqlib.
 
 (** Compute the length of a list, with result in [Z]. *)
 
@@ -599,8 +596,8 @@ Remark list_length_z_aux_shift:
   list_length_z_aux l n = list_length_z_aux l m + (n - m).
 Proof.
   induction l; intros; simpl.
-  omega.
-  replace (n - m) with (Z.succ n - Z.succ m) by omega. auto.
+  lia.
+  replace (n - m) with (Z.succ n - Z.succ m) by lia. auto.
 Qed.
 
 Definition list_length_z (A: Type) (l: list A) : Z :=
@@ -611,15 +608,15 @@ Lemma list_length_z_cons:
   list_length_z (hd :: tl) = list_length_z tl + 1.
 Proof.
   intros. unfold list_length_z. simpl.
-  rewrite (list_length_z_aux_shift tl 1 0). omega.
+  rewrite (list_length_z_aux_shift tl 1 0). lia.
 Qed.
 
 Lemma list_length_z_pos:
   forall (A: Type) (l: list A),
   list_length_z l >= 0.
 Proof.
-  induction l; simpl. unfold list_length_z; simpl. omega.
-  rewrite list_length_z_cons. omega.
+  induction l; simpl. unfold list_length_z; simpl. lia.
+  rewrite list_length_z_cons. lia.
 Qed.
 
 Lemma list_length_z_map:
@@ -663,8 +660,8 @@ Proof.
   induction l; simpl; intros.
   discriminate.
   rewrite list_length_z_cons. destruct (zeq n 0).
-  generalize (list_length_z_pos l); omega.
-  exploit IHl; eauto. omega.
+  generalize (list_length_z_pos l); lia.
+  exploit IHl; eauto. lia.
 Qed.
 
 (** Properties of [List.incl] (list inclusion). *)
@@ -675,7 +672,7 @@ Lemma incl_cons_inv:
 Proof.
   unfold incl; intros. apply H. apply in_cons. auto.
 Qed.
-Hint Resolve incl_cons_inv: coqlib.
+Global Hint Resolve incl_cons_inv: coqlib.
 
 Lemma incl_app_inv_l:
   forall (A: Type) (l1 l2 m: list A),
@@ -691,7 +688,7 @@ Proof.
   unfold incl; intros. apply H. apply in_or_app. right; assumption.
 Qed.
 
-Hint Resolve  incl_tl incl_refl incl_app_inv_l incl_app_inv_r: coqlib.
+Global Hint Resolve  incl_tl incl_refl incl_app_inv_l incl_app_inv_r: coqlib.
 
 Lemma incl_same_head:
   forall (A: Type) (x: A) (l1 l2: list A),
@@ -1015,6 +1012,14 @@ Proof.
   generalize list_norepet_app; firstorder.
 Qed.
 
+Lemma list_norepet_rev:
+  forall (A: Type) (l: list A), list_norepet l -> list_norepet (List.rev l).
+Proof.
+  induction 1; simpl.
+- constructor.
+- apply list_norepet_append_commut. simpl. constructor; auto. rewrite <- List.in_rev; auto.
+Qed.
+
 (** [is_tail l1 l2] holds iff [l2] is of the form [l ++ l1] for some [l]. *)
 
 Inductive is_tail (A: Type): list A -> list A -> Prop :=
@@ -1038,7 +1043,7 @@ Proof.
   constructor. constructor. constructor. auto.
 Qed.
 
-Hint Resolve is_tail_refl is_tail_cons is_tail_in is_tail_cons_left: coqlib.
+Global Hint Resolve is_tail_refl is_tail_cons is_tail_in is_tail_cons_left: coqlib.
 
 Lemma is_tail_incl:
   forall (A: Type) (l1 l2: list A), is_tail l1 l2 -> incl l1 l2.
@@ -1064,7 +1069,7 @@ Proof.
   induction l1; cbn; auto with coqlib.
   intros l2 l3 H; inversion H; eauto with coqlib.
 Qed.
-Hint Resolve is_tail_app_inv: coqlib.
+Global Hint Resolve is_tail_app_inv: coqlib.
 
 Lemma is_tail_app_right A (l2 l1: list A): is_tail l1 (l2++l1).
 Proof.
@@ -1085,7 +1090,7 @@ Lemma is_tail_bound A (l1 l2: list A):
 Proof.
   intros H; destruct (is_tail_app_def H) as (l3 & EQ).
   subst; rewrite app_length.
-  omega.
+  lia.
 Qed.
 
 (** [list_forall2 P [x1 ... xN] [y1 ... yM]] holds iff [N = M] and
@@ -1184,26 +1189,6 @@ Proof.
   destruct l; simpl; auto.
 Qed.
 
-(** A list of [n] elements, all equal to [x]. *)
-
-Fixpoint list_repeat {A: Type} (n: nat) (x: A) {struct n} :=
-  match n with
-  | O => nil
-  | S m => x :: list_repeat m x
-  end.
-
-Lemma length_list_repeat:
-  forall (A: Type) n (x: A), length (list_repeat n x) = n.
-Proof.
-  induction n; simpl; intros. auto. decEq; auto.
-Qed.
-
-Lemma in_list_repeat:
-  forall (A: Type) n (x: A) y, In y (list_repeat n x) -> y = x.
-Proof.
-  induction n; simpl; intros. elim H. destruct H; auto.
-Qed.
-
 (** * Definitions and theorems over boolean types *)
 
 Definition proj_sumbool {P Q: Prop} (a: {P} + {Q}) : bool :=
diff --git a/lib/Decidableplus.v b/lib/Decidableplus.v
index 66dffb3a..69ba4723 100644
--- a/lib/Decidableplus.v
+++ b/lib/Decidableplus.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -126,14 +127,14 @@ Program Instance Decidable_ge_Z : forall (x y: Z), Decidable (x >= y) := {
   Decidable_witness := Z.geb x y
 }.
 Next Obligation.
-  rewrite Z.geb_le. intuition omega.
+  rewrite Z.geb_le. intuition lia.
 Qed.
 
 Program Instance Decidable_gt_Z : forall (x y: Z), Decidable (x > y) := {
   Decidable_witness := Z.gtb x y
 }.
 Next Obligation.
-  rewrite Z.gtb_lt. intuition omega.
+  rewrite Z.gtb_lt. intuition lia.
 Qed.
 
 Program Instance Decidable_divides : forall (x y: Z), Decidable (x | y) := {
@@ -146,7 +147,7 @@ Next Obligation.
   destruct (Z.eq_dec x 0).
   subst x. rewrite Z.mul_0_r in EQ. subst y. reflexivity.
   assert (k = y / x).
-  { apply Zdiv_unique_full with 0. red; omega. rewrite EQ; ring. }
+  { apply Zdiv_unique_full with 0. red; lia. rewrite EQ; ring. }
   congruence.
 Qed.
 
diff --git a/lib/FSetAVLplus.v b/lib/FSetAVLplus.v
index f16805c6..936814c1 100644
--- a/lib/FSetAVLplus.v
+++ b/lib/FSetAVLplus.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Floats.v b/lib/Floats.v
index ac67b88c..b10b3392 100644
--- a/lib/Floats.v
+++ b/lib/Floats.v
@@ -7,10 +7,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -169,7 +170,7 @@ Proof.
   { apply Digits.Zdigits_le_Zpower. rewrite <- H. rewrite Z.abs_eq; tauto. }
   destruct (zeq p' 0).
 - rewrite e. simpl; auto.
-- rewrite Z2Pos.id by omega. omega.
+- rewrite Z2Pos.id by lia. lia.
 Qed.
 
 (** Transform a Nan payload to a quiet Nan payload. *)
@@ -178,7 +179,7 @@ Definition quiet_nan_64_payload (p: positive) :=
   Z.to_pos (P_mod_two_p (Pos.lor p ((iter_nat xO 51 1%positive))) 52%nat).
 
 Lemma quiet_nan_64_proof: forall p, nan_pl 53 (quiet_nan_64_payload p) = true.
-Proof. intros; apply normalized_nan; auto; omega. Qed.
+Proof. intros; apply normalized_nan; auto; lia. Qed.
 
 Definition quiet_nan_64 (sp: bool * positive) : {x :float | is_nan _ _ x = true} :=
   let (s, p) := sp in
@@ -190,7 +191,7 @@ Definition quiet_nan_32_payload (p: positive) :=
   Z.to_pos (P_mod_two_p (Pos.lor p ((iter_nat xO 22 1%positive))) 23%nat).
 
 Lemma quiet_nan_32_proof: forall p, nan_pl 24 (quiet_nan_32_payload p) = true.
-Proof. intros; apply normalized_nan; auto; omega. Qed.
+Proof. intros; apply normalized_nan; auto; lia. Qed.
 
 Definition quiet_nan_32 (sp: bool * positive) : {x :float32 | is_nan _ _ x = true} :=
   let (s, p) := sp in
@@ -224,7 +225,7 @@ Proof.
   rewrite Z.ltb_lt in *.
   unfold Pos.shiftl_nat, nat_rect, Digits.digits2_pos.
   fold (Digits.digits2_pos p).
-  zify; omega.
+  zify; lia.
 Qed.
 
 Definition expand_nan s p H : {x | is_nan _ _ x = true} :=
@@ -397,7 +398,7 @@ Ltac smart_omega :=
   compute_this Int64.modulus; compute_this Int64.half_modulus;
   compute_this Int64.max_unsigned;
   compute_this (Z.pow_pos 2 1024); compute_this (Z.pow_pos 2 53); compute_this (Z.pow_pos 2 52); compute_this (Z.pow_pos 2 32);
-  zify; omega.
+  zify; lia.
 
 (** Commutativity properties of addition and multiplication. *)
 
@@ -493,7 +494,7 @@ Proof.
   intros; unfold of_bits, to_bits, bits_of_b64, b64_of_bits.
   rewrite Int64.unsigned_repr, binary_float_of_bits_of_binary_float; [reflexivity|].
   generalize (bits_of_binary_float_range 52 11 __ __ f).
-  change (2^(52+11+1)) with (Int64.max_unsigned + 1). omega.
+  change (2^(52+11+1)) with (Int64.max_unsigned + 1). lia.
 Qed.
 
 Theorem to_of_bits:
@@ -537,7 +538,7 @@ Proof.
   rewrite BofZ_plus by auto.
   f_equal.
   unfold Int.ltu in H. destruct zlt in H; try discriminate.
-  unfold y, Int.sub. rewrite Int.signed_repr. omega.
+  unfold y, Int.sub. rewrite Int.signed_repr. lia.
   compute_this (Int.unsigned ox8000_0000); smart_omega.
 Qed.
 
@@ -559,8 +560,8 @@ Proof.
     change (Int.and ox7FFF_FFFF ox8000_0000) with Int.zero. rewrite ! Int.and_zero; auto.
   }
   assert (RNG: 0 <= Int.unsigned lo < two_p 31).
-  { unfold lo. change ox7FFF_FFFF with (Int.repr (two_p 31 - 1)). rewrite <- Int.zero_ext_and by omega.
-    apply Int.zero_ext_range. compute_this Int.zwordsize. omega. }
+  { unfold lo. change ox7FFF_FFFF with (Int.repr (two_p 31 - 1)). rewrite <- Int.zero_ext_and by lia.
+    apply Int.zero_ext_range. compute_this Int.zwordsize. lia. }
   assert (B: forall i, 0 <= i < Int.zwordsize -> Int.testbit ox8000_0000 i = if zeq i 31 then true else false).
   { intros; unfold Int.testbit. change (Int.unsigned ox8000_0000) with (2^31).
     destruct (zeq i 31). subst i; auto. apply Z.pow2_bits_false; auto. } 
@@ -573,12 +574,12 @@ Proof.
   assert (SU: - Int.signed hi = Int.unsigned hi).
   { destruct EITHER as [EQ|EQ]; rewrite EQ; reflexivity. }
   unfold Z.sub; rewrite SU, <- E. 
-  unfold Int.add; rewrite Int.unsigned_repr, Int.signed_eq_unsigned. omega.
-  - assert (Int.max_signed = two_p 31 - 1) by reflexivity. omega.
+  unfold Int.add; rewrite Int.unsigned_repr, Int.signed_eq_unsigned. lia.
+  - assert (Int.max_signed = two_p 31 - 1) by reflexivity. lia.
   - assert (Int.unsigned hi = 0 \/ Int.unsigned hi = two_p 31)
     by (destruct EITHER as [EQ|EQ]; rewrite EQ; [left|right]; reflexivity).
     assert (Int.max_unsigned = two_p 31 + two_p 31 - 1) by reflexivity.
-    omega.
+    lia.
 Qed.
 
 Theorem to_intu_to_int_1:
@@ -601,14 +602,14 @@ Proof.
   { rewrite ZofB_correct in C. destruct (is_finite _ _ x) eqn:FINx; congruence. }
   destruct (zeq p 0).
   subst p; smart_omega.
-  destruct (ZofB_range_pos 53 1024 __ __ x p C) as [P Q]. omega.
+  destruct (ZofB_range_pos 53 1024 __ __ x p C) as [P Q]. lia.
   assert (CMP: Bcompare _ _ x y = Some Lt).
   { unfold cmp, cmp_of_comparison, compare in H. destruct (Bcompare _ _ x y) as [[]|]; auto; discriminate. }
   rewrite Bcompare_correct in CMP by auto.
   inv CMP. apply Rcompare_Lt_inv in H1. rewrite EQy in H1.
   assert (p < Int.unsigned ox8000_0000).
   { apply lt_IZR. apply Rle_lt_trans with (1 := P) (2 := H1). }
-  change Int.max_signed with (Int.unsigned ox8000_0000 - 1). omega.
+  change Int.max_signed with (Int.unsigned ox8000_0000 - 1). lia.
 Qed.
 
 Theorem to_intu_to_int_2:
@@ -640,7 +641,7 @@ Proof.
     compute_this (Int.unsigned ox8000_0000). smart_omega.
     apply Rge_le; auto.
   }
-  unfold to_int; rewrite EQ. simpl. unfold Int.sub. rewrite Int.unsigned_repr by omega. auto.
+  unfold to_int; rewrite EQ. simpl. unfold Int.sub. rewrite Int.unsigned_repr by lia. auto.
 Qed.
 
 (** Conversions from ints to floats can be defined as bitwise manipulations
@@ -659,8 +660,8 @@ Proof.
   - f_equal. rewrite Int64.ofwords_add'. reflexivity.
   - apply split_join_bits.
     generalize (Int.unsigned_range x).
-    compute_this Int.modulus; compute_this (2^52); omega.
-    compute_this (2^11); omega.
+    compute_this Int.modulus; compute_this (2^52); lia.
+    compute_this (2^11); lia.
 Qed.
 
 Lemma from_words_value:
@@ -698,7 +699,7 @@ Theorem of_intu_from_words:
 Proof.
   intros. pose proof (Int.unsigned_range x).
   rewrite ! from_words_eq. unfold sub. rewrite BofZ_minus.
-  unfold of_intu. apply (f_equal (BofZ 53 1024 __ __)). rewrite Int.unsigned_zero. omega.
+  unfold of_intu. apply (f_equal (BofZ 53 1024 __ __)). rewrite Int.unsigned_zero. lia.
   apply integer_representable_n; auto; smart_omega.
   apply integer_representable_n; auto; rewrite Int.unsigned_zero; smart_omega.
 Qed.
@@ -725,7 +726,7 @@ Proof.
   rewrite ! from_words_eq. rewrite ox8000_0000_signed_unsigned.
   change (Int.unsigned ox8000_0000) with Int.half_modulus.
   unfold sub. rewrite BofZ_minus.
-  unfold of_int. apply f_equal. omega.
+  unfold of_int. apply f_equal. lia.
   apply integer_representable_n; auto; smart_omega.
   apply integer_representable_n; auto; smart_omega.
 Qed.
@@ -741,8 +742,8 @@ Proof.
   - f_equal. rewrite Int64.ofwords_add'. reflexivity.
   - apply split_join_bits.
     generalize (Int.unsigned_range x).
-    compute_this Int.modulus; compute_this (2^52); omega.
-    compute_this (2^11); omega.
+    compute_this Int.modulus; compute_this (2^52); lia.
+    compute_this (2^11); lia.
 Qed.
 
 Lemma from_words_value':
@@ -772,11 +773,11 @@ Proof.
   destruct (BofZ_representable 53 1024 __ __ (2^84 + Int.unsigned x * 2^32)) as (D & E & F).
   replace (2^84 + Int.unsigned x * 2^32)
     with  ((2^52 + Int.unsigned x) * 2^32) by ring.
-  apply integer_representable_n2p; auto. smart_omega. omega. omega.
+  apply integer_representable_n2p; auto. smart_omega. lia. lia.
   apply B2R_Bsign_inj; auto.
-  rewrite A, D. rewrite <- IZR_Zpower by omega. rewrite <- plus_IZR. auto.
+  rewrite A, D. rewrite <- IZR_Zpower by lia. rewrite <- plus_IZR. auto.
   rewrite C, F. symmetry. apply Zlt_bool_false.
-  compute_this (2^84); compute_this (2^32); omega.
+  compute_this (2^84); compute_this (2^32); lia.
 Qed.
 
 Theorem of_longu_from_words:
@@ -803,12 +804,12 @@ Proof.
   rewrite <- (Int64.ofwords_recompose l) at 1. rewrite Int64.ofwords_add'.
   fold xh; fold xl. compute_this (two_p 32); compute_this p20; ring.
   apply integer_representable_n2p; auto.
-  compute_this p20; smart_omega. omega. omega.
+  compute_this p20; smart_omega. lia. lia.
   apply integer_representable_n; auto; smart_omega.
   replace (2^84 + xh * 2^32) with ((2^52 + xh) * 2^32) by ring.
-  apply integer_representable_n2p; auto. smart_omega. omega. omega.
+  apply integer_representable_n2p; auto. smart_omega. lia. lia.
   change (2^84 + p20 * 2^32) with ((2^52 + 1048576) * 2^32).
-  apply integer_representable_n2p; auto. omega. omega.
+  apply integer_representable_n2p; auto. lia. lia.
 Qed.
 
 Theorem of_long_from_words:
@@ -837,15 +838,15 @@ Proof.
   rewrite <- (Int64.ofwords_recompose l) at 1. rewrite Int64.ofwords_add''.
   fold xh; fold xl. compute_this (two_p 32); ring.
   apply integer_representable_n2p; auto.
-  compute_this (2^20); smart_omega. omega. omega.
+  compute_this (2^20); smart_omega. lia. lia.
   apply integer_representable_n; auto; smart_omega.
   replace (2^84 + (xh + Int.half_modulus) * 2^32)
      with ((2^52 + xh + Int.half_modulus) * 2^32)
        by (compute_this Int.half_modulus; ring).
-  apply integer_representable_n2p; auto. smart_omega. omega. omega.
+  apply integer_representable_n2p; auto. smart_omega. lia. lia.
   change (2^84 + p * 2^32) with ((2^52 + p) * 2^32).
   apply integer_representable_n2p; auto.
-  compute_this p; smart_omega. omega.
+  compute_this p; smart_omega. lia.
 Qed.
 
 (** Conversions from 64-bit integers can be expressed in terms of
@@ -867,7 +868,7 @@ Proof.
   assert (DECOMP: x = yh * 2^32 + yl).
   { unfold x. rewrite <- (Int64.ofwords_recompose l). apply Int64.ofwords_add'. }
   rewrite BofZ_mult. rewrite BofZ_plus. rewrite DECOMP; auto.
-  apply integer_representable_n2p; auto. smart_omega. omega. omega.
+  apply integer_representable_n2p; auto. smart_omega. lia. lia.
   apply integer_representable_n; auto; smart_omega.
   apply integer_representable_n; auto; smart_omega.
   apply integer_representable_n; auto; smart_omega.
@@ -890,7 +891,7 @@ Proof.
   assert (DECOMP: x = yh * 2^32 + yl).
   { unfold x. rewrite <- (Int64.ofwords_recompose l), Int64.ofwords_add''. auto. }
   rewrite BofZ_mult. rewrite BofZ_plus. rewrite DECOMP; auto.
-  apply integer_representable_n2p; auto. smart_omega. omega. omega.
+  apply integer_representable_n2p; auto. smart_omega. lia. lia.
   apply integer_representable_n; auto; smart_omega.
   apply integer_representable_n; auto; smart_omega.
   apply integer_representable_n; auto. compute; intuition congruence.
@@ -932,53 +933,53 @@ Proof.
   { intros; unfold n; autorewrite with ints; auto. rewrite Int64.unsigned_one.
     rewrite Int64.bits_one. compute_this Int64.zwordsize.
     destruct (zeq i 0); simpl proj_sumbool.
-    rewrite zlt_true by omega. rewrite andb_true_r. subst i; auto.
+    rewrite zlt_true by lia. rewrite andb_true_r. subst i; auto.
     rewrite andb_false_r, orb_false_r.
-    destruct (zeq i 63). subst i. apply zlt_false; omega.
-    apply zlt_true; omega. }
+    destruct (zeq i 63). subst i. apply zlt_false; lia.
+    apply zlt_true; lia. }
   assert (NB2: forall i, 0 <= i ->
                Z.testbit (Int64.signed n * 2^1) i =
                if zeq i 0 then false else
                if zeq i 1 then Int64.testbit x 1 || Int64.testbit x 0 else
                Int64.testbit x i).
-  { intros. rewrite Z.mul_pow2_bits by omega. destruct (zeq i 0).
-    apply Z.testbit_neg_r; omega.
-    rewrite Int64.bits_signed by omega. compute_this Int64.zwordsize.
+  { intros. rewrite Z.mul_pow2_bits by lia. destruct (zeq i 0).
+    apply Z.testbit_neg_r; lia.
+    rewrite Int64.bits_signed by lia. compute_this Int64.zwordsize.
     destruct (zlt (i-1) 64).
-    rewrite NB by omega. destruct (zeq i 1).
+    rewrite NB by lia. destruct (zeq i 1).
     subst. rewrite dec_eq_true by auto. auto.
-    rewrite dec_eq_false by omega. destruct (zeq (i - 1) 63).
-    symmetry. apply Int64.bits_above. compute_this Int64.zwordsize; omega.
-    f_equal; omega.
-    rewrite NB by omega. rewrite dec_eq_false by omega. rewrite dec_eq_true by auto.
-    rewrite dec_eq_false by omega. symmetry. apply Int64.bits_above. compute_this Int64.zwordsize; omega.
+    rewrite dec_eq_false by lia. destruct (zeq (i - 1) 63).
+    symmetry. apply Int64.bits_above. compute_this Int64.zwordsize; lia.
+    f_equal; lia.
+    rewrite NB by lia. rewrite dec_eq_false by lia. rewrite dec_eq_true by auto.
+    rewrite dec_eq_false by lia. symmetry. apply Int64.bits_above. compute_this Int64.zwordsize; lia.
   }
   assert (EQ: Int64.signed n * 2 = int_round_odd (Int64.unsigned x) 1).
   {
-  symmetry. apply (int_round_odd_bits 53 1024). omega.
-  intros. rewrite NB2 by omega. replace i with 0 by omega. auto.
-  rewrite NB2 by omega. rewrite dec_eq_false by omega. rewrite dec_eq_true.
+  symmetry. apply int_round_odd_bits. lia.
+  intros. rewrite NB2 by lia. replace i with 0 by lia. auto.
+  rewrite NB2 by lia. rewrite dec_eq_false by lia. rewrite dec_eq_true.
   rewrite orb_comm. unfold Int64.testbit. change (2^1) with 2.
   destruct (Z.testbit (Int64.unsigned x) 0) eqn:B0;
-  [rewrite Z.testbit_true in B0 by omega|rewrite Z.testbit_false in B0 by omega];
+  [rewrite Z.testbit_true in B0 by lia|rewrite Z.testbit_false in B0 by lia];
   change (2^0) with 1 in B0; rewrite Zdiv_1_r in B0; rewrite B0; auto.
-  intros. rewrite NB2 by omega. rewrite ! dec_eq_false by omega. auto.
+  intros. rewrite NB2 by lia. rewrite ! dec_eq_false by lia. auto.
   }
   unfold mul, of_long, of_longu.
   rewrite BofZ_mult_2p.
 - change (2^1) with 2. rewrite EQ. apply BofZ_round_odd with (p := 1).
-+ omega.
++ lia.
 + apply Z.le_trans with Int64.modulus; trivial. smart_omega.
-+ omega.
-+ apply Z.le_trans with (2^63). compute; intuition congruence. xomega.
++ lia.
++ apply Z.le_trans with (2^63). compute; intuition congruence. extlia.
 - apply Z.le_trans with Int64.modulus; trivial.
   pose proof (Int64.signed_range n).
   compute_this Int64.min_signed; compute_this Int64.max_signed;
-  compute_this Int64.modulus; xomega.
+  compute_this Int64.modulus; extlia.
 - assert (2^63 <= int_round_odd (Int64.unsigned x) 1).
-  { change (2^63) with (int_round_odd (2^63) 1). apply (int_round_odd_le 0 0); omega. }
-  rewrite <- EQ in H1. compute_this (2^63). compute_this (2^53). xomega.
-- omega.
+  { change (2^63) with (int_round_odd (2^63) 1). apply int_round_odd_le; lia. }
+  rewrite <- EQ in H1. compute_this (2^63). compute_this (2^53). extlia.
+- lia.
 Qed.
 
 (** Conversions to/from 32-bit integers can be implemented by going through 64-bit integers. *)
@@ -992,8 +993,8 @@ Proof.
   intros. exploit ZofB_range_inversion; eauto. intros (A & B & C).
   unfold ZofB_range; rewrite C.
   replace (min2 <=? n) with true. replace (n <=? max2) with true. auto.
-  symmetry; apply Z.leb_le; omega.
-  symmetry; apply Z.leb_le; omega.
+  symmetry; apply Z.leb_le; lia.
+  symmetry; apply Z.leb_le; lia.
 Qed.
 
 Theorem to_int_to_long:
@@ -1015,7 +1016,7 @@ Proof.
   exploit ZofB_range_inversion; eauto. intros (A & B & C).
   replace (ZofB_range 53 1024 f 0 Int64.max_unsigned) with (Some z).
   simpl. rewrite Int.unsigned_repr; auto.
-  symmetry; eapply ZofB_range_widen; eauto. omega. compute; congruence.
+  symmetry; eapply ZofB_range_widen; eauto. lia. compute; congruence.
 Qed.
 
 Theorem to_intu_to_long:
@@ -1244,7 +1245,7 @@ Theorem cmp_double:
   forall f1 f2 c, cmp c f1 f2 = Float.cmp c (to_double f1) (to_double f2).
 Proof.
   unfold cmp, Float.cmp; intros. f_equal. symmetry. apply Bcompare_Bconv_widen.
-  red; omega. omega. omega.
+  red; lia. lia. lia.
 Qed.
 
 (** Properties of conversions to/from in-memory representation.
@@ -1256,7 +1257,7 @@ Proof.
   intros; unfold of_bits, to_bits, bits_of_b32, b32_of_bits.
   rewrite Int.unsigned_repr, binary_float_of_bits_of_binary_float; [reflexivity|].
   generalize (bits_of_binary_float_range 23 8 __ __ f).
-  change (2^(23+8+1)) with (Int.max_unsigned + 1). omega.
+  change (2^(23+8+1)) with (Int.max_unsigned + 1). lia.
 Qed.
 
 Theorem to_of_bits:
@@ -1296,7 +1297,7 @@ Proof.
   unfold to_int in H.
   destruct (ZofB_range _ _ f Int.min_signed Int.max_signed) as [n'|] eqn:E; inv H.
   unfold Float.to_int, to_double, Float.of_single.
-  erewrite ZofB_range_Bconv; eauto. auto. omega. omega. omega. omega.
+  erewrite ZofB_range_Bconv; eauto. auto. lia. lia. lia. lia.
 Qed.
 
 Theorem to_intu_double:
@@ -1306,7 +1307,7 @@ Proof.
   unfold to_intu in H.
   destruct (ZofB_range _ _ f 0 Int.max_unsigned) as [n'|] eqn:E; inv H.
   unfold Float.to_intu, to_double, Float.of_single.
-  erewrite ZofB_range_Bconv; eauto. auto. omega. omega. omega. omega.
+  erewrite ZofB_range_Bconv; eauto. auto. lia. lia. lia. lia.
 Qed.
 
 Theorem to_long_double:
@@ -1316,7 +1317,7 @@ Proof.
   unfold to_long in H.
   destruct (ZofB_range _ _ f Int64.min_signed Int64.max_signed) as [n'|] eqn:E; inv H.
   unfold Float.to_long, to_double, Float.of_single.
-  erewrite ZofB_range_Bconv; eauto. auto. omega. omega. omega. omega.
+  erewrite ZofB_range_Bconv; eauto. auto. lia. lia. lia. lia.
 Qed.
 
 Theorem to_longu_double:
@@ -1326,7 +1327,7 @@ Proof.
   unfold to_longu in H.
   destruct (ZofB_range _ _ f 0 Int64.max_unsigned) as [n'|] eqn:E; inv H.
   unfold Float.to_longu, to_double, Float.of_single.
-  erewrite ZofB_range_Bconv; eauto. auto. omega. omega. omega. omega.
+  erewrite ZofB_range_Bconv; eauto. auto. lia. lia. lia. lia.
 Qed.
 
 (** Conversions from 64-bit integers to single-precision floats can be expressed
@@ -1341,37 +1342,37 @@ Proof.
   intros.
   assert (POS: 0 < 2^p) by (apply (Zpower_gt_0 radix2); auto).
   assert (A: Z.land n (2^p-1) = n mod 2^p).
-  { rewrite <- Z.land_ones by auto. f_equal. rewrite Z.ones_equiv. omega. }
+  { rewrite <- Z.land_ones by auto. f_equal. rewrite Z.ones_equiv. lia. }
   rewrite A.
   assert (B: 0 <= n mod 2^p < 2^p).
-  { apply Z_mod_lt. omega. }
+  { apply Z_mod_lt. lia. }
   set (m := n mod 2^p + (2^p-1)) in *.
   assert (C: m / 2^p = if zeq (n mod 2^p) 0 then 0 else 1).
   { unfold m. destruct (zeq (n mod 2^p) 0).
-    rewrite e. apply Z.div_small. omega.
-    eapply Coqlib.Zdiv_unique with (n mod 2^p - 1). ring. omega. }
+    rewrite e. apply Z.div_small. lia.
+    eapply Coqlib.Zdiv_unique with (n mod 2^p - 1). ring. lia. }
   assert (D: Z.testbit m p = if zeq (n mod 2^p) 0 then false else true).
   { destruct (zeq (n mod 2^p) 0).
     apply Z.testbit_false; auto. rewrite C; auto.
     apply Z.testbit_true; auto. rewrite C; auto. }
   assert (E: forall i, p < i -> Z.testbit m i = false).
-  { intros. apply Z.testbit_false. omega.
+  { intros. apply Z.testbit_false. lia.
     replace (m / 2^i) with 0. auto. symmetry. apply Z.div_small.
-    unfold m. split. omega. apply Z.lt_le_trans with (2 * 2^p). omega.
-    change 2 with (2^1) at 1. rewrite <- (Zpower_plus radix2) by omega.
-    apply Zpower_le. omega. }
+    unfold m. split. lia. apply Z.lt_le_trans with (2 * 2^p). lia.
+    change 2 with (2^1) at 1. rewrite <- (Zpower_plus radix2) by lia.
+    apply Zpower_le. lia. }
   assert (F: forall i, 0 <= i -> Z.testbit (-2^p) i = if zlt i p then false else true).
   { intros. rewrite Z.bits_opp by auto. rewrite <- Z.ones_equiv.
     destruct (zlt i p).
-    rewrite Z.ones_spec_low by omega. auto.
-    rewrite Z.ones_spec_high by omega. auto. }
+    rewrite Z.ones_spec_low by lia. auto.
+    rewrite Z.ones_spec_high by lia. auto. }
   apply int_round_odd_bits; auto.
-  - intros. rewrite Z.land_spec, F, zlt_true by omega. apply andb_false_r.
-  - rewrite Z.land_spec, Z.lor_spec, D, F, zlt_false, andb_true_r by omega.
+  - intros. rewrite Z.land_spec, F, zlt_true by lia. apply andb_false_r.
+  - rewrite Z.land_spec, Z.lor_spec, D, F, zlt_false, andb_true_r by lia.
     destruct (Z.eqb (n mod 2^p) 0) eqn:Z.
     rewrite Z.eqb_eq in Z. rewrite Z, zeq_true. apply orb_false_r.
     rewrite Z.eqb_neq in Z. rewrite zeq_false by auto. apply orb_true_r.
-  - intros. rewrite Z.land_spec, Z.lor_spec, E, F, zlt_false, andb_true_r by omega.
+  - intros. rewrite Z.land_spec, Z.lor_spec, E, F, zlt_false, andb_true_r by lia.
     apply orb_false_r.
 Qed.
 
@@ -1380,22 +1381,22 @@ Lemma of_long_round_odd:
   2^36 <= Z.abs n < 2^64 ->
   BofZ 24 128 __ __ n = Bconv _ _ 24 128 __ __ conv_nan mode_NE (BofZ 53 1024 __ __ (Z.land (Z.lor n ((Z.land n 2047) + 2047)) (-2048))).
 Proof.
-  intros. rewrite <- (int_round_odd_plus 11) by omega.
+  intros. rewrite <- (int_round_odd_plus 11) by lia.
   assert (-2^64 <= int_round_odd n 11).
-  { change (-2^64) with (int_round_odd (-2^64) 11). apply (int_round_odd_le 0 0); xomega. }
+  { change (-2^64) with (int_round_odd (-2^64) 11). apply int_round_odd_le; extlia. }
   assert (int_round_odd n 11 <= 2^64).
-  { change (2^64) with (int_round_odd (2^64) 11). apply (int_round_odd_le 0 0); xomega. }
+  { change (2^64) with (int_round_odd (2^64) 11). apply int_round_odd_le; extlia. }
   rewrite Bconv_BofZ.
   apply BofZ_round_odd with (p := 11).
-  omega.
-  apply Z.le_trans with (2^64). omega. compute; intuition congruence.
-  omega.
+  lia.
+  apply Z.le_trans with (2^64). lia. compute; intuition congruence.
+  lia.
   exact (proj1 H).
-  unfold int_round_odd. apply integer_representable_n2p_wide. auto. omega.
+  unfold int_round_odd. apply integer_representable_n2p_wide. auto. lia.
   unfold int_round_odd in H0, H1.
   split; (apply Zmult_le_reg_r with (2^11); [compute; auto | assumption]).
-  omega.
-  omega.
+  lia.
+  lia.
 Qed.
 
 Theorem of_longu_double_1:
@@ -1404,7 +1405,7 @@ Theorem of_longu_double_1:
   of_longu n = of_double (Float.of_longu n).
 Proof.
   intros. symmetry; apply Bconv_BofZ. apply integer_representable_n; auto.
-  pose proof (Int64.unsigned_range n); omega.
+  pose proof (Int64.unsigned_range n); lia.
 Qed.
 
 Theorem of_longu_double_2:
@@ -1422,14 +1423,14 @@ Proof.
   unfold of_double, Float.to_single. instantiate (1 := Float.to_single_nan).
   f_equal. unfold Float.of_longu. f_equal.
   set (n' := Z.land (Z.lor (Int64.unsigned n) (Z.land (Int64.unsigned n) 2047 + 2047)) (-2048)).
-  assert (int_round_odd (Int64.unsigned n) 11 = n') by (apply int_round_odd_plus; omega).
+  assert (int_round_odd (Int64.unsigned n) 11 = n') by (apply int_round_odd_plus; lia).
   assert (0 <= n').
-  { rewrite <- H1. change 0 with (int_round_odd 0 11). apply (int_round_odd_le 0 0); omega. }
+  { rewrite <- H1. change 0 with (int_round_odd 0 11). apply int_round_odd_le; lia. }
   assert (n' < Int64.modulus).
   { apply Z.le_lt_trans with (int_round_odd (Int64.modulus - 1) 11).
-    rewrite <- H1. apply (int_round_odd_le 0 0); omega.
+    rewrite <- H1. apply int_round_odd_le; lia.
     compute; auto. }
-  rewrite <- (Int64.unsigned_repr n') by (unfold Int64.max_unsigned; omega).
+  rewrite <- (Int64.unsigned_repr n') by (unfold Int64.max_unsigned; lia).
   f_equal. Int64.bit_solve. rewrite Int64.testbit_repr by auto. unfold n'.
   rewrite Z.land_spec, Z.lor_spec. f_equal. f_equal.
   unfold Int64.testbit. rewrite Int64.add_unsigned.
@@ -1438,11 +1439,11 @@ Proof.
          Int64.unsigned (Int64.repr 2047))) i).
   rewrite Int64.testbit_repr by auto. f_equal. f_equal. unfold Int64.and.
   symmetry. apply Int64.unsigned_repr. change 2047 with (Z.ones 11).
-  rewrite Z.land_ones by omega.
+  rewrite Z.land_ones by lia.
   exploit (Z_mod_lt (Int64.unsigned n) (2^11)). compute; auto.
-  assert (2^11 < Int64.max_unsigned) by (compute; auto). omega.
+  assert (2^11 < Int64.max_unsigned) by (compute; auto). lia.
   apply Int64.same_bits_eqm; auto. exists (-1); auto.
-  split. xomega. change (2^64) with Int64.modulus. xomega.
+  split. extlia. change (2^64) with Int64.modulus. extlia.
 Qed.
 
 Theorem of_long_double_1:
@@ -1450,7 +1451,7 @@ Theorem of_long_double_1:
   Z.abs (Int64.signed n) <= 2^53 ->
   of_long n = of_double (Float.of_long n).
 Proof.
-  intros. symmetry; apply Bconv_BofZ. apply integer_representable_n; auto. xomega.
+  intros. symmetry; apply Bconv_BofZ. apply integer_representable_n; auto. extlia.
 Qed.
 
 Theorem of_long_double_2:
@@ -1468,34 +1469,34 @@ Proof.
   unfold of_double, Float.to_single. instantiate (1 := Float.to_single_nan).
   f_equal. unfold Float.of_long. f_equal.
   set (n' := Z.land (Z.lor (Int64.signed n) (Z.land (Int64.signed n) 2047 + 2047)) (-2048)).
-  assert (int_round_odd (Int64.signed n) 11 = n') by (apply int_round_odd_plus; omega).
+  assert (int_round_odd (Int64.signed n) 11 = n') by (apply int_round_odd_plus; lia).
   assert (Int64.min_signed <= n').
-  { rewrite <- H1. change Int64.min_signed with (int_round_odd Int64.min_signed 11). apply (int_round_odd_le 0 0); omega. }
+  { rewrite <- H1. change Int64.min_signed with (int_round_odd Int64.min_signed 11). apply int_round_odd_le; lia. }
   assert (n' <= Int64.max_signed).
   { apply Z.le_trans with (int_round_odd Int64.max_signed 11).
-    rewrite <- H1. apply (int_round_odd_le 0 0); omega.
+    rewrite <- H1. apply int_round_odd_le; lia.
     compute; intuition congruence. }
-  rewrite <- (Int64.signed_repr n') by omega.
+  rewrite <- (Int64.signed_repr n') by lia.
   f_equal. Int64.bit_solve. rewrite Int64.testbit_repr by auto. unfold n'.
   rewrite Z.land_spec, Z.lor_spec. f_equal. f_equal.
-  rewrite Int64.bits_signed by omega. rewrite zlt_true by omega. auto.
+  rewrite Int64.bits_signed by lia. rewrite zlt_true by lia. auto.
   unfold Int64.testbit. rewrite Int64.add_unsigned.
   fold (Int64.testbit (Int64.repr
         (Int64.unsigned (Int64.and n (Int64.repr 2047)) +
          Int64.unsigned (Int64.repr 2047))) i).
   rewrite Int64.testbit_repr by auto. f_equal. f_equal. unfold Int64.and.
   change (Int64.unsigned (Int64.repr 2047)) with 2047.
-  change 2047 with (Z.ones 11). rewrite ! Z.land_ones by omega.
+  change 2047 with (Z.ones 11). rewrite ! Z.land_ones by lia.
   rewrite Int64.unsigned_repr. apply eqmod_mod_eq.
-  apply Z.lt_gt. apply (Zpower_gt_0 radix2); omega.
+  apply Z.lt_gt. apply (Zpower_gt_0 radix2); lia.
   apply eqmod_divides with (2^64). apply Int64.eqm_signed_unsigned.
   exists (2^(64-11)); auto.
   exploit (Z_mod_lt (Int64.unsigned n) (2^11)). compute; auto.
-  assert (2^11 < Int64.max_unsigned) by (compute; auto). omega.
+  assert (2^11 < Int64.max_unsigned) by (compute; auto). lia.
   apply Int64.same_bits_eqm; auto. exists (-1); auto.
   split. auto. assert (-2^64 < Int64.min_signed) by (compute; auto).
   assert (Int64.max_signed < 2^64) by (compute; auto).
-  xomega.
+  extlia.
 Qed.
 
 End Float32.
diff --git a/lib/HashedSet.v b/lib/HashedSet.v
index cb2ee1b2..48798a1b 100644
--- a/lib/HashedSet.v
+++ b/lib/HashedSet.v
@@ -118,7 +118,7 @@ Proof.
   destruct i; simpl; reflexivity.
 Qed.
 
-Hint Resolve gempty : pset.
+Global Hint Resolve gempty : pset.
 Hint Rewrite gempty : pset.
 
 Definition node (b0 : pset) (f : bool) (b1 : pset) : pset :=
@@ -139,7 +139,7 @@ Proof.
   all: reflexivity.
 Qed.
 
-Hint Resolve wf_node: pset.
+Global Hint Resolve wf_node: pset.
 
 Lemma gnode :
   forall b0 f b1 i,
@@ -180,7 +180,7 @@ Proof.
 Qed.
 
 Hint Rewrite add_nonempty : pset.
-Hint Resolve add_nonempty : pset.
+Global Hint Resolve add_nonempty : pset.
 
 Lemma wf_add:
   forall i s, (iswf s) -> (iswf (add i s)).
@@ -194,7 +194,7 @@ Proof.
   all: intuition.
 Qed.
 
-Hint Resolve wf_add : pset.
+Global Hint Resolve wf_add : pset.
 
 Theorem gadds :
   forall i : positive,
@@ -204,7 +204,7 @@ Proof.
   induction i; destruct s; simpl; auto.
 Qed.
 
-Hint Resolve gadds : pset.
+Global Hint Resolve gadds : pset.
 Hint Rewrite gadds : pset.
 
 Theorem gaddo :
@@ -220,7 +220,7 @@ Proof.
   all: apply gempty.
 Qed.
 
-Hint Resolve gaddo : pset.
+Global Hint Resolve gaddo : pset.
 
 Fixpoint remove (i : positive) (s : pset) { struct i } : pset :=
   match i with
@@ -290,7 +290,7 @@ Proof.
 Qed.
 
 Hint Rewrite remove_empty : pset.
-Hint Resolve remove_empty : pset.
+Global Hint Resolve remove_empty : pset.
 
 Lemma gremove_noncanon_s :
   forall i : positive,
@@ -310,7 +310,7 @@ Proof.
   apply gremove_noncanon_s.
 Qed.
 
-Hint Resolve gremoves : pset.
+Global Hint Resolve gremoves : pset.
 Hint Rewrite gremoves : pset.
 
 Lemma gremove_noncanon_o :
@@ -337,7 +337,7 @@ Proof.
   assumption.
 Qed.
 
-Hint Resolve gremoveo : pset.
+Global Hint Resolve gremoveo : pset.
 
 Fixpoint union_nonopt (s s' : pset) : pset :=
   match s, s' with
@@ -382,7 +382,7 @@ Proof.
   all: destruct pset_eq; simpl; trivial; discriminate.
 Qed.
 
-Hint Resolve union_nonempty1 union_nonempty2 : pset.
+Global Hint Resolve union_nonempty1 union_nonempty2 : pset.
 
 Lemma wf_union :
   forall s s', (iswf s) -> (iswf s') -> (iswf (union s s')).
@@ -403,7 +403,7 @@ Proof.
   intuition auto with pset.
 Qed.
 
-Hint Resolve wf_union : pset.
+Global Hint Resolve wf_union : pset.
 
 Theorem gunion:
   forall s s' : pset,
@@ -463,7 +463,7 @@ Proof.
   intuition.
 Qed.
 
-Hint Resolve wf_inter : pset.
+Global Hint Resolve wf_inter : pset.
 
 Lemma inter_noncanon_same:
   forall s s' j, (contains (inter s s') j) = (contains (inter_noncanon s s') j).
@@ -483,7 +483,7 @@ Proof.
   apply ginter_noncanon.
 Qed.
 
-Hint Resolve ginter gunion : pset.
+Global Hint Resolve ginter gunion : pset.
 Hint Rewrite ginter gunion : pset.
 
 Fixpoint subtract_noncanon (s s' : pset) : pset :=
@@ -535,7 +535,7 @@ Proof.
   intuition.
 Qed.
 
-Hint Resolve wf_subtract : pset.
+Global Hint Resolve wf_subtract : pset.
 
 Lemma subtract_noncanon_same:
   forall s s' j, (contains (subtract s s') j) = (contains (subtract_noncanon s s') j).
@@ -555,7 +555,7 @@ Proof.
   apply gsubtract_noncanon.
 Qed.
 
-Hint Resolve gsubtract : pset.
+Global Hint Resolve gsubtract : pset.
 Hint Rewrite gsubtract : pset.
 
 Lemma wf_is_nonempty :
@@ -585,7 +585,7 @@ Proof.
     assumption.
 Qed.
 
-Hint Resolve wf_is_nonempty : pset.
+Global Hint Resolve wf_is_nonempty : pset.
 
 Lemma wf_is_empty1 :
   forall s, iswf s -> (forall i, (contains s i) = false) -> is_empty s = true.
@@ -618,7 +618,7 @@ Proof.
     assumption.
 Qed.
   
-Hint Resolve wf_is_empty1 : pset.
+Global Hint Resolve wf_is_empty1 : pset.
 
 Lemma wf_eq :
   forall s s', iswf s -> iswf s' -> s <> s' ->
@@ -1376,7 +1376,7 @@ Proof.
   all: assumption.
 Qed.
 
-Hint Resolve is_subset_spec1 is_subset_spec2 : pset.
+Global Hint Resolve is_subset_spec1 is_subset_spec2 : pset.
 
 Theorem is_subset_spec:
   forall s s',
@@ -1409,6 +1409,6 @@ Proof.
 Qed.
 End PSet.
 
-Hint Resolve PSet.gaddo PSet.gadds PSet.gremoveo PSet.gremoves PSet.gunion PSet.ginter PSet.gsubtract PSet.gfilter PSet.is_subset_spec1 PSet.is_subset_spec2 : pset.
+Global Hint Resolve PSet.gaddo PSet.gadds PSet.gremoveo PSet.gremoves PSet.gunion PSet.ginter PSet.gsubtract PSet.gfilter PSet.is_subset_spec1 PSet.is_subset_spec2 : pset.
 
 Hint Rewrite PSet.gadds PSet.gremoves PSet.gunion PSet.ginter PSet.gsubtract PSet.gfilter : pset.
diff --git a/lib/Heaps.v b/lib/Heaps.v
index 85343998..def9da97 100644
--- a/lib/Heaps.v
+++ b/lib/Heaps.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/IEEE754_extra.v b/lib/IEEE754_extra.v
index 18313ec1..b0d1944e 100644
--- a/lib/IEEE754_extra.v
+++ b/lib/IEEE754_extra.v
@@ -7,10 +7,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -119,7 +120,7 @@ Definition integer_representable (n: Z): Prop :=
 Let int_upper_bound_eq: 2^emax - 2^(emax - prec) = (2^prec - 1) * 2^(emax - prec).
 Proof.
   red in prec_gt_0_.
-  ring_simplify. rewrite <- (Zpower_plus radix2) by omega. f_equal. f_equal. omega.
+  ring_simplify. rewrite <- (Zpower_plus radix2) by lia. f_equal. f_equal. lia.
 Qed.
 
 Lemma integer_representable_n2p:
@@ -130,14 +131,14 @@ Proof.
   intros; split.
 - red in prec_gt_0_. replace (Z.abs (n * 2^p)) with (Z.abs n * 2^p).
   rewrite int_upper_bound_eq.
-  apply Zmult_le_compat. zify; omega. apply (Zpower_le radix2); omega.
-  zify; omega. apply (Zpower_ge_0 radix2).
+  apply Zmult_le_compat. zify; lia. apply (Zpower_le radix2); lia.
+  zify; lia. apply (Zpower_ge_0 radix2).
   rewrite Z.abs_mul. f_equal. rewrite Z.abs_eq. auto. apply (Zpower_ge_0 radix2).
 - apply generic_format_FLT. exists (Float radix2 n p).
   unfold F2R; simpl.
   rewrite <- IZR_Zpower by auto. apply mult_IZR.
-  simpl; zify; omega.
-  unfold emin, Fexp; red in prec_gt_0_; omega.
+  simpl; zify; lia.
+  unfold emin, Fexp; red in prec_gt_0_; lia.
 Qed.
 
 Lemma integer_representable_2p:
@@ -149,19 +150,19 @@ Proof.
 - red in prec_gt_0_.
   rewrite Z.abs_eq by (apply (Zpower_ge_0 radix2)).
   apply Z.le_trans with (2^(emax-1)).
-  apply (Zpower_le radix2); omega.
+  apply (Zpower_le radix2); lia.
   assert (2^emax = 2^(emax-1)*2).
-  { change 2 with (2^1) at 3. rewrite <- (Zpower_plus radix2) by omega.
-    f_equal. omega. }
+  { change 2 with (2^1) at 3. rewrite <- (Zpower_plus radix2) by lia.
+    f_equal. lia. }
   assert (2^(emax - prec) <= 2^(emax - 1)).
-  { apply (Zpower_le radix2). omega. }
-  omega.
+  { apply (Zpower_le radix2). lia. }
+  lia.
 - red in prec_gt_0_.
   apply generic_format_FLT. exists (Float radix2 1 p).
   unfold F2R; simpl.
-  rewrite Rmult_1_l. rewrite <- IZR_Zpower. auto. omega.
-  simpl Z.abs. change 1 with (2^0). apply (Zpower_lt radix2). omega. auto.
-  unfold emin, Fexp; omega.
+  rewrite Rmult_1_l. rewrite <- IZR_Zpower. auto. lia.
+  simpl Z.abs. change 1 with (2^0). apply (Zpower_lt radix2). lia. auto.
+  unfold emin, Fexp; lia.
 Qed.
 
 Lemma integer_representable_opp:
@@ -178,12 +179,12 @@ Lemma integer_representable_n2p_wide:
 Proof.
   intros. red in prec_gt_0_.
   destruct (Z.eq_dec n (2^prec)); [idtac | destruct (Z.eq_dec n (-2^prec))].
-- rewrite e. rewrite <- (Zpower_plus radix2) by omega.
-  apply integer_representable_2p. omega.
+- rewrite e. rewrite <- (Zpower_plus radix2) by lia.
+  apply integer_representable_2p. lia.
 - rewrite e. rewrite <- Zopp_mult_distr_l. apply integer_representable_opp.
-  rewrite <- (Zpower_plus radix2) by omega.
-  apply integer_representable_2p. omega.
-- apply integer_representable_n2p; omega.
+  rewrite <- (Zpower_plus radix2) by lia.
+  apply integer_representable_2p. lia.
+- apply integer_representable_n2p; lia.
 Qed.
 
 Lemma integer_representable_n:
@@ -191,7 +192,7 @@ Lemma integer_representable_n:
 Proof.
   red in prec_gt_0_. intros.
   replace n with (n * 2^0) by (change (2^0) with 1; ring).
-  apply integer_representable_n2p_wide. auto. omega. omega.
+  apply integer_representable_n2p_wide. auto. lia. lia.
 Qed.
 
 Lemma round_int_no_overflow:
@@ -205,14 +206,14 @@ Proof.
   apply round_le_generic. apply fexp_correct; auto. apply valid_rnd_N.
   apply generic_format_FLT. exists (Float radix2 (2^prec-1) (emax-prec)).
   rewrite int_upper_bound_eq. unfold F2R; simpl.
-  rewrite <- IZR_Zpower by omega. rewrite <- mult_IZR. auto.
-  assert (0 < 2^prec) by (apply (Zpower_gt_0 radix2); omega).
-  unfold Fnum; simpl; zify; omega.
-  unfold emin, Fexp; omega.
+  rewrite <- IZR_Zpower by lia. rewrite <- mult_IZR. auto.
+  assert (0 < 2^prec) by (apply (Zpower_gt_0 radix2); lia).
+  unfold Fnum; simpl; zify; lia.
+  unfold emin, Fexp; lia.
   rewrite <- abs_IZR. apply IZR_le. auto.
-  rewrite <- IZR_Zpower by omega. apply IZR_lt. simpl.
-  assert (0 < 2^(emax-prec)) by (apply (Zpower_gt_0 radix2); omega).
-  omega.
+  rewrite <- IZR_Zpower by lia. apply IZR_lt. simpl.
+  assert (0 < 2^(emax-prec)) by (apply (Zpower_gt_0 radix2); lia).
+  lia.
   apply fexp_correct. auto.
 Qed.
 
@@ -299,8 +300,8 @@ Proof.
   { apply round_le_generic. apply fexp_correct. auto. apply valid_rnd_N.
     apply (integer_representable_opp 1).
     apply (integer_representable_2p 0).
-    red in prec_gt_0_; omega.
-    apply IZR_le; omega.
+    red in prec_gt_0_; lia.
+    apply IZR_le; lia.
   }
   lra.
 Qed.
@@ -335,7 +336,7 @@ Proof.
   rewrite R, W, C, F.
   rewrite Rcompare_IZR. unfold Z.ltb at 3.
   generalize (Zcompare_spec (p + q) 0); intros SPEC; inversion SPEC; auto.
-  assert (EITHER: 0 <= p \/ 0 <= q) by omega.
+  assert (EITHER: 0 <= p \/ 0 <= q) by lia.
   destruct EITHER; [apply andb_false_intro1 | apply andb_false_intro2];
   apply Zlt_bool_false; auto.
 - intros P (U & V).
@@ -343,8 +344,8 @@ Proof.
   rewrite P, U, C. f_equal. rewrite C, F in V.
   generalize (Zlt_bool_spec p 0) (Zlt_bool_spec q 0). rewrite <- V.
   intros SPEC1 SPEC2; inversion SPEC1; inversion SPEC2; try congruence; symmetry.
-  apply Zlt_bool_true; omega.
-  apply Zlt_bool_false; omega.
+  apply Zlt_bool_true; lia.
+  apply Zlt_bool_false; lia.
 Qed.
 
 Theorem BofZ_minus:
@@ -365,7 +366,7 @@ Proof.
   rewrite R, W, C, F.
   rewrite Rcompare_IZR. unfold Z.ltb at 3.
   generalize (Zcompare_spec (p - q) 0); intros SPEC; inversion SPEC; auto.
-  assert (EITHER: 0 <= p \/ q < 0) by omega.
+  assert (EITHER: 0 <= p \/ q < 0) by lia.
   destruct EITHER; [apply andb_false_intro1 | apply andb_false_intro2].
   rewrite Zlt_bool_false; auto.
   rewrite Zlt_bool_true; auto.
@@ -375,8 +376,8 @@ Proof.
   generalize (Zlt_bool_spec p 0) (Zlt_bool_spec q 0). rewrite V.
   intros SPEC1 SPEC2; inversion SPEC1; inversion SPEC2; symmetry.
   rewrite <- H3 in H1; discriminate.
-  apply Zlt_bool_true; omega.
-  apply Zlt_bool_false; omega.
+  apply Zlt_bool_true; lia.
+  apply Zlt_bool_false; lia.
   rewrite <- H3 in H1; discriminate.
 Qed.
 
@@ -389,10 +390,10 @@ Proof.
   intros.
   assert (SIGN: xorb (p <? 0) (q <? 0) = (p * q <? 0)).
   {
-    rewrite (Zlt_bool_false q) by omega.
+    rewrite (Zlt_bool_false q) by lia.
     generalize (Zlt_bool_spec p 0); intros SPEC; inversion SPEC; simpl; symmetry.
-    apply Zlt_bool_true. rewrite Z.mul_comm. apply Z.mul_pos_neg; omega.
-    apply Zlt_bool_false. apply Zsame_sign_imp; omega.
+    apply Zlt_bool_true. rewrite Z.mul_comm. apply Z.mul_pos_neg; lia.
+    apply Zlt_bool_false. apply Zsame_sign_imp; lia.
   }
   destruct (BofZ_representable p) as (A & B & C); auto.
   destruct (BofZ_representable q) as (D & E & F); auto.
@@ -420,10 +421,10 @@ Proof.
   destruct (Z.eq_dec x 0).
 - subst x. apply BofZ_mult.
     apply integer_representable_n.
-    generalize (Zpower_ge_0 radix2 prec). simpl; omega.
+    generalize (Zpower_ge_0 radix2 prec). simpl; lia.
     apply integer_representable_2p. auto.
     apply (Zpower_gt_0 radix2).
-    omega.
+    lia.
 - assert (IZR x <> 0%R) by (apply (IZR_neq _ _ n)).
   destruct (BofZ_finite x H) as (A & B & C).
   destruct (BofZ_representable (2^p)) as (D & E & F).
@@ -432,16 +433,16 @@ Proof.
           cexp radix2 fexp (IZR x) + p).
   {
     unfold cexp, fexp. rewrite mult_IZR.
-    change (2^p) with (radix2^p). rewrite IZR_Zpower by omega.
+    change (2^p) with (radix2^p). rewrite IZR_Zpower by lia.
     rewrite mag_mult_bpow by auto.
     assert (prec + 1 <= mag radix2 (IZR x)).
     { rewrite <- (mag_abs radix2 (IZR x)).
       rewrite <- (mag_bpow radix2 prec).
       apply mag_le.
-      apply bpow_gt_0. rewrite <- IZR_Zpower by (red in prec_gt_0_;omega).
+      apply bpow_gt_0. rewrite <- IZR_Zpower by (red in prec_gt_0_;lia).
       rewrite <- abs_IZR. apply IZR_le; auto. }
     unfold FLT_exp.
-    unfold emin; red in prec_gt_0_; zify; omega.
+    unfold emin; red in prec_gt_0_; zify; lia.
   }
   assert (forall m, round radix2 fexp m (IZR x) * IZR (2^p) =
                     round radix2 fexp m (IZR (x * 2^p)))%R.
@@ -451,11 +452,11 @@ Proof.
     set (a := IZR x); set (b := bpow radix2 (- cexp radix2 fexp a)).
     replace (a * IZR (2^p) * (b * bpow radix2 (-p)))%R with (a * b)%R.
     unfold F2R; simpl. rewrite Rmult_assoc. f_equal.
-    rewrite bpow_plus.  f_equal. apply (IZR_Zpower radix2). omega.
+    rewrite bpow_plus.  f_equal. apply (IZR_Zpower radix2). lia.
     transitivity ((a * b) * (IZR (2^p) * bpow radix2 (-p)))%R.
     rewrite (IZR_Zpower radix2). rewrite <- bpow_plus.
-    replace (p + -p) with 0 by omega. change (bpow radix2 0) with 1%R. ring.
-    omega.
+    replace (p + -p) with 0 by lia. change (bpow radix2 0) with 1%R. ring.
+    lia.
     ring.
   }
   assert (forall m x,
@@ -468,11 +469,11 @@ Proof.
   }
   assert (xorb (x <? 0) (2^p <? 0) = (x * 2^p <? 0)).
   {
-    assert (0 < 2^p) by (apply (Zpower_gt_0 radix2); omega).
-    rewrite (Zlt_bool_false (2^p)) by omega. rewrite xorb_false_r.
+    assert (0 < 2^p) by (apply (Zpower_gt_0 radix2); lia).
+    rewrite (Zlt_bool_false (2^p)) by lia. rewrite xorb_false_r.
     symmetry. generalize (Zlt_bool_spec x 0); intros SPEC; inversion SPEC.
     apply Zlt_bool_true. apply Z.mul_neg_pos; auto.
-    apply Zlt_bool_false. apply Z.mul_nonneg_nonneg; omega.
+    apply Zlt_bool_false. apply Z.mul_nonneg_nonneg; lia.
   }
   generalize (Bmult_correct _ _ _ Hmax nan mode_NE (BofZ x) (BofZ (2^p)))
              (BofZ_correct (x * 2^p)).
@@ -496,10 +497,10 @@ Lemma round_odd_flt:
   round radix2 fexp (Znearest choice) x.
 Proof.
   intros. apply round_N_odd. auto. apply fexp_correct; auto.
-  apply exists_NE_FLT. right; omega.
-  apply FLT_exp_valid. red; omega.
-  apply exists_NE_FLT. right; omega.
-  unfold fexp, FLT_exp; intros. zify; omega.
+  apply exists_NE_FLT. right; lia.
+  apply FLT_exp_valid. red; lia.
+  apply exists_NE_FLT. right; lia.
+  unfold fexp, FLT_exp; intros. zify; lia.
 Qed.
 
 Corollary round_odd_fix:
@@ -522,8 +523,8 @@ Proof.
                  cexp radix2 (FIX_exp p) x).
   {
     unfold cexp, FLT_exp, FIX_exp.
-    replace (mag radix2 x - prec') with p by (unfold prec'; omega).
-    apply Z.max_l. unfold emin', emin. red in prec_gt_0_; omega.
+    replace (mag radix2 x - prec') with p by (unfold prec'; lia).
+    apply Z.max_l. unfold emin', emin. red in prec_gt_0_; lia.
   }
   assert (RND: round radix2 (FIX_exp p) Zrnd_odd x =
                round radix2 (FLT_exp emin' prec') Zrnd_odd x).
@@ -532,9 +533,9 @@ Proof.
   }
   rewrite RND.
   apply round_odd_flt. auto.
-  unfold prec'. red in prec_gt_0_; omega.
-  unfold prec'. omega.
-  unfold emin'. omega.
+  unfold prec'. red in prec_gt_0_; lia.
+  unfold prec'. lia.
+  unfold emin'. lia.
 Qed.
 
 Definition int_round_odd (x: Z) (p: Z) :=
@@ -545,23 +546,23 @@ Lemma Zrnd_odd_int:
   Zrnd_odd (IZR n * bpow radix2 (-p)) * 2^p =
   int_round_odd n p.
 Proof.
-  intros.
-  assert (0 < 2^p) by (apply (Zpower_gt_0 radix2); omega).
-  assert (n = (n / 2^p) * 2^p + n mod 2^p) by (rewrite Z.mul_comm; apply Z.div_mod; omega).
-  assert (0 <= n mod 2^p < 2^p) by (apply Z_mod_lt; omega).
+  clear. intros.
+  assert (0 < 2^p) by (apply (Zpower_gt_0 radix2); lia).
+  assert (n = (n / 2^p) * 2^p + n mod 2^p) by (rewrite Z.mul_comm; apply Z.div_mod; lia).
+  assert (0 <= n mod 2^p < 2^p) by (apply Z_mod_lt; lia).
   unfold int_round_odd. set (q := n / 2^p) in *; set (r := n mod 2^p) in *.
   f_equal.
   pose proof (bpow_gt_0 radix2 (-p)).
   assert (bpow radix2 p * bpow radix2 (-p) = 1)%R.
-  { rewrite <- bpow_plus. replace (p + -p) with 0 by omega. auto. }
+  { rewrite <- bpow_plus. replace (p + -p) with 0 by lia. auto. }
   assert (IZR n * bpow radix2 (-p) = IZR q + IZR r * bpow radix2 (-p))%R.
   { rewrite H1. rewrite plus_IZR, mult_IZR.
     change (IZR (2^p)) with (IZR (radix2^p)).
-    rewrite IZR_Zpower by omega. ring_simplify.
+    rewrite IZR_Zpower by lia. ring_simplify.
     rewrite Rmult_assoc. rewrite H4. ring. }
   assert (0 <= IZR r < bpow radix2 p)%R.
-  { split. apply IZR_le; omega.
-    rewrite <- IZR_Zpower by omega. apply IZR_lt; tauto. }
+  { split. apply IZR_le; lia.
+    rewrite <- IZR_Zpower by lia. apply IZR_lt; tauto. }
   assert (0 <= IZR r * bpow radix2 (-p) < 1)%R.
   { generalize (bpow_gt_0 radix2 (-p)). intros.
     split. apply Rmult_le_pos; lra.
@@ -586,7 +587,7 @@ Lemma int_round_odd_le:
   forall p x y, 0 <= p ->
   x <= y -> int_round_odd x p <= int_round_odd y p.
 Proof.
-  intros.
+  clear. intros.
   assert (Zrnd_odd (IZR x * bpow radix2 (-p)) <= Zrnd_odd (IZR y * bpow radix2 (-p))).
   { apply Zrnd_le. apply valid_rnd_odd. apply Rmult_le_compat_r. apply bpow_ge_0.
     apply IZR_le; auto. }
@@ -598,7 +599,7 @@ Lemma int_round_odd_exact:
   forall p x, 0 <= p ->
   (2^p | x) -> int_round_odd x p = x.
 Proof.
-  intros. unfold int_round_odd. apply Znumtheory.Zdivide_mod in H0.
+  clear. intros. unfold int_round_odd. apply Znumtheory.Zdivide_mod in H0.
   rewrite H0. simpl. rewrite Z.mul_comm. symmetry. apply Z_div_exact_2.
   apply Z.lt_gt. apply (Zpower_gt_0 radix2). auto. auto.
 Qed.
@@ -615,15 +616,15 @@ Proof.
   assert (DIV: (2^p | 2^emax - 2^(emax - prec))).
   { rewrite int_upper_bound_eq. apply Z.divide_mul_r.
     exists (2^(emax - prec - p)). red in prec_gt_0_.
-    rewrite <- (Zpower_plus radix2) by omega. f_equal; omega. }
+    rewrite <- (Zpower_plus radix2) by lia. f_equal; lia. }
   assert (YRANGE: Z.abs (int_round_odd x p) <= 2^emax - 2^(emax-prec)).
   { apply Z.abs_le. split.
     replace (-(2^emax - 2^(emax-prec))) with (int_round_odd (-(2^emax - 2^(emax-prec))) p).
-    apply int_round_odd_le; zify; omega.
-    apply int_round_odd_exact. omega. apply Z.divide_opp_r. auto.
+    apply int_round_odd_le; zify; lia.
+    apply int_round_odd_exact. lia. apply Z.divide_opp_r. auto.
     replace (2^emax - 2^(emax-prec)) with (int_round_odd (2^emax - 2^(emax-prec)) p).
-    apply int_round_odd_le; zify; omega.
-    apply int_round_odd_exact. omega. auto. }
+    apply int_round_odd_le; zify; lia.
+    apply int_round_odd_exact. lia. auto. }
   destruct (BofZ_finite x XRANGE) as (X1 & X2 & X3).
   destruct (BofZ_finite (int_round_odd x p) YRANGE) as (Y1 & Y2 & Y3).
   apply BofZ_finite_equal; auto.
@@ -631,12 +632,12 @@ Proof.
   assert (IZR (int_round_odd x p) = round radix2 (FIX_exp p) Zrnd_odd (IZR x)).
   {
      unfold round, scaled_mantissa, cexp, FIX_exp.
-     rewrite <- Zrnd_odd_int by omega.
-     unfold F2R; simpl. rewrite mult_IZR. f_equal. apply (IZR_Zpower radix2). omega.
+     rewrite <- Zrnd_odd_int by lia.
+     unfold F2R; simpl. rewrite mult_IZR. f_equal. apply (IZR_Zpower radix2). lia.
   }
-  rewrite H. symmetry. apply round_odd_fix. auto. omega.
+  rewrite H. symmetry. apply round_odd_fix. auto. lia.
   rewrite <- IZR_Zpower. rewrite <- abs_IZR. apply IZR_le; auto.
-  red in prec_gt_0_; omega.
+  red in prec_gt_0_; lia.
 Qed.
 
 Lemma int_round_odd_shifts:
@@ -644,7 +645,7 @@ Lemma int_round_odd_shifts:
   int_round_odd x p =
   Z.shiftl (if Z.eqb (x mod 2^p) 0 then Z.shiftr x p else Z.lor (Z.shiftr x p) 1) p.
 Proof.
-  intros.
+  clear. intros.
   unfold int_round_odd. rewrite Z.shiftl_mul_pow2 by auto. f_equal.
   rewrite Z.shiftr_div_pow2 by auto.
   destruct (x mod 2^p =? 0) eqn:E. auto.
@@ -662,22 +663,22 @@ Lemma int_round_odd_bits:
   (forall i, p < i -> Z.testbit y i = Z.testbit x i) ->
   int_round_odd x p = y.
 Proof.
-  intros until p; intros PPOS BELOW AT ABOVE.
+  clear. intros until p; intros PPOS BELOW AT ABOVE.
   rewrite int_round_odd_shifts by auto.
   apply Z.bits_inj'. intros.
   generalize (Zcompare_spec n p); intros SPEC; inversion SPEC.
 - rewrite BELOW by auto. apply Z.shiftl_spec_low; auto.
-- subst n. rewrite AT. rewrite Z.shiftl_spec_high by omega.
-  replace (p - p) with 0 by omega.
+- subst n. rewrite AT. rewrite Z.shiftl_spec_high by lia.
+  replace (p - p) with 0 by lia.
   destruct (x mod 2^p =? 0).
-  + rewrite Z.shiftr_spec by omega. f_equal; omega.
+  + rewrite Z.shiftr_spec by lia. f_equal; lia.
   + rewrite Z.lor_spec. apply orb_true_r.
-- rewrite ABOVE by auto.  rewrite Z.shiftl_spec_high by omega.
+- rewrite ABOVE by auto.  rewrite Z.shiftl_spec_high by lia.
   destruct (x mod 2^p =? 0).
-  rewrite Z.shiftr_spec by omega. f_equal; omega.
-  rewrite Z.lor_spec, Z.shiftr_spec by omega.
-  change 1 with (Z.ones 1). rewrite Z.ones_spec_high by omega. rewrite orb_false_r.
-  f_equal; omega.
+  rewrite Z.shiftr_spec by lia. f_equal; lia.
+  rewrite Z.lor_spec, Z.shiftr_spec by lia.
+  change 1 with (Z.ones 1). rewrite Z.ones_spec_high by lia. rewrite orb_false_r.
+  f_equal; lia.
 Qed.
 
 (** ** Conversion from a FP number to an integer *)
@@ -709,7 +710,7 @@ Proof.
     }
     rewrite EQ. f_equal.
     generalize (Zpower_pos_gt_0 2 p (eq_refl _)); intros.
-    rewrite Ztrunc_floor. symmetry. apply Zfloor_div. omega.
+    rewrite Ztrunc_floor. symmetry. apply Zfloor_div. lia.
     apply Rmult_le_pos. apply IZR_le. compute; congruence.
     apply Rlt_le. apply Rinv_0_lt_compat. apply IZR_lt. auto.
 Qed.
@@ -727,7 +728,7 @@ Proof.
   assert (-x < 0)%R.
   { apply Rlt_le_trans with (IZR (Zfloor (-x)) + 1)%R. apply Zfloor_ub.
     rewrite <- plus_IZR.
-    apply IZR_le. omega. }
+    apply IZR_le. lia. }
   lra.
 Qed.
 
@@ -741,7 +742,7 @@ Proof.
 - rewrite Ztrunc_ceil in H by (apply Rlt_le; auto). split.
   + apply (Ropp_lt_cancel (-(1))). rewrite Ropp_involutive.
     replace 1%R with (IZR (Zfloor (-x)) + 1)%R. apply Zfloor_ub.
-    unfold Zceil in H. replace (Zfloor (-x)) with 0 by omega. simpl. apply Rplus_0_l.
+    unfold Zceil in H. replace (Zfloor (-x)) with 0 by lia. simpl. apply Rplus_0_l.
   + apply Rlt_le_trans with 0%R; auto. apply Rle_0_1.
 Qed.
 
@@ -758,10 +759,10 @@ Proof.
   intros. rewrite ZofB_correct in H. destruct (is_finite prec emax f) eqn:FIN; inversion H.
   set (x := B2R prec emax f) in *. set (y := (-x)%R).
   assert (A: (IZR (Ztrunc y) <= y < IZR (Ztrunc y + 1)%Z)%R).
-  { apply Ztrunc_range_pos. unfold y. rewrite Ztrunc_opp. omega. }
+  { apply Ztrunc_range_pos. unfold y. rewrite Ztrunc_opp. lia. }
   destruct A as [B C].
   unfold y in B, C. rewrite Ztrunc_opp in B, C.
-  replace (- Ztrunc x + 1) with (- (Ztrunc x - 1)) in C by omega.
+  replace (- Ztrunc x + 1) with (- (Ztrunc x - 1)) in C by lia.
   rewrite opp_IZR in B, C. lra.
 Qed.
 
@@ -777,7 +778,7 @@ Theorem ZofB_range_nonneg:
 Proof.
   intros. destruct (Z.eq_dec n 0).
 - subst n. apply ZofB_range_zero. auto.
-- destruct (ZofB_range_pos f n) as (A & B). auto. omega.
+- destruct (ZofB_range_pos f n) as (A & B). auto. lia.
   split; auto. apply Rlt_le_trans with 0%R. simpl; lra.
   apply Rle_trans with (IZR n); auto. apply IZR_le; auto.
 Qed.
@@ -796,7 +797,7 @@ Qed.
 Remark Zfloor_minus:
   forall x n, Zfloor (x - IZR n) = Zfloor x - n.
 Proof.
-  intros. apply Zfloor_imp. replace (Zfloor x - n + 1) with ((Zfloor x + 1) - n) by omega.
+  intros. apply Zfloor_imp. replace (Zfloor x - n + 1) with ((Zfloor x + 1) - n) by lia.
   rewrite ! minus_IZR. unfold Rminus. split.
   apply Rplus_le_compat_r. apply Zfloor_lb.
   apply Rplus_lt_compat_r. rewrite plus_IZR. apply Zfloor_ub.
@@ -809,11 +810,11 @@ Theorem ZofB_minus:
 Proof.
   intros.
   assert (Q: -2^prec <= q <= 2^prec).
-  { split; auto.  generalize (Zpower_ge_0 radix2 prec); simpl; omega. }
-  assert (RANGE: (-1 < B2R _ _ f < IZR (p + 1)%Z)%R) by (apply ZofB_range_nonneg; auto; omega).
+  { split; auto.  generalize (Zpower_ge_0 radix2 prec); simpl; lia. }
+  assert (RANGE: (-1 < B2R _ _ f < IZR (p + 1)%Z)%R) by (apply ZofB_range_nonneg; auto; lia).
   rewrite ZofB_correct in H. destruct (is_finite prec emax f) eqn:FIN; try discriminate.
   assert (PQ2: (IZR (p + 1) <= IZR q * 2)%R).
-  { rewrite <- mult_IZR. apply IZR_le. omega. }
+  { rewrite <- mult_IZR. apply IZR_le. lia. }
   assert (EXACT: round radix2 fexp (round_mode m) (B2R _ _ f - IZR q)%R = (B2R _ _ f - IZR q)%R).
   { apply round_generic. apply valid_rnd_round_mode.
     apply sterbenz_aux. now apply FLT_exp_valid. apply FLT_exp_monotone. apply generic_format_B2R.
@@ -828,7 +829,7 @@ Proof.
 - rewrite A. fold emin; fold fexp. rewrite EXACT.
   apply Rle_lt_trans with (bpow radix2 prec).
   apply Rle_trans with (IZR q). apply Rabs_le. lra.
-  rewrite <- IZR_Zpower. apply IZR_le; auto. red in prec_gt_0_; omega.
+  rewrite <- IZR_Zpower. apply IZR_le; auto. red in prec_gt_0_; lia.
   apply bpow_lt. auto.
 Qed.
 
@@ -874,8 +875,8 @@ Proof.
   intros. destruct (ZofB_range_inversion _ _ _ _ H) as (A & B & C).
   set (f' := Bminus prec emax prec_gt_0_ Hmax minus_nan m f (BofZ q)).
   assert (D: ZofB f' = Some (p - q)).
-  { apply ZofB_minus. auto. omega. auto. auto. }
-  unfold ZofB_range. rewrite D. rewrite Zle_bool_true by omega. rewrite Zle_bool_true by omega. auto.
+  { apply ZofB_minus. auto. lia. auto. auto. }
+  unfold ZofB_range. rewrite D. rewrite Zle_bool_true by lia. rewrite Zle_bool_true by lia. auto.
 Qed.
 
 (** ** Algebraic identities *)
@@ -961,7 +962,7 @@ Theorem Bmult2_Bplus:
 Proof.
   intros until f; intros NAN.
   destruct (BofZ_representable 2) as (A & B & C).
-  apply (integer_representable_2p 1). red in prec_gt_0_; omega.
+  apply (integer_representable_2p 1). red in prec_gt_0_; lia.
   pose proof (Bmult_correct _ _ _ Hmax mult_nan mode f (BofZ 2%Z)). fold emin in H.
   rewrite A, B, C in H. rewrite xorb_false_r in H.
   destruct (is_finite _ _ f) eqn:FIN.
@@ -979,7 +980,7 @@ Proof.
     replace 0%R with (@F2R radix2 {| Fnum := 0%Z; Fexp := e |}).
     rewrite Rcompare_F2R. destruct s; auto.
     unfold F2R. simpl. ring.
-    apply IZR_lt. omega.
+    apply IZR_lt. lia.
     destruct (Bmult prec emax prec_gt_0_ Hmax mult_nan mode f (BofZ 2)); reflexivity || discriminate.
   + destruct H0 as (P & Q). apply B2FF_inj. rewrite P, H. auto.
 - destruct f as [sf|sf|sf pf Hf|sf mf ef Hf]; try discriminate.
@@ -1000,11 +1001,11 @@ Proof.
   assert (REC: forall n, Z.pos (nat_rect _ xH (fun _ => xO) n) = 2 ^ (Z.of_nat n)).
   { induction n. reflexivity.
     simpl nat_rect. transitivity (2 * Z.pos (nat_rect _ xH (fun _ => xO) n)). reflexivity.
-    rewrite Nat2Z.inj_succ. rewrite IHn. unfold Z.succ. rewrite Zpower_plus by omega.
+    rewrite Nat2Z.inj_succ. rewrite IHn. unfold Z.succ. rewrite Zpower_plus by lia.
     change (2 ^ 1) with 2. ring. }
   red in prec_gt_0_.
-  unfold Bexact_inverse_mantissa. rewrite iter_nat_of_Z by omega. rewrite REC.
-  rewrite Zabs2Nat.id_abs. rewrite Z.abs_eq by omega. auto.
+  unfold Bexact_inverse_mantissa. rewrite iter_nat_of_Z by lia. rewrite REC.
+  rewrite Zabs2Nat.id_abs. rewrite Z.abs_eq by lia. auto.
 Qed.
 
 Remark Bexact_inverse_mantissa_digits2_pos:
@@ -1013,11 +1014,11 @@ Proof.
   assert (DIGITS: forall n, digits2_pos (nat_rect _ xH (fun _ => xO) n) = Pos.of_nat (n+1)).
   { induction n; simpl. auto. rewrite IHn. destruct n; auto. }
   red in prec_gt_0_.
-  unfold Bexact_inverse_mantissa. rewrite iter_nat_of_Z by omega. rewrite DIGITS.
-  rewrite Zabs2Nat.abs_nat_nonneg, Z2Nat.inj_sub by omega.
+  unfold Bexact_inverse_mantissa. rewrite iter_nat_of_Z by lia. rewrite DIGITS.
+  rewrite Zabs2Nat.abs_nat_nonneg, Z2Nat.inj_sub by lia.
   destruct prec; try  discriminate. rewrite Nat.sub_add.
   simpl. rewrite Pos2Nat.id. auto.
-  simpl. zify; omega.
+  simpl. zify; lia.
 Qed.
 
 Remark bounded_Bexact_inverse:
@@ -1028,8 +1029,8 @@ Proof.
   rewrite <- Zeq_is_eq_bool. rewrite <- Zle_is_le_bool.
   rewrite Bexact_inverse_mantissa_digits2_pos.
   split.
-- intros; split. unfold FLT_exp. unfold emin in H. zify; omega. omega.
-- intros [A B]. unfold FLT_exp in A. unfold emin. zify; omega.
+- intros; split. unfold FLT_exp. unfold emin in H. zify; lia. lia.
+- intros [A B]. unfold FLT_exp in A. unfold emin. zify; lia.
 Qed.
 
 Program Definition Bexact_inverse (f: binary_float) : option binary_float :=
@@ -1045,7 +1046,7 @@ Program Definition Bexact_inverse (f: binary_float) : option binary_float :=
   end.
 Next Obligation.
   rewrite <- bounded_Bexact_inverse in B. rewrite <- bounded_Bexact_inverse.
-  unfold emin in *. omega.
+  unfold emin in *. lia.
 Qed.
 
 Lemma Bexact_inverse_correct:
@@ -1067,9 +1068,9 @@ Proof with (try discriminate).
   rewrite <- ! cond_Ropp_mult_l.
   red in prec_gt_0_.
   replace (IZR (2 ^ (prec - 1))) with (bpow radix2 (prec - 1))
-  by (symmetry; apply (IZR_Zpower radix2); omega).
+  by (symmetry; apply (IZR_Zpower radix2); lia).
   rewrite <- ! bpow_plus.
-  replace (prec - 1 + e') with (- (prec - 1 + e)) by (unfold e'; omega).
+  replace (prec - 1 + e') with (- (prec - 1 + e)) by (unfold e'; lia).
   rewrite bpow_opp. unfold cond_Ropp; destruct s; auto.
   rewrite Ropp_inv_permute. auto. apply Rgt_not_eq. apply bpow_gt_0.
   split. simpl. apply F2R_neq_0. destruct s; simpl in H; discriminate.
@@ -1163,9 +1164,9 @@ Proof.
   assert (C: 0 <= Z.log2_up base) by apply Z.log2_up_nonneg.
   destruct (Z.log2_spec base) as [D E]; auto.
   destruct (Z.log2_up_spec base) as [F G]. apply radix_gt_1.
-  assert (K: 0 <= 2 ^ Z.log2 base) by (apply Z.pow_nonneg; omega).
-  rewrite ! (Z.mul_comm n). rewrite ! Z.pow_mul_r by omega.
-  split; apply Z.pow_le_mono_l; omega.
+  assert (K: 0 <= 2 ^ Z.log2 base) by (apply Z.pow_nonneg; lia).
+  rewrite ! (Z.mul_comm n). rewrite ! Z.pow_mul_r by lia.
+  split; apply Z.pow_le_mono_l; lia.
 Qed.
 
 Lemma bpow_log_pos:
@@ -1174,8 +1175,8 @@ Lemma bpow_log_pos:
   (bpow radix2 (n * Z.log2 base)%Z <= bpow base n)%R.
 Proof.
   intros. rewrite <- ! IZR_Zpower. apply IZR_le; apply Zpower_log; auto.
-  omega.
-  rewrite Z.mul_comm; apply Zmult_gt_0_le_0_compat. omega. apply Z.log2_nonneg.
+  lia.
+  rewrite Z.mul_comm; apply Zmult_gt_0_le_0_compat. lia. apply Z.log2_nonneg.
 Qed.
 
 Lemma bpow_log_neg:
@@ -1183,10 +1184,10 @@ Lemma bpow_log_neg:
   n < 0 ->
   (bpow base n <= bpow radix2 (n * Z.log2 base)%Z)%R.
 Proof.
-  intros. set (m := -n). replace n with (-m) by (unfold m; omega).
+  intros. set (m := -n). replace n with (-m) by (unfold m; lia).
   rewrite ! Z.mul_opp_l, ! bpow_opp. apply Rinv_le.
   apply bpow_gt_0.
-  apply bpow_log_pos. unfold m; omega.
+  apply bpow_log_pos. unfold m; lia.
 Qed.
 
 (** Overflow and underflow conditions. *)
@@ -1203,12 +1204,12 @@ Proof.
   rewrite <- (Rmult_1_l (bpow radix2 emax)). apply Rmult_le_compat.
   apply Rle_0_1.
   apply bpow_ge_0.
-  apply IZR_le. zify; omega.
+  apply IZR_le. zify; lia.
   eapply Rle_trans. eapply bpow_le. eassumption. apply bpow_log_pos; auto.
   apply generic_format_FLT. exists (Float radix2 1 emax).
   unfold F2R; simpl. ring.
   simpl. apply (Zpower_gt_1 radix2); auto.
-  simpl. unfold emin; red in prec_gt_0_; omega.
+  simpl. unfold emin; red in prec_gt_0_; lia.
 Qed.
 
 Lemma round_NE_underflows:
@@ -1221,10 +1222,10 @@ Proof.
   assert (A: round radix2 fexp (round_mode mode_NE) eps = 0%R).
   { unfold round. simpl.
     assert (E: cexp radix2 fexp eps = emin).
-    { unfold cexp, eps. rewrite mag_bpow. unfold fexp, FLT_exp. zify; red in prec_gt_0_; omega. }
+    { unfold cexp, eps. rewrite mag_bpow. unfold fexp, FLT_exp. zify; red in prec_gt_0_; lia. }
     unfold scaled_mantissa; rewrite E.
     assert (P: (eps * bpow radix2 (-emin) = / 2)%R).
-    { unfold eps. rewrite <- bpow_plus. replace (emin - 1 + -emin) with (-1) by omega. auto. }
+    { unfold eps. rewrite <- bpow_plus. replace (emin - 1 + -emin) with (-1) by lia. auto. }
     rewrite P. unfold Znearest.
     assert (F: Zfloor (/ 2)%R = 0).
     { apply Zfloor_imp. simpl. lra. }
@@ -1244,18 +1245,18 @@ Lemma round_integer_underflow:
   round radix2 fexp (round_mode mode_NE) (IZR (Zpos m) * bpow base e) = 0%R.
 Proof.
   intros. apply round_NE_underflows. split.
-- apply Rmult_le_pos. apply IZR_le. zify; omega. apply bpow_ge_0.
+- apply Rmult_le_pos. apply IZR_le. zify; lia. apply bpow_ge_0.
 - apply Rle_trans with (bpow radix2 (Z.log2_up (Z.pos m) + e * Z.log2 base)).
 + rewrite bpow_plus. apply Rmult_le_compat.
-  apply IZR_le; zify; omega.
+  apply IZR_le; zify; lia.
   apply bpow_ge_0.
   rewrite <- IZR_Zpower. apply IZR_le.
   destruct (Z.eq_dec (Z.pos m) 1).
-  rewrite e0. simpl. omega.
-  apply Z.log2_up_spec. zify; omega.
+  rewrite e0. simpl. lia.
+  apply Z.log2_up_spec. zify; lia.
   apply Z.log2_up_nonneg.
   apply bpow_log_neg. auto.
-+ apply bpow_le. omega.
++ apply bpow_le. lia.
 Qed.
 
 (** Correctness of Bparse *)
@@ -1281,20 +1282,20 @@ Proof.
 - (* e = Zpos e *)
   destruct (Z.ltb_spec (Z.pos e * Z.log2 (Z.pos b)) emax).
 + (* no overflow *)
-  rewrite pos_pow_spec. rewrite <- IZR_Zpower by (zify; omega). rewrite <- mult_IZR.
+  rewrite pos_pow_spec. rewrite <- IZR_Zpower by (zify; lia). rewrite <- mult_IZR.
   replace false with (Z.pos m * Z.pos b ^ Z.pos e <? 0).
   exact (BofZ_correct (Z.pos m * Z.pos b ^ Z.pos e)).
-  rewrite Z.ltb_ge. rewrite Z.mul_comm. apply Zmult_gt_0_le_0_compat. zify; omega.  apply (Zpower_ge_0 base).
+  rewrite Z.ltb_ge. rewrite Z.mul_comm. apply Zmult_gt_0_le_0_compat. zify; lia.  apply (Zpower_ge_0 base).
 + (* overflow *)
   rewrite Rlt_bool_false. auto. eapply Rle_trans; [idtac|apply Rle_abs].
-  apply (round_integer_overflow base). zify; omega. auto.
+  apply (round_integer_overflow base). zify; lia. auto.
 - (* e = Zneg e *)
   destruct (Z.ltb_spec (Z.neg e * Z.log2 (Z.pos b) + Z.log2_up (Z.pos m)) emin).
 + (* undeflow *)
   rewrite round_integer_underflow; auto.
   rewrite Rlt_bool_true. auto.
   replace (Rabs 0)%R with 0%R. apply bpow_gt_0. apply (abs_IZR 0).
-  zify; omega.
+  zify; lia.
 + (* no underflow *)
   generalize (Bdiv_correct_aux prec emax prec_gt_0_ Hmax mode_NE false m 0 false (pos_pow b e) 0).
   set (f := let '(mz, ez, lz) := Fdiv_core_binary prec emax (Z.pos m) 0 (Z.pos (pos_pow b e)) 0
@@ -1384,13 +1385,13 @@ Proof.
     apply Rlt_le_trans with (bpow radix2 emax1).
     rewrite F2R_cond_Zopp. rewrite abs_cond_Ropp. rewrite <- F2R_Zabs. simpl Z.abs.
     eapply bounded_lt_emax; eauto.
-    apply bpow_le. omega.
+    apply bpow_le. lia.
   }
   assert (EQ: round radix2 fexp2 (round_mode m) (B2R prec1 emax1 f) = B2R prec1 emax1 f).
   {
     apply round_generic. apply valid_rnd_round_mode. eapply generic_inclusion_le.
     5: apply generic_format_B2R. apply fexp_correct; auto. apply fexp_correct; auto.
-    instantiate (1 := emax2). intros. unfold fexp2, FLT_exp. unfold emin2. zify; omega.
+    instantiate (1 := emax2). intros. unfold fexp2, FLT_exp. unfold emin2. zify; lia.
     apply Rlt_le; auto.
   }
   rewrite EQ. rewrite Rlt_bool_true by auto. auto.
@@ -1444,7 +1445,7 @@ Proof.
   intros.
   destruct (ZofB_range_inversion _ _ _ _ _ _ H3) as (A & B & C).
   unfold ZofB_range. erewrite ZofB_Bconv by eauto.
-  rewrite ! Zle_bool_true by omega. auto.
+  rewrite ! Zle_bool_true by lia. auto.
 Qed.
 
 (** Change of format (to higher precision) and comparison. *)
diff --git a/lib/Integers.v b/lib/Integers.v
index 246c708c..2addc78b 100644
--- a/lib/Integers.v
+++ b/lib/Integers.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherstestche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -18,6 +19,7 @@
 Require Import Eqdep_dec Zquot Zwf.
 Require Import Coqlib Zbits Axioms.
 Require Archi.
+Require Import Lia.
 
 (** * Comparisons *)
 
@@ -77,7 +79,7 @@ Definition min_signed : Z := - half_modulus.
 
 Remark wordsize_pos: zwordsize > 0.
 Proof.
-  unfold zwordsize, wordsize. generalize WS.wordsize_not_zero. omega.
+  unfold zwordsize, wordsize. generalize WS.wordsize_not_zero. lia.
 Qed.
 
 Remark modulus_power: modulus = two_p zwordsize.
@@ -88,15 +90,15 @@ Qed.
 Remark modulus_gt_one: modulus > 1.
 Proof.
   rewrite modulus_power. apply Z.lt_gt. apply (two_p_monotone_strict 0).
-  generalize wordsize_pos; omega.
+  generalize wordsize_pos; lia.
 Qed.
 
 Remark modulus_pos: modulus > 0.
 Proof.
-  generalize modulus_gt_one; omega.
+  generalize modulus_gt_one; lia.
 Qed.
 
-Hint Resolve modulus_pos: ints.
+Global Hint Resolve modulus_pos: ints.
 
 (** * Representation of machine integers *)
 
@@ -326,16 +328,16 @@ Proof.
   unfold half_modulus. rewrite modulus_power.
   set (ws1 := zwordsize - 1).
   replace (zwordsize) with (Z.succ ws1).
-  rewrite two_p_S. rewrite Z.mul_comm. apply Z_div_mult. omega.
-  unfold ws1. generalize wordsize_pos; omega.
-  unfold ws1. omega.
+  rewrite two_p_S. rewrite Z.mul_comm. apply Z_div_mult. lia.
+  unfold ws1. generalize wordsize_pos; lia.
+  unfold ws1. lia.
 Qed.
 
 Remark half_modulus_modulus: modulus = 2 * half_modulus.
 Proof.
   rewrite half_modulus_power. rewrite modulus_power.
-  rewrite <- two_p_S. apply f_equal. omega.
-  generalize wordsize_pos; omega.
+  rewrite <- two_p_S. apply f_equal. lia.
+  generalize wordsize_pos; lia.
 Qed.
 
 (** Relative positions, from greatest to smallest:
@@ -351,38 +353,38 @@ Qed.
 
 Remark half_modulus_pos: half_modulus > 0.
 Proof.
-  rewrite half_modulus_power. apply two_p_gt_ZERO. generalize wordsize_pos; omega.
+  rewrite half_modulus_power. apply two_p_gt_ZERO. generalize wordsize_pos; lia.
 Qed.
 
 Remark min_signed_neg: min_signed < 0.
 Proof.
-  unfold min_signed. generalize half_modulus_pos. omega.
+  unfold min_signed. generalize half_modulus_pos. lia.
 Qed.
 
 Remark max_signed_pos: max_signed >= 0.
 Proof.
-  unfold max_signed. generalize half_modulus_pos. omega.
+  unfold max_signed. generalize half_modulus_pos. lia.
 Qed.
 
 Remark wordsize_max_unsigned: zwordsize <= max_unsigned.
 Proof.
   assert (zwordsize < modulus).
     rewrite modulus_power. apply two_p_strict.
-    generalize wordsize_pos. omega.
-  unfold max_unsigned. omega.
+    generalize wordsize_pos. lia.
+  unfold max_unsigned. lia.
 Qed.
 
 Remark two_wordsize_max_unsigned: 2 * zwordsize - 1 <= max_unsigned.
 Proof.
   assert (2 * zwordsize - 1 < modulus).
-    rewrite modulus_power. apply two_p_strict_2. generalize wordsize_pos; omega.
-  unfold max_unsigned; omega.
+    rewrite modulus_power. apply two_p_strict_2. generalize wordsize_pos; lia.
+  unfold max_unsigned; lia.
 Qed.
 
 Remark max_signed_unsigned: max_signed < max_unsigned.
 Proof.
   unfold max_signed, max_unsigned. rewrite half_modulus_modulus.
-  generalize half_modulus_pos. omega.
+  generalize half_modulus_pos. lia.
 Qed.
 
 Lemma unsigned_repr_eq:
@@ -405,45 +407,45 @@ Definition eqm := eqmod modulus.
 
 Lemma eqm_refl: forall x, eqm x x.
 Proof (eqmod_refl modulus).
-Hint Resolve eqm_refl: ints.
+Global Hint Resolve eqm_refl: ints.
 
 Lemma eqm_refl2:
   forall x y, x = y -> eqm x y.
 Proof (eqmod_refl2 modulus).
-Hint Resolve eqm_refl2: ints.
+Global Hint Resolve eqm_refl2: ints.
 
 Lemma eqm_sym: forall x y, eqm x y -> eqm y x.
 Proof (eqmod_sym modulus).
-Hint Resolve eqm_sym: ints.
+Global Hint Resolve eqm_sym: ints.
 
 Lemma eqm_trans: forall x y z, eqm x y -> eqm y z -> eqm x z.
 Proof (eqmod_trans modulus).
-Hint Resolve eqm_trans: ints.
+Global Hint Resolve eqm_trans: ints.
 
 Lemma eqm_small_eq:
   forall x y, eqm x y -> 0 <= x < modulus -> 0 <= y < modulus -> x = y.
 Proof (eqmod_small_eq modulus).
-Hint Resolve eqm_small_eq: ints.
+Global Hint Resolve eqm_small_eq: ints.
 
 Lemma eqm_add:
   forall a b c d, eqm a b -> eqm c d -> eqm (a + c) (b + d).
 Proof (eqmod_add modulus).
-Hint Resolve eqm_add: ints.
+Global Hint Resolve eqm_add: ints.
 
 Lemma eqm_neg:
   forall x y, eqm x y -> eqm (-x) (-y).
 Proof (eqmod_neg modulus).
-Hint Resolve eqm_neg: ints.
+Global Hint Resolve eqm_neg: ints.
 
 Lemma eqm_sub:
   forall a b c d, eqm a b -> eqm c d -> eqm (a - c) (b - d).
 Proof (eqmod_sub modulus).
-Hint Resolve eqm_sub: ints.
+Global Hint Resolve eqm_sub: ints.
 
 Lemma eqm_mult:
   forall a b c d, eqm a c -> eqm b d -> eqm (a * b) (c * d).
 Proof (eqmod_mult modulus).
-Hint Resolve eqm_mult: ints.
+Global Hint Resolve eqm_mult: ints.
 
 Lemma eqm_same_bits:
   forall x y,
@@ -471,7 +473,7 @@ Lemma eqm_unsigned_repr:
 Proof.
   unfold eqm; intros. rewrite unsigned_repr_eq. apply eqmod_mod. auto with ints.
 Qed.
-Hint Resolve eqm_unsigned_repr: ints.
+Global Hint Resolve eqm_unsigned_repr: ints.
 
 Lemma eqm_unsigned_repr_l:
   forall a b, eqm a b -> eqm (unsigned (repr a)) b.
@@ -479,7 +481,7 @@ Proof.
   intros. apply eqm_trans with a.
   apply eqm_sym. apply eqm_unsigned_repr. auto.
 Qed.
-Hint Resolve eqm_unsigned_repr_l: ints.
+Global Hint Resolve eqm_unsigned_repr_l: ints.
 
 Lemma eqm_unsigned_repr_r:
   forall a b, eqm a b -> eqm a (unsigned (repr b)).
@@ -487,7 +489,7 @@ Proof.
   intros. apply eqm_trans with b. auto.
   apply eqm_unsigned_repr.
 Qed.
-Hint Resolve eqm_unsigned_repr_r: ints.
+Global Hint Resolve eqm_unsigned_repr_r: ints.
 
 Lemma eqm_signed_unsigned:
   forall x, eqm (signed x) (unsigned x).
@@ -500,17 +502,17 @@ Qed.
 Theorem unsigned_range:
   forall i, 0 <= unsigned i < modulus.
 Proof.
-  destruct i. simpl. omega.
+  destruct i. simpl. lia.
 Qed.
-Hint Resolve unsigned_range: ints.
+Global Hint Resolve unsigned_range: ints.
 
 Theorem unsigned_range_2:
   forall i, 0 <= unsigned i <= max_unsigned.
 Proof.
   intro; unfold max_unsigned.
-  generalize (unsigned_range i). omega.
+  generalize (unsigned_range i). lia.
 Qed.
-Hint Resolve unsigned_range_2: ints.
+Global Hint Resolve unsigned_range_2: ints.
 
 Theorem signed_range:
   forall i, min_signed <= signed i <= max_signed.
@@ -518,18 +520,18 @@ Proof.
   intros. unfold signed.
   generalize (unsigned_range i). set (n := unsigned i). intros.
   case (zlt n half_modulus); intro.
-  unfold max_signed. generalize min_signed_neg. omega.
+  unfold max_signed. generalize min_signed_neg. lia.
   unfold min_signed, max_signed.
-  rewrite half_modulus_modulus in *. omega.
+  rewrite half_modulus_modulus in *. lia.
 Qed.
 
 Theorem repr_unsigned:
   forall i, repr (unsigned i) = i.
 Proof.
   destruct i; simpl. unfold repr. apply mkint_eq.
-  rewrite Z_mod_modulus_eq. apply Z.mod_small; omega.
+  rewrite Z_mod_modulus_eq. apply Z.mod_small; lia.
 Qed.
-Hint Resolve repr_unsigned: ints.
+Global Hint Resolve repr_unsigned: ints.
 
 Lemma repr_signed:
   forall i, repr (signed i) = i.
@@ -537,7 +539,7 @@ Proof.
   intros. transitivity (repr (unsigned i)).
   apply eqm_samerepr. apply eqm_signed_unsigned. auto with ints.
 Qed.
-Hint Resolve repr_signed: ints.
+Global Hint Resolve repr_signed: ints.
 
 Opaque repr.
 
@@ -550,34 +552,34 @@ Theorem unsigned_repr:
   forall z, 0 <= z <= max_unsigned -> unsigned (repr z) = z.
 Proof.
   intros. rewrite unsigned_repr_eq.
-  apply Z.mod_small. unfold max_unsigned in H. omega.
+  apply Z.mod_small. unfold max_unsigned in H. lia.
 Qed.
-Hint Resolve unsigned_repr: ints.
+Global Hint Resolve unsigned_repr: ints.
 
 Theorem signed_repr:
   forall z, min_signed <= z <= max_signed -> signed (repr z) = z.
 Proof.
   intros. unfold signed. destruct (zle 0 z).
   replace (unsigned (repr z)) with z.
-  rewrite zlt_true. auto. unfold max_signed in H. omega.
-  symmetry. apply unsigned_repr. generalize max_signed_unsigned. omega.
+  rewrite zlt_true. auto. unfold max_signed in H. lia.
+  symmetry. apply unsigned_repr. generalize max_signed_unsigned. lia.
   pose (z' := z + modulus).
   replace (repr z) with (repr z').
   replace (unsigned (repr z')) with z'.
-  rewrite zlt_false. unfold z'. omega.
+  rewrite zlt_false. unfold z'. lia.
   unfold z'. unfold min_signed in H.
-  rewrite half_modulus_modulus. omega.
+  rewrite half_modulus_modulus. lia.
   symmetry. apply unsigned_repr.
   unfold z', max_unsigned. unfold min_signed, max_signed in H.
-  rewrite half_modulus_modulus. omega.
-  apply eqm_samerepr. unfold z'; red. exists 1. omega.
+  rewrite half_modulus_modulus. lia.
+  apply eqm_samerepr. unfold z'; red. exists 1. lia.
 Qed.
 
 Theorem signed_eq_unsigned:
   forall x, unsigned x <= max_signed -> signed x = unsigned x.
 Proof.
   intros. unfold signed. destruct (zlt (unsigned x) half_modulus).
-  auto. unfold max_signed in H. omegaContradiction.
+  auto. unfold max_signed in H. extlia.
 Qed.
 
 Theorem signed_positive:
@@ -585,7 +587,7 @@ Theorem signed_positive:
 Proof.
   intros. unfold signed, max_signed.
   generalize (unsigned_range x) half_modulus_modulus half_modulus_pos; intros.
-  destruct (zlt (unsigned x) half_modulus); omega.
+  destruct (zlt (unsigned x) half_modulus); lia.
 Qed.
 
 (** ** Properties of zero, one, minus one *)
@@ -597,11 +599,11 @@ Qed.
 
 Theorem unsigned_one: unsigned one = 1.
 Proof.
-  unfold one; rewrite unsigned_repr_eq. apply Z.mod_small. split. omega.
+  unfold one; rewrite unsigned_repr_eq. apply Z.mod_small. split. lia.
   unfold modulus. replace wordsize with (S(Init.Nat.pred wordsize)).
   rewrite two_power_nat_S. generalize (two_power_nat_pos (Init.Nat.pred wordsize)).
-  omega.
-  generalize wordsize_pos. unfold zwordsize. omega.
+  lia.
+  generalize wordsize_pos. unfold zwordsize. lia.
 Qed.
 
 Theorem unsigned_mone: unsigned mone = modulus - 1.
@@ -609,25 +611,25 @@ Proof.
   unfold mone; rewrite unsigned_repr_eq.
   replace (-1) with ((modulus - 1) + (-1) * modulus).
   rewrite Z_mod_plus_full. apply Z.mod_small.
-  generalize modulus_pos. omega. omega.
+  generalize modulus_pos. lia. lia.
 Qed.
 
 Theorem signed_zero: signed zero = 0.
 Proof.
-  unfold signed. rewrite unsigned_zero. apply zlt_true. generalize half_modulus_pos; omega.
+  unfold signed. rewrite unsigned_zero. apply zlt_true. generalize half_modulus_pos; lia.
 Qed.
 
 Theorem signed_one: zwordsize > 1 -> signed one = 1.
 Proof.
   intros. unfold signed. rewrite unsigned_one. apply zlt_true. 
-  change 1 with (two_p 0). rewrite half_modulus_power. apply two_p_monotone_strict. omega. 
+  change 1 with (two_p 0). rewrite half_modulus_power. apply two_p_monotone_strict. lia. 
 Qed.
 
 Theorem signed_mone: signed mone = -1.
 Proof.
   unfold signed. rewrite unsigned_mone.
-  rewrite zlt_false. omega.
-  rewrite half_modulus_modulus. generalize half_modulus_pos. omega.
+  rewrite zlt_false. lia.
+  rewrite half_modulus_modulus. generalize half_modulus_pos. lia.
 Qed.
 
 Theorem one_not_zero: one <> zero.
@@ -641,7 +643,7 @@ Theorem unsigned_repr_wordsize:
   unsigned iwordsize = zwordsize.
 Proof.
   unfold iwordsize; rewrite unsigned_repr_eq. apply Z.mod_small.
-  generalize wordsize_pos wordsize_max_unsigned; unfold max_unsigned; omega.
+  generalize wordsize_pos wordsize_max_unsigned; unfold max_unsigned; lia.
 Qed.
 
 (** ** Properties of equality *)
@@ -700,7 +702,7 @@ Proof.
 Qed.
 
 Theorem add_commut: forall x y, add x y = add y x.
-Proof. intros; unfold add. decEq. omega. Qed.
+Proof. intros; unfold add. decEq. lia. Qed.
 
 Theorem add_zero: forall x, add x zero = x.
 Proof.
@@ -734,7 +736,7 @@ Theorem add_neg_zero: forall x, add x (neg x) = zero.
 Proof.
   intros; unfold add, neg, zero. apply eqm_samerepr.
   replace 0 with (unsigned x + (- (unsigned x))).
-  auto with ints. omega.
+  auto with ints. lia.
 Qed.
 
 Theorem unsigned_add_carry:
@@ -746,8 +748,8 @@ Proof.
   rewrite unsigned_repr_eq.
   generalize (unsigned_range x) (unsigned_range y). intros.
   destruct (zlt (unsigned x + unsigned y) modulus).
-  rewrite unsigned_zero. apply Zmod_unique with 0. omega. omega.
-  rewrite unsigned_one. apply Zmod_unique with 1. omega. omega.
+  rewrite unsigned_zero. apply Zmod_unique with 0. lia. lia.
+  rewrite unsigned_one. apply Zmod_unique with 1. lia. lia.
 Qed.
 
 Corollary unsigned_add_either:
@@ -758,8 +760,8 @@ Proof.
   intros. rewrite unsigned_add_carry. unfold add_carry.
   rewrite unsigned_zero. rewrite Z.add_0_r.
   destruct (zlt (unsigned x + unsigned y) modulus).
-  rewrite unsigned_zero. left; omega.
-  rewrite unsigned_one. right; omega.
+  rewrite unsigned_zero. left; lia.
+  rewrite unsigned_one. right; lia.
 Qed.
 
 (** ** Properties of negation *)
@@ -778,7 +780,7 @@ Theorem neg_involutive: forall x, neg (neg x) = x.
 Proof.
   intros; unfold neg.
   apply eqm_repr_eq. eapply eqm_trans. apply eqm_neg.
-  apply eqm_unsigned_repr_l. apply eqm_refl. apply eqm_refl2. omega.
+  apply eqm_unsigned_repr_l. apply eqm_refl. apply eqm_refl2. lia.
 Qed.
 
 Theorem neg_add_distr: forall x y, neg(add x y) = add (neg x) (neg y).
@@ -788,7 +790,7 @@ Proof.
   auto with ints.
   replace (- (unsigned x + unsigned y))
      with ((- unsigned x) + (- unsigned y)).
-  auto with ints. omega.
+  auto with ints. lia.
 Qed.
 
 (** ** Properties of subtraction *)
@@ -796,7 +798,7 @@ Qed.
 Theorem sub_zero_l: forall x, sub x zero = x.
 Proof.
   intros; unfold sub. rewrite unsigned_zero.
-  replace (unsigned x - 0) with (unsigned x) by omega. apply repr_unsigned.
+  replace (unsigned x - 0) with (unsigned x) by lia. apply repr_unsigned.
 Qed.
 
 Theorem sub_zero_r: forall x, sub zero x = neg x.
@@ -812,7 +814,7 @@ Qed.
 
 Theorem sub_idem: forall x, sub x x = zero.
 Proof.
-  intros; unfold sub. unfold zero. decEq. omega.
+  intros; unfold sub. unfold zero. decEq. lia.
 Qed.
 
 Theorem sub_add_l: forall x y z, sub (add x y) z = add (sub x z) y.
@@ -855,8 +857,8 @@ Proof.
   rewrite unsigned_repr_eq.
   generalize (unsigned_range x) (unsigned_range y). intros.
   destruct (zlt (unsigned x - unsigned y) 0).
-  rewrite unsigned_one. apply Zmod_unique with (-1). omega. omega.
-  rewrite unsigned_zero. apply Zmod_unique with 0. omega. omega.
+  rewrite unsigned_one. apply Zmod_unique with (-1). lia. lia.
+  rewrite unsigned_zero. apply Zmod_unique with 0. lia. lia.
 Qed.
 
 (** ** Properties of multiplication *)
@@ -883,9 +885,9 @@ Theorem mul_mone: forall x, mul x mone = neg x.
 Proof.
   intros; unfold mul, neg. rewrite unsigned_mone.
   apply eqm_samerepr.
-  replace (-unsigned x) with (0 - unsigned x) by omega.
+  replace (-unsigned x) with (0 - unsigned x) by lia.
   replace (unsigned x * (modulus - 1)) with (unsigned x * modulus - unsigned x) by ring.
-  apply eqm_sub. exists (unsigned x). omega. apply eqm_refl.
+  apply eqm_sub. exists (unsigned x). lia. apply eqm_refl.
 Qed.
 
 Theorem mul_assoc: forall x y z, mul (mul x y) z = mul x (mul y z).
@@ -960,7 +962,7 @@ Proof.
   generalize (unsigned_range y); intro.
   assert (unsigned y <> 0). red; intro.
   elim H. rewrite <- (repr_unsigned y). unfold zero. congruence.
-  unfold y'. omega.
+  unfold y'. lia.
   auto with ints.
 Qed.
 
@@ -1030,7 +1032,7 @@ Proof.
   assert (Z.quot x' one = x').
   symmetry. apply Zquot_unique_full with 0. red.
   change (Z.abs one) with 1.
-  destruct (zle 0 x'). left. omega. right. omega.
+  destruct (zle 0 x'). left. lia. right. lia.
   unfold one; ring.
   congruence.
 Qed.
@@ -1058,12 +1060,12 @@ Proof.
   assert (unsigned d <> 0).
   { red; intros. elim H. rewrite <- (repr_unsigned d). rewrite H0; auto. }
   assert (0 < D).
-  { unfold D. generalize (unsigned_range d); intros. omega. }
+  { unfold D. generalize (unsigned_range d); intros. lia. }
   assert (0 <= Q <= max_unsigned).
   { unfold Q. apply Zdiv_interval_2.
     rewrite <- E1; apply unsigned_range_2.
-    omega. unfold max_unsigned; generalize modulus_pos; omega. omega. }
-  omega.
+    lia. unfold max_unsigned; generalize modulus_pos; lia. lia. }
+  lia.
 Qed.
 
 Lemma unsigned_signed:
@@ -1072,8 +1074,8 @@ Proof.
   intros. unfold lt. rewrite signed_zero. unfold signed.
   generalize (unsigned_range n). rewrite half_modulus_modulus. intros.
   destruct (zlt (unsigned n) half_modulus).
-- rewrite zlt_false by omega. auto.
-- rewrite zlt_true by omega. ring.
+- rewrite zlt_false by lia. auto.
+- rewrite zlt_true by lia. ring.
 Qed.
 
 Theorem divmods2_divs_mods:
@@ -1101,24 +1103,24 @@ Proof.
   - (* D = 1 *)
     rewrite e. rewrite Z.quot_1_r; auto.
   - (* D = -1 *)
-    rewrite e. change (-1) with (Z.opp 1). rewrite Z.quot_opp_r by omega.
+    rewrite e. change (-1) with (Z.opp 1). rewrite Z.quot_opp_r by lia.
     rewrite Z.quot_1_r.
     assert (N <> min_signed).
     { red; intros; destruct H0.
     + elim H0. rewrite <- (repr_signed n). rewrite <- H2. rewrite H4. auto.
     + elim H0. rewrite <- (repr_signed d). unfold D in e; rewrite e; auto. }
-    unfold min_signed, max_signed in *. omega.
+    unfold min_signed, max_signed in *. lia.
   - (* |D| > 1 *)
     assert (Z.abs (Z.quot N D) < half_modulus).
-    { rewrite <- Z.quot_abs by omega. apply Zquot_lt_upper_bound.
-      xomega. xomega.
+    { rewrite <- Z.quot_abs by lia. apply Zquot_lt_upper_bound.
+      extlia. extlia.
       apply Z.le_lt_trans with (half_modulus * 1).
-      rewrite Z.mul_1_r. unfold min_signed, max_signed in H3; xomega.
-      apply Zmult_lt_compat_l. generalize half_modulus_pos; omega. xomega. }
+      rewrite Z.mul_1_r. unfold min_signed, max_signed in H3; extlia.
+      apply Zmult_lt_compat_l. generalize half_modulus_pos; lia. extlia. }
     rewrite Z.abs_lt in H4.
-    unfold min_signed, max_signed; omega.
+    unfold min_signed, max_signed; lia.
   }
-  unfold proj_sumbool; rewrite ! zle_true by omega; simpl.
+  unfold proj_sumbool; rewrite ! zle_true by lia; simpl.
   unfold Q, R; rewrite H2; auto.
 Qed.
 
@@ -1169,7 +1171,7 @@ Qed.
 Lemma bits_mone:
   forall i, 0 <= i < zwordsize -> testbit mone i = true.
 Proof.
-  intros. unfold mone. rewrite testbit_repr; auto. apply Ztestbit_m1. omega.
+  intros. unfold mone. rewrite testbit_repr; auto. apply Ztestbit_m1. lia.
 Qed.
 
 Hint Rewrite bits_zero bits_mone : ints.
@@ -1186,7 +1188,7 @@ Proof.
     unfold zwordsize, ws1, wordsize.
     destruct WS.wordsize as [] eqn:E.
     elim WS.wordsize_not_zero; auto.
-    rewrite Nat2Z.inj_succ. simpl. omega.
+    rewrite Nat2Z.inj_succ. simpl. lia.
   assert (half_modulus = two_power_nat ws1).
     rewrite two_power_nat_two_p. rewrite <- H. apply half_modulus_power.
   rewrite H; rewrite H0.
@@ -1205,20 +1207,20 @@ Proof.
   simpl.
   pose proof half_modulus_pos as HMOD.
   destruct (zlt 0 half_modulus) as [HMOD' | HMOD'].
-  2: omega.
+  2: lia.
   clear HMOD'.
   destruct (zlt (intval x) half_modulus) as [ LOW | HIGH].
   {
     destruct x as [ix RANGE].
     simpl in *.
-    destruct (zlt ix 0). omega.
+    destruct (zlt ix 0). lia.
     reflexivity.
   }
   destruct (zlt _ _) as [LOW' | HIGH']; trivial.
   destruct x as [ix RANGE].
   simpl in *.
   rewrite half_modulus_modulus in *.
-  omega.
+  lia.
 Qed.
 Local Opaque repr.
 
@@ -1228,11 +1230,11 @@ Lemma bits_signed:
 Proof.
   intros.
   destruct (zlt i zwordsize).
-  - apply same_bits_eqm. apply eqm_signed_unsigned. omega.
+  - apply same_bits_eqm. apply eqm_signed_unsigned. lia.
   - unfold signed. rewrite sign_bit_of_unsigned. destruct (zlt (unsigned x) half_modulus).
     + apply Ztestbit_above with wordsize. apply unsigned_range. auto.
     + apply Ztestbit_above_neg with wordsize.
-      fold modulus. generalize (unsigned_range x). omega. auto.
+      fold modulus. generalize (unsigned_range x). lia. auto.
 Qed.
 
 Lemma bits_le:
@@ -1240,9 +1242,9 @@ Lemma bits_le:
   (forall i, 0 <= i < zwordsize -> testbit x i = true -> testbit y i = true) ->
   unsigned x <= unsigned y.
 Proof.
-  intros. apply Ztestbit_le. generalize (unsigned_range y); omega.
+  intros. apply Ztestbit_le. generalize (unsigned_range y); lia.
   intros. fold (testbit y i). destruct (zlt i zwordsize).
-  apply H. omega. auto.
+  apply H. lia. auto.
   fold (testbit x i) in H1. rewrite bits_above in H1; auto. congruence.
 Qed.
 
@@ -1510,10 +1512,10 @@ Lemma unsigned_not:
   forall x, unsigned (not x) = max_unsigned - unsigned x.
 Proof.
   intros. transitivity (unsigned (repr(-unsigned x - 1))).
-  f_equal. bit_solve. rewrite testbit_repr; auto. symmetry. apply Z_one_complement. omega.
+  f_equal. bit_solve. rewrite testbit_repr; auto. symmetry. apply Z_one_complement. lia.
   rewrite unsigned_repr_eq. apply Zmod_unique with (-1).
-  unfold max_unsigned. omega.
-  generalize (unsigned_range x). unfold max_unsigned. omega.
+  unfold max_unsigned. lia.
+  generalize (unsigned_range x). unfold max_unsigned. lia.
 Qed.
 
 Theorem not_neg:
@@ -1523,9 +1525,9 @@ Proof.
   rewrite <- (repr_unsigned x) at 1. unfold add.
   rewrite !testbit_repr; auto.
   transitivity (Z.testbit (-unsigned x - 1) i).
-  symmetry. apply Z_one_complement. omega.
+  symmetry. apply Z_one_complement. lia.
   apply same_bits_eqm; auto.
-  replace (-unsigned x - 1) with (-unsigned x + (-1)) by omega.
+  replace (-unsigned x - 1) with (-unsigned x + (-1)) by lia.
   apply eqm_add.
   unfold neg. apply eqm_unsigned_repr.
   rewrite unsigned_mone. exists (-1). ring.
@@ -1567,9 +1569,9 @@ Proof.
   replace (unsigned (xor b one)) with (1 - unsigned b).
   destruct (zlt (unsigned x - unsigned y - unsigned b)).
   rewrite zlt_true. rewrite xor_zero_l; auto.
-  unfold max_unsigned; omega.
+  unfold max_unsigned; lia.
   rewrite zlt_false. rewrite xor_idem; auto.
-  unfold max_unsigned; omega.
+  unfold max_unsigned; lia.
   destruct H; subst b.
   rewrite xor_zero_l. rewrite unsigned_one, unsigned_zero; auto.
   rewrite xor_idem. rewrite unsigned_one, unsigned_zero; auto.
@@ -1588,16 +1590,16 @@ Proof.
   rewrite (Zdecomp x) in *. rewrite (Zdecomp y) in *.
   transitivity (Z.testbit (Zshiftin (Z.odd x || Z.odd y) (Z.div2 x + Z.div2 y)) i).
   - f_equal. rewrite !Zshiftin_spec.
-    exploit (EXCL 0). omega. rewrite !Ztestbit_shiftin_base. intros.
+    exploit (EXCL 0). lia. rewrite !Ztestbit_shiftin_base. intros.
 Opaque Z.mul.
     destruct (Z.odd x); destruct (Z.odd y); simpl in *; discriminate || ring.
   - rewrite !Ztestbit_shiftin; auto.
     destruct (zeq i 0).
     + auto.
-    + apply IND. omega. intros.
-      exploit (EXCL (Z.succ j)). omega.
+    + apply IND. lia. intros.
+      exploit (EXCL (Z.succ j)). lia.
       rewrite !Ztestbit_shiftin_succ. auto.
-      omega. omega.
+      lia. lia.
 Qed.
 
 Theorem add_is_or:
@@ -1606,10 +1608,10 @@ Theorem add_is_or:
   add x y = or x y.
 Proof.
   bit_solve. unfold add. rewrite testbit_repr; auto.
-  apply Z_add_is_or. omega.
+  apply Z_add_is_or. lia.
   intros.
   assert (testbit (and x y) j = testbit zero j) by congruence.
-  autorewrite with ints in H2. assumption. omega.
+  autorewrite with ints in H2. assumption. lia.
 Qed.
 
 Theorem xor_is_or:
@@ -1655,7 +1657,7 @@ Proof.
   intros. unfold shl. rewrite testbit_repr; auto.
   destruct (zlt i (unsigned y)).
   apply Z.shiftl_spec_low. auto.
-  apply Z.shiftl_spec_high. omega. omega.
+  apply Z.shiftl_spec_high. lia. lia.
 Qed.
 
 Lemma bits_shru:
@@ -1669,7 +1671,7 @@ Proof.
   destruct (zlt (i + unsigned y) zwordsize).
   auto.
   apply bits_above; auto.
-  omega.
+  lia.
 Qed.
 
 Lemma bits_shr:
@@ -1680,15 +1682,15 @@ Lemma bits_shr:
 Proof.
   intros. unfold shr. rewrite testbit_repr; auto.
   rewrite Z.shiftr_spec. apply bits_signed.
-  generalize (unsigned_range y); omega.
-  omega.
+  generalize (unsigned_range y); lia.
+  lia.
 Qed.
 
 Hint Rewrite bits_shl bits_shru bits_shr: ints.
 
 Theorem shl_zero: forall x, shl x zero = x.
 Proof.
-  bit_solve. rewrite unsigned_zero. rewrite zlt_false. f_equal; omega. omega.
+  bit_solve. rewrite unsigned_zero. rewrite zlt_false. f_equal; lia. lia.
 Qed.
 
 Lemma bitwise_binop_shl:
@@ -1700,7 +1702,7 @@ Proof.
   intros. apply same_bits_eq; intros.
   rewrite H; auto. rewrite !bits_shl; auto.
   destruct (zlt i (unsigned n)); auto.
-  rewrite H; auto. generalize (unsigned_range n); omega.
+  rewrite H; auto. generalize (unsigned_range n); lia.
 Qed.
 
 Theorem and_shl:
@@ -1728,7 +1730,7 @@ Lemma ltu_inv:
   forall x y, ltu x y = true -> 0 <= unsigned x < unsigned y.
 Proof.
   unfold ltu; intros. destruct (zlt (unsigned x) (unsigned y)).
-  split; auto. generalize (unsigned_range x); omega.
+  split; auto. generalize (unsigned_range x); lia.
   discriminate.
 Qed.
 
@@ -1749,15 +1751,15 @@ Proof.
   generalize (ltu_iwordsize_inv _ H) (ltu_iwordsize_inv _ H0); intros.
   assert (unsigned (add y z) = unsigned y + unsigned z).
     unfold add. apply unsigned_repr.
-    generalize two_wordsize_max_unsigned; omega.
+    generalize two_wordsize_max_unsigned; lia.
   apply same_bits_eq; intros.
   rewrite bits_shl; auto.
   destruct (zlt i (unsigned z)).
-  - rewrite bits_shl; auto. rewrite zlt_true. auto. omega.
+  - rewrite bits_shl; auto. rewrite zlt_true. auto. lia.
   - rewrite bits_shl. destruct (zlt (i - unsigned z) (unsigned y)).
-    + rewrite bits_shl; auto. rewrite zlt_true. auto. omega.
-    + rewrite bits_shl; auto. rewrite zlt_false. f_equal. omega. omega.
-    + omega.
+    + rewrite bits_shl; auto. rewrite zlt_true. auto. lia.
+    + rewrite bits_shl; auto. rewrite zlt_false. f_equal. lia. lia.
+    + lia.
 Qed.
 
 Theorem sub_ltu:
@@ -1767,12 +1769,12 @@ Theorem sub_ltu:
 Proof.
   intros.
   generalize (ltu_inv x y H). intros .
-  split. omega. omega.
+  split. lia. lia.
 Qed.
 
 Theorem shru_zero: forall x, shru x zero = x.
 Proof.
-  bit_solve. rewrite unsigned_zero. rewrite zlt_true. f_equal; omega. omega.
+  bit_solve. rewrite unsigned_zero. rewrite zlt_true. f_equal; lia. lia.
 Qed.
 
 Lemma bitwise_binop_shru:
@@ -1784,7 +1786,7 @@ Proof.
   intros. apply same_bits_eq; intros.
   rewrite H; auto. rewrite !bits_shru; auto.
   destruct (zlt (i + unsigned n) zwordsize); auto.
-  rewrite H; auto. generalize (unsigned_range n); omega.
+  rewrite H; auto. generalize (unsigned_range n); lia.
 Qed.
 
 Theorem and_shru:
@@ -1819,20 +1821,20 @@ Proof.
   generalize (ltu_iwordsize_inv _ H) (ltu_iwordsize_inv _ H0); intros.
   assert (unsigned (add y z) = unsigned y + unsigned z).
     unfold add. apply unsigned_repr.
-    generalize two_wordsize_max_unsigned; omega.
+    generalize two_wordsize_max_unsigned; lia.
   apply same_bits_eq; intros.
   rewrite bits_shru; auto.
   destruct (zlt (i + unsigned z) zwordsize).
   - rewrite bits_shru. destruct (zlt (i + unsigned z + unsigned y) zwordsize).
-    + rewrite bits_shru; auto. rewrite zlt_true. f_equal. omega. omega.
-    + rewrite bits_shru; auto. rewrite zlt_false. auto. omega.
-    + omega.
-  - rewrite bits_shru; auto. rewrite zlt_false. auto. omega.
+    + rewrite bits_shru; auto. rewrite zlt_true. f_equal. lia. lia.
+    + rewrite bits_shru; auto. rewrite zlt_false. auto. lia.
+    + lia.
+  - rewrite bits_shru; auto. rewrite zlt_false. auto. lia.
 Qed.
 
 Theorem shr_zero: forall x, shr x zero = x.
 Proof.
-  bit_solve. rewrite unsigned_zero. rewrite zlt_true. f_equal; omega. omega.
+  bit_solve. rewrite unsigned_zero. rewrite zlt_true. f_equal; lia. lia.
 Qed.
 
 Lemma bitwise_binop_shr:
@@ -1844,8 +1846,8 @@ Proof.
   rewrite H; auto. rewrite !bits_shr; auto.
   rewrite H; auto.
   destruct (zlt (i + unsigned n) zwordsize).
-  generalize (unsigned_range n); omega.
-  omega.
+  generalize (unsigned_range n); lia.
+  lia.
 Qed.
 
 Theorem and_shr:
@@ -1880,15 +1882,15 @@ Proof.
   generalize (ltu_iwordsize_inv _ H) (ltu_iwordsize_inv _ H0); intros.
   assert (unsigned (add y z) = unsigned y + unsigned z).
     unfold add. apply unsigned_repr.
-    generalize two_wordsize_max_unsigned; omega.
+    generalize two_wordsize_max_unsigned; lia.
   apply same_bits_eq; intros.
   rewrite !bits_shr; auto. f_equal.
   destruct (zlt (i + unsigned z) zwordsize).
-  rewrite H4. replace (i + (unsigned y + unsigned z)) with (i + unsigned z + unsigned y) by omega. auto.
+  rewrite H4. replace (i + (unsigned y + unsigned z)) with (i + unsigned z + unsigned y) by lia. auto.
   rewrite (zlt_false _ (i + unsigned (add y z))).
-  destruct (zlt (zwordsize - 1 + unsigned y) zwordsize); omega.
-  omega.
-  destruct (zlt (i + unsigned z) zwordsize); omega.
+  destruct (zlt (zwordsize - 1 + unsigned y) zwordsize); lia.
+  lia.
+  destruct (zlt (i + unsigned z) zwordsize); lia.
 Qed.
 
 Theorem and_shr_shru:
@@ -1898,7 +1900,7 @@ Proof.
   intros. apply same_bits_eq; intros.
   rewrite bits_and; auto. rewrite bits_shr; auto. rewrite !bits_shru; auto.
   destruct (zlt (i + unsigned z) zwordsize).
-  - rewrite bits_and; auto. generalize (unsigned_range z); omega.
+  - rewrite bits_and; auto. generalize (unsigned_range z); lia.
   - apply andb_false_r.
 Qed.
 
@@ -1924,17 +1926,17 @@ Proof.
   rewrite sign_bit_of_unsigned.
   unfold lt. rewrite signed_zero. unfold signed.
   destruct (zlt (unsigned x) half_modulus).
-  rewrite zlt_false. auto. generalize (unsigned_range x); omega.
+  rewrite zlt_false. auto. generalize (unsigned_range x); lia.
   rewrite zlt_true. unfold one; rewrite testbit_repr; auto.
-  generalize (unsigned_range x); omega.
-  omega.
+  generalize (unsigned_range x); lia.
+  lia.
   rewrite zlt_false.
   unfold testbit. rewrite Ztestbit_eq. rewrite zeq_false.
   destruct (lt x zero).
   rewrite unsigned_one. simpl Z.div2. rewrite Z.testbit_0_l; auto.
   rewrite unsigned_zero. simpl Z.div2. rewrite Z.testbit_0_l; auto.
-  auto. omega. omega.
-  generalize wordsize_max_unsigned; omega.
+  auto. lia. lia.
+  generalize wordsize_max_unsigned; lia.
 Qed.
 
 Theorem shr_lt_zero:
@@ -1945,13 +1947,13 @@ Proof.
   rewrite bits_shr; auto.
   rewrite unsigned_repr.
   transitivity (testbit x (zwordsize - 1)).
-  f_equal. destruct (zlt (i + (zwordsize - 1)) zwordsize); omega.
+  f_equal. destruct (zlt (i + (zwordsize - 1)) zwordsize); lia.
   rewrite sign_bit_of_unsigned.
   unfold lt. rewrite signed_zero. unfold signed.
   destruct (zlt (unsigned x) half_modulus).
-  rewrite zlt_false. rewrite bits_zero; auto. generalize (unsigned_range x); omega.
-  rewrite zlt_true. rewrite bits_mone; auto. generalize (unsigned_range x); omega.
-  generalize wordsize_max_unsigned; omega.
+  rewrite zlt_false. rewrite bits_zero; auto. generalize (unsigned_range x); lia.
+  rewrite zlt_true. rewrite bits_mone; auto. generalize (unsigned_range x); lia.
+  generalize wordsize_max_unsigned; lia.
 Qed.
 
 (** ** Properties of rotations *)
@@ -1968,20 +1970,20 @@ Proof.
   exploit (Z_mod_lt (unsigned y) zwordsize). apply wordsize_pos.
   fold j. intros RANGE.
   rewrite testbit_repr; auto.
-  rewrite Z.lor_spec. rewrite Z.shiftr_spec. 2: omega.
+  rewrite Z.lor_spec. rewrite Z.shiftr_spec. 2: lia.
   destruct (zlt i j).
   - rewrite Z.shiftl_spec_low; auto. simpl.
     unfold testbit. f_equal.
     symmetry. apply Zmod_unique with (-k - 1).
     rewrite EQ. ring.
-    omega.
+    lia.
   - rewrite Z.shiftl_spec_high.
     fold (testbit x (i + (zwordsize - j))).
     rewrite bits_above. rewrite orb_false_r.
     fold (testbit x (i - j)).
     f_equal. symmetry. apply Zmod_unique with (-k).
     rewrite EQ. ring.
-    omega. omega. omega. omega.
+    lia. lia. lia. lia.
 Qed.
 
 Lemma bits_ror:
@@ -1996,20 +1998,20 @@ Proof.
   exploit (Z_mod_lt (unsigned y) zwordsize). apply wordsize_pos.
   fold j. intros RANGE.
   rewrite testbit_repr; auto.
-  rewrite Z.lor_spec. rewrite Z.shiftr_spec. 2: omega.
+  rewrite Z.lor_spec. rewrite Z.shiftr_spec. 2: lia.
   destruct (zlt (i + j) zwordsize).
   - rewrite Z.shiftl_spec_low; auto. rewrite orb_false_r.
     unfold testbit. f_equal.
     symmetry. apply Zmod_unique with k.
     rewrite EQ. ring.
-    omega. omega.
+    lia. lia.
   - rewrite Z.shiftl_spec_high.
     fold (testbit x (i + j)).
     rewrite bits_above. simpl.
     unfold testbit. f_equal.
     symmetry. apply Zmod_unique with (k + 1).
     rewrite EQ. ring.
-    omega. omega. omega. omega.
+    lia. lia. lia. lia.
 Qed.
 
 Hint Rewrite bits_rol bits_ror: ints.
@@ -2026,8 +2028,8 @@ Proof.
   - rewrite andb_false_r; auto.
   - generalize (unsigned_range n); intros.
     rewrite bits_mone. rewrite andb_true_r. f_equal.
-    symmetry. apply Z.mod_small. omega.
-    omega.
+    symmetry. apply Z.mod_small. lia.
+    lia.
 Qed.
 
 Theorem shru_rolm:
@@ -2042,9 +2044,9 @@ Proof.
   - generalize (unsigned_range n); intros.
     rewrite bits_mone. rewrite andb_true_r. f_equal.
     unfold sub. rewrite unsigned_repr. rewrite unsigned_repr_wordsize.
-    symmetry. apply Zmod_unique with (-1). ring. omega.
-    rewrite unsigned_repr_wordsize. generalize wordsize_max_unsigned. omega.
-    omega.
+    symmetry. apply Zmod_unique with (-1). ring. lia.
+    rewrite unsigned_repr_wordsize. generalize wordsize_max_unsigned. lia.
+    lia.
   - rewrite andb_false_r; auto.
 Qed.
 
@@ -2098,11 +2100,11 @@ Proof.
   apply eqmod_sub.
   apply eqmod_sym. apply eqmod_mod. apply wordsize_pos.
   apply eqmod_refl.
-  replace (i - M - N) with (i - (M + N)) by omega.
+  replace (i - M - N) with (i - (M + N)) by lia.
   apply eqmod_sub.
   apply eqmod_refl.
   apply eqmod_trans with (Z.modulo (unsigned n + unsigned m) zwordsize).
-  replace (M + N) with (N + M) by omega. apply eqmod_mod. apply wordsize_pos.
+  replace (M + N) with (N + M) by lia. apply eqmod_mod. apply wordsize_pos.
   unfold modu, add. fold M; fold N. rewrite unsigned_repr_wordsize.
   assert (forall a, eqmod zwordsize a (unsigned (repr a))).
     intros. eapply eqmod_divides. apply eqm_unsigned_repr. assumption.
@@ -2149,7 +2151,7 @@ Proof.
   unfold sub. rewrite unsigned_repr. rewrite unsigned_repr_wordsize.
   apply eqmod_mod_eq. apply wordsize_pos. exists 1. ring.
   rewrite unsigned_repr_wordsize.
-  generalize wordsize_pos; generalize wordsize_max_unsigned; omega.
+  generalize wordsize_pos; generalize wordsize_max_unsigned; lia.
 Qed.
 
 Theorem ror_rol_neg:
@@ -2157,9 +2159,9 @@ Theorem ror_rol_neg:
 Proof.
   intros. apply same_bits_eq; intros.
   rewrite bits_ror by auto. rewrite bits_rol by auto.
-  f_equal. apply eqmod_mod_eq. omega.
+  f_equal. apply eqmod_mod_eq. lia.
   apply eqmod_trans with (i - (- unsigned y)).
-  apply eqmod_refl2; omega.
+  apply eqmod_refl2; lia.
   apply eqmod_sub. apply eqmod_refl.
   apply eqmod_divides with modulus.
   apply eqm_unsigned_repr. auto.
@@ -2182,8 +2184,8 @@ Proof.
     assert (unsigned (add y z) = zwordsize).
       rewrite H1. apply unsigned_repr_wordsize.
     unfold add in H5. rewrite unsigned_repr in H5.
-    omega.
-    generalize two_wordsize_max_unsigned; omega.
+    lia.
+    generalize two_wordsize_max_unsigned; lia.
   - apply eqm_unsigned_repr_r. apply eqm_refl2. f_equal.
     apply Z.mod_small; auto.
 Qed.
@@ -2199,10 +2201,10 @@ Proof.
   destruct (Z_is_power2 (unsigned n)) as [i|] eqn:E; inv H.
   assert (0 <= i < zwordsize).
   { apply Z_is_power2_range with (unsigned n). 
-    generalize wordsize_pos; omega.
+    generalize wordsize_pos; lia.
     rewrite <- modulus_power. apply unsigned_range.
     auto. }
-  rewrite unsigned_repr; auto. generalize wordsize_max_unsigned; omega.
+  rewrite unsigned_repr; auto. generalize wordsize_max_unsigned; lia.
 Qed.
 
 Lemma is_power2_rng:
@@ -2236,10 +2238,10 @@ Remark two_p_range:
   0 <= two_p n <= max_unsigned.
 Proof.
   intros. split.
-  assert (two_p n > 0). apply two_p_gt_ZERO. omega. omega.
+  assert (two_p n > 0). apply two_p_gt_ZERO. lia. lia.
   generalize (two_p_monotone_strict _ _ H).
   unfold zwordsize; rewrite <- two_power_nat_two_p.
-  unfold max_unsigned, modulus. omega.
+  unfold max_unsigned, modulus. lia.
 Qed.
 
 Lemma is_power2_two_p:
@@ -2247,7 +2249,7 @@ Lemma is_power2_two_p:
   is_power2 (repr (two_p n)) = Some (repr n).
 Proof.
   intros. unfold is_power2. rewrite unsigned_repr.
-  rewrite Z_is_power2_complete by omega; auto.
+  rewrite Z_is_power2_complete by lia; auto.
   apply two_p_range. auto.
 Qed.
 
@@ -2261,7 +2263,7 @@ Lemma shl_mul_two_p:
 Proof.
   intros. unfold shl, mul. apply eqm_samerepr.
   rewrite Zshiftl_mul_two_p. auto with ints.
-  generalize (unsigned_range y); omega.
+  generalize (unsigned_range y); lia.
 Qed.
 
 Theorem shl_mul:
@@ -2297,19 +2299,19 @@ Proof.
     rewrite shl_mul_two_p. unfold mul. apply eqm_unsigned_repr_l.
     apply eqm_mult; auto with ints. apply eqm_unsigned_repr_l.
     apply eqm_refl2. rewrite unsigned_repr. auto.
-    generalize wordsize_max_unsigned; omega.
+    generalize wordsize_max_unsigned; lia.
   - bit_solve.
     rewrite unsigned_repr.
     destruct (zlt i n).
     + auto.
     + replace (testbit y i) with false. apply andb_false_r.
       symmetry. unfold testbit.
-      assert (EQ: Z.of_nat (Z.to_nat n) = n) by (apply Z2Nat.id; omega).
+      assert (EQ: Z.of_nat (Z.to_nat n) = n) by (apply Z2Nat.id; lia).
       apply Ztestbit_above with (Z.to_nat n).
       rewrite <- EQ in H0. rewrite <- two_power_nat_two_p in H0.
-      generalize (unsigned_range y); omega.
+      generalize (unsigned_range y); lia.
       rewrite EQ; auto.
-    + generalize wordsize_max_unsigned; omega.
+    + generalize wordsize_max_unsigned; lia.
 Qed.
 
 (** Unsigned right shifts and unsigned divisions by powers of 2. *)
@@ -2320,7 +2322,7 @@ Lemma shru_div_two_p:
 Proof.
   intros. unfold shru.
   rewrite Zshiftr_div_two_p. auto.
-  generalize (unsigned_range y); omega.
+  generalize (unsigned_range y); lia.
 Qed.
 
 Theorem divu_pow2:
@@ -2340,7 +2342,7 @@ Lemma shr_div_two_p:
 Proof.
   intros. unfold shr.
   rewrite Zshiftr_div_two_p. auto.
-  generalize (unsigned_range y); omega.
+  generalize (unsigned_range y); lia.
 Qed.
 
 Theorem divs_pow2:
@@ -2393,24 +2395,24 @@ Proof.
   set (uy := unsigned y).
   assert (0 <= uy < zwordsize - 1).
     generalize (ltu_inv _ _ H). rewrite unsigned_repr. auto.
-    generalize wordsize_pos wordsize_max_unsigned; omega.
+    generalize wordsize_pos wordsize_max_unsigned; lia.
   rewrite shr_div_two_p. unfold shrx. unfold divs.
   assert (shl one y = repr (two_p uy)).
     transitivity (mul one (repr (two_p uy))).
     symmetry. apply mul_pow2. replace y with (repr uy).
-    apply is_power2_two_p. omega. apply repr_unsigned.
+    apply is_power2_two_p. lia. apply repr_unsigned.
     rewrite mul_commut. apply mul_one.
-  assert (two_p uy > 0). apply two_p_gt_ZERO. omega.
+  assert (two_p uy > 0). apply two_p_gt_ZERO. lia.
   assert (two_p uy < half_modulus).
     rewrite half_modulus_power.
     apply two_p_monotone_strict. auto.
   assert (two_p uy < modulus).
-    rewrite modulus_power. apply two_p_monotone_strict. omega.
+    rewrite modulus_power. apply two_p_monotone_strict. lia.
   assert (unsigned (shl one y) = two_p uy).
-    rewrite H1. apply unsigned_repr. unfold max_unsigned. omega.
+    rewrite H1. apply unsigned_repr. unfold max_unsigned. lia.
   assert (signed (shl one y) = two_p uy).
     rewrite H1. apply signed_repr.
-    unfold max_signed. generalize min_signed_neg. omega.
+    unfold max_signed. generalize min_signed_neg. lia.
   rewrite H6.
   rewrite Zquot_Zdiv; auto.
   unfold lt. rewrite signed_zero.
@@ -2419,10 +2421,10 @@ Proof.
   assert (signed (sub (shl one y) one) = two_p uy - 1).
     unfold sub. rewrite H5. rewrite unsigned_one.
     apply signed_repr.
-    generalize min_signed_neg. unfold max_signed. omega.
-  rewrite H7. rewrite signed_repr. f_equal. f_equal. omega.
+    generalize min_signed_neg. unfold max_signed. lia.
+  rewrite H7. rewrite signed_repr. f_equal. f_equal. lia.
   generalize (signed_range x). intros.
-  assert (two_p uy - 1 <= max_signed). unfold max_signed. omega. omega.
+  assert (two_p uy - 1 <= max_signed). unfold max_signed. lia. lia.
 Qed.
 
 Theorem shrx_shr_2:
@@ -2437,19 +2439,19 @@ Proof.
   generalize (unsigned_range y); fold uy; intros.
   assert (0 <= uy < zwordsize - 1).
     generalize (ltu_inv _ _ H). rewrite unsigned_repr. auto.
-    generalize wordsize_pos wordsize_max_unsigned; omega.
+    generalize wordsize_pos wordsize_max_unsigned; lia.
   assert (two_p uy < modulus).
-    rewrite modulus_power. apply two_p_monotone_strict. omega.
+    rewrite modulus_power. apply two_p_monotone_strict. lia.
   f_equal. rewrite shl_mul_two_p. fold uy. rewrite mul_commut. rewrite mul_one.
   unfold sub. rewrite unsigned_one. rewrite unsigned_repr.
   rewrite unsigned_repr_wordsize. fold uy.
   apply same_bits_eq; intros. rewrite bits_shru by auto.
-  rewrite testbit_repr by auto. rewrite Ztestbit_two_p_m1 by omega.
-  rewrite unsigned_repr by (generalize wordsize_max_unsigned; omega).
+  rewrite testbit_repr by auto. rewrite Ztestbit_two_p_m1 by lia.
+  rewrite unsigned_repr by (generalize wordsize_max_unsigned; lia).
   destruct (zlt i uy).
-  rewrite zlt_true by omega. rewrite bits_mone by omega. auto.
-  rewrite zlt_false by omega. auto.
-  assert (two_p uy > 0) by (apply two_p_gt_ZERO; omega). unfold max_unsigned; omega.
+  rewrite zlt_true by lia. rewrite bits_mone by lia. auto.
+  rewrite zlt_false by lia. auto.
+  assert (two_p uy > 0) by (apply two_p_gt_ZERO; lia). unfold max_unsigned; lia.
 - replace (shru zero (sub iwordsize y)) with zero.
   rewrite add_zero; auto.
   bit_solve. destruct (zlt (i + unsigned (sub iwordsize y)) zwordsize); auto.
@@ -2482,20 +2484,20 @@ Proof.
       clear H.
       rewrite two_power_nat_two_p.
       split.
-      omega.
+      lia.
       set (w := (Z.of_nat wordsize)) in *.
       assert ((two_p 2) <= (two_p w)) as MONO.
       {
         apply two_p_monotone.
-        omega.
+        lia.
       }
       change (two_p 2) with 4 in MONO.
-      omega.
+      lia.
     }
     generalize wordsize_max_unsigned.
     fold zwordsize.
     generalize wordsize_pos.
-    omega.
+    lia.
   }
   rewrite unsigned_repr by assumption.
   simpl.
@@ -2518,23 +2520,23 @@ Proof.
   set (uy := unsigned y).
   assert (0 <= uy < zwordsize - 1).
     generalize (ltu_inv _ _ H). rewrite unsigned_repr. auto.
-    generalize wordsize_pos wordsize_max_unsigned; omega.
+    generalize wordsize_pos wordsize_max_unsigned; lia.
   assert (shl one y = repr (two_p uy)).
     rewrite shl_mul_two_p. rewrite mul_commut. apply mul_one.
   assert (and x (sub (shl one y) one) = modu x (repr (two_p uy))).
     symmetry. rewrite H1. apply modu_and with (logn := y).
     rewrite is_power2_two_p. unfold uy. rewrite repr_unsigned. auto.
-    omega.
+    lia.
   rewrite H2. rewrite H1.
   repeat rewrite shr_div_two_p. fold sx. fold uy.
-  assert (two_p uy > 0). apply two_p_gt_ZERO. omega.
+  assert (two_p uy > 0). apply two_p_gt_ZERO. lia.
   assert (two_p uy < modulus).
-    rewrite modulus_power. apply two_p_monotone_strict. omega.
+    rewrite modulus_power. apply two_p_monotone_strict. lia.
   assert (two_p uy < half_modulus).
     rewrite half_modulus_power.
     apply two_p_monotone_strict. auto.
   assert (two_p uy < modulus).
-    rewrite modulus_power. apply two_p_monotone_strict. omega.
+    rewrite modulus_power. apply two_p_monotone_strict. lia.
   assert (sub (repr (two_p uy)) one = repr (two_p uy - 1)).
     unfold sub. apply eqm_samerepr. apply eqm_sub. apply eqm_sym; apply eqm_unsigned_repr.
     rewrite unsigned_one. apply eqm_refl.
@@ -2547,17 +2549,17 @@ Proof.
     fold eqm. unfold sx. apply eqm_sym. apply eqm_signed_unsigned.
     unfold modulus. rewrite two_power_nat_two_p.
     exists (two_p (zwordsize - uy)). rewrite <- two_p_is_exp.
-    f_equal. fold zwordsize; omega. omega. omega.
+    f_equal. fold zwordsize; lia. lia. lia.
   rewrite H8. rewrite Zdiv_shift; auto.
   unfold add. apply eqm_samerepr. apply eqm_add.
   apply eqm_unsigned_repr.
   destruct (zeq (sx mod two_p uy) 0); simpl.
   rewrite unsigned_zero. apply eqm_refl.
   rewrite unsigned_one. apply eqm_refl.
-  generalize (Z_mod_lt (unsigned x) (two_p uy) H3). unfold max_unsigned. omega.
-  unfold max_unsigned; omega.
-  generalize (signed_range x). fold sx. intros. split. omega. unfold max_signed. omega.
-  generalize min_signed_neg. unfold max_signed. omega.
+  generalize (Z_mod_lt (unsigned x) (two_p uy) H3). unfold max_unsigned. lia.
+  unfold max_unsigned; lia.
+  generalize (signed_range x). fold sx. intros. split. lia. unfold max_signed. lia.
+  generalize min_signed_neg. unfold max_signed. lia.
 Qed.
 
 (** Connections between [shr] and [shru]. *)
@@ -2576,14 +2578,14 @@ Lemma and_positive:
   forall x y, signed y >= 0 -> signed (and x y) >= 0.
 Proof.
   intros.
-  assert (unsigned y < half_modulus). rewrite signed_positive in H. unfold max_signed in H; omega.
+  assert (unsigned y < half_modulus). rewrite signed_positive in H. unfold max_signed in H; lia.
   generalize (sign_bit_of_unsigned y). rewrite zlt_true; auto. intros A.
   generalize (sign_bit_of_unsigned (and x y)). rewrite bits_and. rewrite A.
   rewrite andb_false_r. unfold signed.
   destruct (zlt (unsigned (and x y)) half_modulus).
-  intros. generalize (unsigned_range (and x y)); omega.
+  intros. generalize (unsigned_range (and x y)); lia.
   congruence.
-  generalize wordsize_pos; omega.
+  generalize wordsize_pos; lia.
 Qed.
 
 Theorem shr_and_is_shru_and:
@@ -2610,7 +2612,7 @@ Lemma bits_sign_ext:
   testbit (sign_ext n x) i = testbit x (if zlt i n then i else n - 1).
 Proof.
   intros. unfold sign_ext.
-  rewrite testbit_repr; auto. apply Zsign_ext_spec. omega. 
+  rewrite testbit_repr; auto. apply Zsign_ext_spec. lia. 
 Qed.
 
 Hint Rewrite bits_zero_ext bits_sign_ext: ints.
@@ -2619,13 +2621,13 @@ Theorem zero_ext_above:
   forall n x, n >= zwordsize -> zero_ext n x = x.
 Proof.
   intros. apply same_bits_eq; intros.
-  rewrite bits_zero_ext. apply zlt_true. omega. omega.
+  rewrite bits_zero_ext. apply zlt_true. lia. lia.
 Qed.
 
 Theorem zero_ext_below:
   forall n x, n <= 0 -> zero_ext n x = zero.
 Proof.
-  intros. bit_solve. destruct (zlt i n); auto. apply bits_below; omega. omega.
+  intros. bit_solve. destruct (zlt i n); auto. apply bits_below; lia. lia.
 Qed.
 
 Theorem sign_ext_above:
@@ -2633,13 +2635,13 @@ Theorem sign_ext_above:
 Proof.
   intros. apply same_bits_eq; intros.
   unfold sign_ext; rewrite testbit_repr; auto.
-  rewrite Zsign_ext_spec. rewrite zlt_true. auto. omega. omega.
+  rewrite Zsign_ext_spec. rewrite zlt_true. auto. lia. lia.
 Qed.
 
 Theorem sign_ext_below:
   forall n x, n <= 0 -> sign_ext n x = zero.
 Proof.
-  intros. bit_solve. apply bits_below. destruct (zlt i n); omega.
+  intros. bit_solve. apply bits_below. destruct (zlt i n); lia.
 Qed.
 
 Theorem zero_ext_and:
@@ -2661,8 +2663,8 @@ Proof.
   fold (testbit (zero_ext n x) i).
   destruct (zlt i zwordsize).
   rewrite bits_zero_ext; auto.
-  rewrite bits_above. rewrite zlt_false; auto. omega. omega.
-  omega.
+  rewrite bits_above. rewrite zlt_false; auto. lia. lia.
+  lia.
 Qed.
 
 Theorem zero_ext_widen:
@@ -2670,7 +2672,7 @@ Theorem zero_ext_widen:
   zero_ext n' (zero_ext n x) = zero_ext n x.
 Proof.
   bit_solve. destruct (zlt i n).
-  apply zlt_true. omega.
+  apply zlt_true. lia.
   destruct (zlt i n'); auto.
   tauto. tauto.
 Qed.
@@ -2683,9 +2685,9 @@ Proof.
   bit_solve. destruct (zlt i n').
   auto.
   rewrite (zlt_false _ i n).
-  destruct (zlt (n' - 1) n); f_equal; omega.
-  omega.
-  destruct (zlt i n'); omega.
+  destruct (zlt (n' - 1) n); f_equal; lia.
+  lia.
+  destruct (zlt i n'); lia.
   apply sign_ext_above; auto.
 Qed.
 
@@ -2697,8 +2699,8 @@ Proof.
   bit_solve.
   destruct (zlt i n').
   auto.
-  rewrite !zlt_false. auto. omega. omega. omega.
-  destruct (zlt i n'); omega.
+  rewrite !zlt_false. auto. lia. lia. lia.
+  destruct (zlt i n'); lia.
   apply sign_ext_above; auto.
 Qed.
 
@@ -2707,9 +2709,9 @@ Theorem zero_ext_narrow:
   zero_ext n (zero_ext n' x) = zero_ext n x.
 Proof.
   bit_solve. destruct (zlt i n).
-  apply zlt_true. omega.
+  apply zlt_true. lia.
   auto.
-  omega. omega. omega.
+  lia. lia. lia.
 Qed.
 
 Theorem sign_ext_narrow:
@@ -2717,9 +2719,9 @@ Theorem sign_ext_narrow:
   sign_ext n (sign_ext n' x) = sign_ext n x.
 Proof.
   intros. destruct (zlt n zwordsize).
-  bit_solve. destruct (zlt i n); f_equal; apply zlt_true; omega.
-  destruct (zlt i n); omega.
-  rewrite (sign_ext_above n'). auto. omega.
+  bit_solve. destruct (zlt i n); f_equal; apply zlt_true; lia.
+  destruct (zlt i n); lia.
+  rewrite (sign_ext_above n'). auto. lia.
 Qed.
 
 Theorem zero_sign_ext_narrow:
@@ -2729,21 +2731,21 @@ Proof.
   intros. destruct (zlt n' zwordsize).
   bit_solve.
   destruct (zlt i n); auto.
-  rewrite zlt_true; auto. omega.
-  omega. omega.
+  rewrite zlt_true; auto. lia.
+  lia. lia.
   rewrite sign_ext_above; auto.
 Qed.
 
 Theorem zero_ext_idem:
   forall n x, 0 <= n -> zero_ext n (zero_ext n x) = zero_ext n x.
 Proof.
-  intros. apply zero_ext_widen. omega.
+  intros. apply zero_ext_widen. lia.
 Qed.
 
 Theorem sign_ext_idem:
   forall n x, 0 < n -> sign_ext n (sign_ext n x) = sign_ext n x.
 Proof.
-  intros. apply sign_ext_widen. omega.
+  intros. apply sign_ext_widen. lia.
 Qed.
  
 Theorem sign_ext_zero_ext:
@@ -2753,15 +2755,15 @@ Proof.
   bit_solve.
   destruct (zlt i n).
   rewrite zlt_true; auto.
-  rewrite zlt_true; auto. omega.
-  destruct (zlt i n); omega.
+  rewrite zlt_true; auto. lia.
+  destruct (zlt i n); lia.
   rewrite zero_ext_above; auto.
 Qed.
 
 Theorem zero_ext_sign_ext:
   forall n x, 0 < n -> zero_ext n (sign_ext n x) = zero_ext n x.
 Proof.
-  intros. apply zero_sign_ext_narrow. omega.
+  intros. apply zero_sign_ext_narrow. lia.
 Qed.
 
 Theorem sign_ext_equal_if_zero_equal:
@@ -2784,21 +2786,21 @@ Proof.
   apply same_bits_eq; intros. rewrite bits_shru by auto. fold Z.
   destruct (zlt Z Y).
 - assert (A: unsigned (sub y z) = Y - Z).
-  { apply unsigned_repr. generalize wordsize_max_unsigned; omega. }
-  symmetry; rewrite bits_shl, A by omega.
+  { apply unsigned_repr. generalize wordsize_max_unsigned; lia. }
+  symmetry; rewrite bits_shl, A by lia.
   destruct (zlt (i + Z) zwordsize).
-+ rewrite bits_shl by omega. fold Y.
-  destruct (zlt i (Y - Z)); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
-  rewrite bits_zero_ext by omega. rewrite zlt_true by omega. f_equal; omega.
-+ rewrite bits_zero_ext by omega. rewrite ! zlt_false by omega. auto.
++ rewrite bits_shl by lia. fold Y.
+  destruct (zlt i (Y - Z)); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
+  rewrite bits_zero_ext by lia. rewrite zlt_true by lia. f_equal; lia.
++ rewrite bits_zero_ext by lia. rewrite ! zlt_false by lia. auto.
 - assert (A: unsigned (sub z y) = Z - Y).
-  { apply unsigned_repr. generalize wordsize_max_unsigned; omega. }
-  rewrite bits_zero_ext, bits_shru, A by omega.
-  destruct (zlt (i + Z) zwordsize); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
-  rewrite bits_shl by omega. fold Y.
+  { apply unsigned_repr. generalize wordsize_max_unsigned; lia. }
+  rewrite bits_zero_ext, bits_shru, A by lia.
+  destruct (zlt (i + Z) zwordsize); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
+  rewrite bits_shl by lia. fold Y.
   destruct (zlt (i + Z) Y).
-+ rewrite zlt_false by omega. auto.
-+ rewrite zlt_true by omega. f_equal; omega.
++ rewrite zlt_false by lia. auto.
++ rewrite zlt_true by lia. f_equal; lia.
 Qed.
 
 Corollary zero_ext_shru_shl:
@@ -2809,11 +2811,11 @@ Corollary zero_ext_shru_shl:
 Proof.
   intros.
   assert (A: unsigned y = zwordsize - n).
-  { unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. omega. }
+  { unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. lia. }
   assert (B: ltu y iwordsize = true).
-  { unfold ltu; rewrite A, unsigned_repr_wordsize. apply zlt_true; omega. }
-  rewrite shru_shl by auto. unfold ltu; rewrite zlt_false by omega.
-  rewrite sub_idem, shru_zero. f_equal. rewrite A; omega.
+  { unfold ltu; rewrite A, unsigned_repr_wordsize. apply zlt_true; lia. }
+  rewrite shru_shl by auto. unfold ltu; rewrite zlt_false by lia.
+  rewrite sub_idem, shru_zero. f_equal. rewrite A; lia.
 Qed.
 
 Theorem shr_shl:
@@ -2825,26 +2827,26 @@ Proof.
   intros. apply ltu_iwordsize_inv in H; apply ltu_iwordsize_inv in H0.
   unfold ltu. set (Y := unsigned y) in *; set (Z := unsigned z) in *.
   apply same_bits_eq; intros. rewrite bits_shr by auto. fold Z.
-  rewrite bits_shl by (destruct (zlt (i + Z) zwordsize); omega). fold Y.
+  rewrite bits_shl by (destruct (zlt (i + Z) zwordsize); lia). fold Y.
   destruct (zlt Z Y).
 - assert (A: unsigned (sub y z) = Y - Z).
-  { apply unsigned_repr. generalize wordsize_max_unsigned; omega. }
-  rewrite bits_shl, A by omega.
+  { apply unsigned_repr. generalize wordsize_max_unsigned; lia. }
+  rewrite bits_shl, A by lia.
   destruct (zlt i (Y - Z)).
-+ apply zlt_true. destruct (zlt (i + Z) zwordsize); omega.
-+ rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega).
-  rewrite bits_sign_ext by omega. f_equal. 
++ apply zlt_true. destruct (zlt (i + Z) zwordsize); lia.
++ rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); lia).
+  rewrite bits_sign_ext by lia. f_equal. 
   destruct (zlt (i + Z) zwordsize).
-  rewrite zlt_true by omega. omega.
-  rewrite zlt_false by omega. omega.
+  rewrite zlt_true by lia. lia.
+  rewrite zlt_false by lia. lia.
 - assert (A: unsigned (sub z y) = Z - Y).
-  { apply unsigned_repr. generalize wordsize_max_unsigned; omega. }
-  rewrite bits_sign_ext by omega.
-  rewrite bits_shr by (destruct (zlt i (zwordsize - Z)); omega).
-  rewrite A. rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega).
+  { apply unsigned_repr. generalize wordsize_max_unsigned; lia. }
+  rewrite bits_sign_ext by lia.
+  rewrite bits_shr by (destruct (zlt i (zwordsize - Z)); lia).
+  rewrite A. rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); lia).
   f_equal. destruct (zlt i (zwordsize - Z)).
-+ rewrite ! zlt_true by omega. omega.
-+ rewrite ! zlt_false by omega. rewrite zlt_true by omega. omega.
++ rewrite ! zlt_true by lia. lia.
++ rewrite ! zlt_false by lia. rewrite zlt_true by lia. lia.
 Qed.
 
 Corollary sign_ext_shr_shl:
@@ -2855,11 +2857,11 @@ Corollary sign_ext_shr_shl:
 Proof.
   intros.
   assert (A: unsigned y = zwordsize - n).
-  { unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. omega. }
+  { unfold y. apply unsigned_repr. generalize wordsize_max_unsigned. lia. }
   assert (B: ltu y iwordsize = true).
-  { unfold ltu; rewrite A, unsigned_repr_wordsize. apply zlt_true; omega. }
-  rewrite shr_shl by auto. unfold ltu; rewrite zlt_false by omega.
-  rewrite sub_idem, shr_zero. f_equal. rewrite A; omega.
+  { unfold ltu; rewrite A, unsigned_repr_wordsize. apply zlt_true; lia. }
+  rewrite shr_shl by auto. unfold ltu; rewrite zlt_false by lia.
+  rewrite sub_idem, shr_zero. f_equal. rewrite A; lia.
 Qed.
 
 (** [zero_ext n x] is the unique integer congruent to [x] modulo [2^n]
@@ -2868,14 +2870,14 @@ Qed.
 Lemma zero_ext_range:
   forall n x, 0 <= n < zwordsize -> 0 <= unsigned (zero_ext n x) < two_p n.
 Proof.
-  intros. rewrite zero_ext_mod; auto. apply Z_mod_lt. apply two_p_gt_ZERO. omega.
+  intros. rewrite zero_ext_mod; auto. apply Z_mod_lt. apply two_p_gt_ZERO. lia.
 Qed.
 
 Lemma eqmod_zero_ext:
   forall n x, 0 <= n < zwordsize -> eqmod (two_p n) (unsigned (zero_ext n x)) (unsigned x).
 Proof.
   intros. rewrite zero_ext_mod; auto. apply eqmod_sym. apply eqmod_mod.
-  apply two_p_gt_ZERO. omega.
+  apply two_p_gt_ZERO. lia.
 Qed.
 
 (** [sign_ext n x] is the unique integer congruent to [x] modulo [2^n]
@@ -2886,26 +2888,26 @@ Lemma sign_ext_range:
 Proof.
   intros. rewrite sign_ext_shr_shl; auto.
   set (X := shl x (repr (zwordsize - n))).
-  assert (two_p (n - 1) > 0) by (apply two_p_gt_ZERO; omega).
+  assert (two_p (n - 1) > 0) by (apply two_p_gt_ZERO; lia).
   assert (unsigned (repr (zwordsize - n)) = zwordsize - n).
     apply unsigned_repr.
-    split. omega. generalize wordsize_max_unsigned; omega.
+    split. lia. generalize wordsize_max_unsigned; lia.
   rewrite shr_div_two_p.
   rewrite signed_repr.
   rewrite H1.
   apply Zdiv_interval_1.
-  omega. omega. apply two_p_gt_ZERO; omega.
+  lia. lia. apply two_p_gt_ZERO; lia.
   replace (- two_p (n - 1) * two_p (zwordsize - n))
      with (- (two_p (n - 1) * two_p (zwordsize - n))) by ring.
   rewrite <- two_p_is_exp.
-  replace (n - 1 + (zwordsize - n)) with (zwordsize - 1) by omega.
+  replace (n - 1 + (zwordsize - n)) with (zwordsize - 1) by lia.
   rewrite <- half_modulus_power.
-  generalize (signed_range X). unfold min_signed, max_signed. omega.
-  omega. omega.
+  generalize (signed_range X). unfold min_signed, max_signed. lia.
+  lia. lia.
   apply Zdiv_interval_2. apply signed_range.
-  generalize min_signed_neg; omega.
-  generalize max_signed_pos; omega.
-  rewrite H1. apply two_p_gt_ZERO. omega.
+  generalize min_signed_neg; lia.
+  generalize max_signed_pos; lia.
+  rewrite H1. apply two_p_gt_ZERO. lia.
 Qed.
 
 Lemma eqmod_sign_ext':
@@ -2914,12 +2916,12 @@ Lemma eqmod_sign_ext':
 Proof.
   intros.
   set (N := Z.to_nat n).
-  assert (Z.of_nat N = n) by (apply Z2Nat.id; omega).
+  assert (Z.of_nat N = n) by (apply Z2Nat.id; lia).
   rewrite <- H0. rewrite <- two_power_nat_two_p.
   apply eqmod_same_bits; intros.
   rewrite H0 in H1. rewrite H0.
   fold (testbit (sign_ext n x) i). rewrite bits_sign_ext.
-  rewrite zlt_true. auto. omega. omega.
+  rewrite zlt_true. auto. lia. lia.
 Qed.
 
 Lemma eqmod_sign_ext:
@@ -2930,7 +2932,7 @@ Proof.
   apply eqmod_divides with modulus. apply eqm_signed_unsigned.
   exists (two_p (zwordsize - n)).
   unfold modulus. rewrite two_power_nat_two_p. fold zwordsize.
-  rewrite <- two_p_is_exp. f_equal. omega. omega. omega.
+  rewrite <- two_p_is_exp. f_equal. lia. lia. lia.
   apply eqmod_sign_ext'; auto.
 Qed.
 
@@ -2941,11 +2943,11 @@ Lemma shl_zero_ext:
   shl (zero_ext n x) m = zero_ext (n + unsigned m) (shl x m).
 Proof.
   intros. apply same_bits_eq; intros.
-  rewrite bits_zero_ext, ! bits_shl by omega.
+  rewrite bits_zero_ext, ! bits_shl by lia.
   destruct (zlt i (unsigned m)).
-- rewrite zlt_true by omega; auto.
-- rewrite bits_zero_ext by omega.
-  destruct (zlt (i - unsigned m) n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
+- rewrite zlt_true by lia; auto.
+- rewrite bits_zero_ext by lia.
+  destruct (zlt (i - unsigned m) n); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
 Qed.
 
 Lemma shl_sign_ext:
@@ -2954,12 +2956,12 @@ Lemma shl_sign_ext:
 Proof.
   intros. generalize (unsigned_range m); intros.
   apply same_bits_eq; intros.
-  rewrite bits_sign_ext, ! bits_shl by omega.
+  rewrite bits_sign_ext, ! bits_shl by lia.
   destruct (zlt i (n + unsigned m)).
 - rewrite bits_shl by auto. destruct (zlt i (unsigned m)); auto.
-  rewrite bits_sign_ext by omega. f_equal. apply zlt_true. omega.
-- rewrite zlt_false by omega. rewrite bits_shl by omega. rewrite zlt_false by omega.
-  rewrite bits_sign_ext by omega. f_equal. rewrite zlt_false by omega. omega.
+  rewrite bits_sign_ext by lia. f_equal. apply zlt_true. lia.
+- rewrite zlt_false by lia. rewrite bits_shl by lia. rewrite zlt_false by lia.
+  rewrite bits_sign_ext by lia. f_equal. rewrite zlt_false by lia. lia.
 Qed.
 
 Lemma shru_zero_ext:
@@ -2968,10 +2970,10 @@ Lemma shru_zero_ext:
 Proof.
   intros. bit_solve.
 - destruct (zlt (i + unsigned m) zwordsize).
-* destruct (zlt i n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
+* destruct (zlt i n); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
 * destruct (zlt i n); auto.
-- generalize (unsigned_range m); omega.
-- omega.
+- generalize (unsigned_range m); lia.
+- lia.
 Qed.
 
 Lemma shru_zero_ext_0:
@@ -2980,8 +2982,8 @@ Lemma shru_zero_ext_0:
 Proof.
   intros. bit_solve.
 - destruct (zlt (i + unsigned m) zwordsize); auto.
-  apply zlt_false. omega.
-- generalize (unsigned_range m); omega.
+  apply zlt_false. lia.
+- generalize (unsigned_range m); lia.
 Qed.
 
 Lemma shr_sign_ext:
@@ -2994,12 +2996,12 @@ Proof.
   rewrite bits_sign_ext, bits_shr.
 - f_equal.
   destruct (zlt i n), (zlt (i + unsigned m) zwordsize).
-+ apply zlt_true; omega.
-+ apply zlt_true; omega.
-+ rewrite zlt_false by omega. rewrite zlt_true by omega. omega.
-+ rewrite zlt_false by omega. rewrite zlt_true by omega. omega.
-- destruct (zlt i n); omega.
-- destruct (zlt (i + unsigned m) zwordsize); omega.
++ apply zlt_true; lia.
++ apply zlt_true; lia.
++ rewrite zlt_false by lia. rewrite zlt_true by lia. lia.
++ rewrite zlt_false by lia. rewrite zlt_true by lia. lia.
+- destruct (zlt i n); lia.
+- destruct (zlt (i + unsigned m) zwordsize); lia.
 Qed.
 
 Lemma zero_ext_shru_min:
@@ -3008,10 +3010,10 @@ Lemma zero_ext_shru_min:
 Proof.
   intros. apply ltu_iwordsize_inv in H.
   apply Z.min_case_strong; intros; auto.
-  bit_solve; try omega.
+  bit_solve; try lia.
   destruct (zlt i (zwordsize - unsigned n)).
-  rewrite zlt_true by omega. auto.
-  destruct (zlt i s); auto. rewrite zlt_false by omega; auto.
+  rewrite zlt_true by lia. auto.
+  destruct (zlt i s); auto. rewrite zlt_false by lia; auto.
 Qed.
 
 Lemma sign_ext_shr_min:
@@ -3023,12 +3025,12 @@ Proof.
   destruct (Z.min_spec (zwordsize - unsigned n) s) as [[A B] | [A B]]; rewrite B; auto.
   apply same_bits_eq; intros. rewrite ! bits_sign_ext by auto.
   destruct (zlt i (zwordsize - unsigned n)). 
-  rewrite zlt_true by omega. auto.
+  rewrite zlt_true by lia. auto.
   assert (C: testbit (shr x n) (zwordsize - unsigned n - 1) = testbit x (zwordsize - 1)).
-  { rewrite bits_shr by omega. rewrite zlt_true by omega. f_equal; omega. }
-  rewrite C. destruct (zlt i s); rewrite bits_shr by omega.
-  rewrite zlt_false by omega. auto.
-  rewrite zlt_false by omega. auto.
+  { rewrite bits_shr by lia. rewrite zlt_true by lia. f_equal; lia. }
+  rewrite C. destruct (zlt i s); rewrite bits_shr by lia.
+  rewrite zlt_false by lia. auto.
+  rewrite zlt_false by lia. auto.
 Qed.
 
 Lemma shl_zero_ext_min:
@@ -3039,10 +3041,10 @@ Proof.
   apply Z.min_case_strong; intros; auto.
   apply same_bits_eq; intros. rewrite ! bits_shl by auto.
   destruct (zlt i (unsigned n)); auto.
-  rewrite ! bits_zero_ext by omega.
+  rewrite ! bits_zero_ext by lia.
   destruct (zlt (i - unsigned n) s).
-  rewrite zlt_true by omega; auto.
-  rewrite zlt_false by omega; auto.
+  rewrite zlt_true by lia; auto.
+  rewrite zlt_false by lia; auto.
 Qed.
 
 Lemma shl_sign_ext_min:
@@ -3054,10 +3056,10 @@ Proof.
   destruct (Z.min_spec (zwordsize - unsigned n) s) as [[A B] | [A B]]; rewrite B; auto.
   apply same_bits_eq; intros. rewrite ! bits_shl by auto.
   destruct (zlt i (unsigned n)); auto.
-  rewrite ! bits_sign_ext by omega. f_equal.
+  rewrite ! bits_sign_ext by lia. f_equal.
   destruct (zlt (i - unsigned n) s).
-  rewrite zlt_true by omega; auto.
-  omegaContradiction.
+  rewrite zlt_true by lia; auto.
+  extlia.
 Qed.
 
 (** ** Properties of [one_bits] (decomposition in sum of powers of two) *)
@@ -3068,8 +3070,8 @@ Proof.
   assert (A: forall p, 0 <= p < zwordsize -> ltu (repr p) iwordsize = true).
     intros. unfold ltu, iwordsize. apply zlt_true.
     repeat rewrite unsigned_repr. tauto.
-    generalize wordsize_max_unsigned; omega.
-    generalize wordsize_max_unsigned; omega.
+    generalize wordsize_max_unsigned; lia.
+    generalize wordsize_max_unsigned; lia.
   unfold one_bits. intros.
   destruct (list_in_map_inv _ _ _ H) as [i0 [EQ IN]].
   subst i. apply A. apply Z_one_bits_range with (unsigned x); auto.
@@ -3099,7 +3101,7 @@ Proof.
   rewrite mul_one. apply eqm_unsigned_repr_r.
   rewrite unsigned_repr. auto with ints.
   generalize (H a (in_eq _ _)). change (Z.of_nat wordsize) with zwordsize.
-  generalize wordsize_max_unsigned. omega.
+  generalize wordsize_max_unsigned. lia.
   auto with ints.
   intros; apply H; auto with coqlib.
 Qed.
@@ -3143,7 +3145,7 @@ Proof.
   apply eqm_sub. apply eqm_trans with (unsigned (repr (unsigned x + unsigned d))).
   eauto with ints. apply eqm_trans with (unsigned (repr (unsigned y + unsigned d))).
   eauto with ints. eauto with ints. eauto with ints.
-  omega. omega.
+  lia. lia.
 Qed.
 
 Lemma translate_ltu:
@@ -3154,8 +3156,8 @@ Lemma translate_ltu:
 Proof.
   intros. unfold add. unfold ltu.
   repeat rewrite unsigned_repr; auto. case (zlt (unsigned x) (unsigned y)); intro.
-  apply zlt_true. omega.
-  apply zlt_false. omega.
+  apply zlt_true. lia.
+  apply zlt_false. lia.
 Qed.
 
 Theorem translate_cmpu:
@@ -3176,8 +3178,8 @@ Lemma translate_lt:
 Proof.
   intros. repeat rewrite add_signed. unfold lt.
   repeat rewrite signed_repr; auto. case (zlt (signed x) (signed y)); intro.
-  apply zlt_true. omega.
-  apply zlt_false. omega.
+  apply zlt_true. lia.
+  apply zlt_false. lia.
 Qed.
 
 Theorem translate_cmp:
@@ -3213,7 +3215,7 @@ Proof.
   intros.
   unfold ltu in H. destruct (zlt (unsigned x) (unsigned y)); try discriminate.
   rewrite signed_eq_unsigned.
-  generalize (unsigned_range x). omega. omega.
+  generalize (unsigned_range x). lia. lia.
 Qed.
 
 Theorem lt_sub_overflow:
@@ -3227,30 +3229,30 @@ Proof.
   unfold min_signed, max_signed in *.
   generalize half_modulus_pos half_modulus_modulus; intros HM MM.
   destruct (zle 0 (X - Y)).
-- unfold proj_sumbool at 1; rewrite zle_true at 1 by omega. simpl.
-  rewrite (zlt_false _ X) by omega.
+- unfold proj_sumbool at 1; rewrite zle_true at 1 by lia. simpl.
+  rewrite (zlt_false _ X) by lia.
   destruct (zlt (X - Y) half_modulus).
-  + unfold proj_sumbool; rewrite zle_true by omega.
-    rewrite signed_repr. rewrite zlt_false by omega. apply xor_idem.
-    unfold min_signed, max_signed; omega.
-  + unfold proj_sumbool; rewrite zle_false by omega.
+  + unfold proj_sumbool; rewrite zle_true by lia.
+    rewrite signed_repr. rewrite zlt_false by lia. apply xor_idem.
+    unfold min_signed, max_signed; lia.
+  + unfold proj_sumbool; rewrite zle_false by lia.
     replace (signed (repr (X - Y))) with (X - Y - modulus).
-    rewrite zlt_true by omega. apply xor_idem.
+    rewrite zlt_true by lia. apply xor_idem.
     rewrite signed_repr_eq. replace ((X - Y) mod modulus) with (X - Y).
     rewrite zlt_false; auto.
-    symmetry. apply Zmod_unique with 0; omega.
-- unfold proj_sumbool at 2. rewrite zle_true at 1 by omega. rewrite andb_true_r.
-  rewrite (zlt_true _ X) by omega.
+    symmetry. apply Zmod_unique with 0; lia.
+- unfold proj_sumbool at 2. rewrite zle_true at 1 by lia. rewrite andb_true_r.
+  rewrite (zlt_true _ X) by lia.
   destruct (zlt (X - Y) (-half_modulus)).
-  + unfold proj_sumbool; rewrite zle_false by omega.
+  + unfold proj_sumbool; rewrite zle_false by lia.
     replace (signed (repr (X - Y))) with (X - Y + modulus).
-    rewrite zlt_false by omega. apply xor_zero.
+    rewrite zlt_false by lia. apply xor_zero.
     rewrite signed_repr_eq. replace ((X - Y) mod modulus) with (X - Y + modulus).
-    rewrite zlt_true by omega; auto.
-    symmetry. apply Zmod_unique with (-1); omega.
-  + unfold proj_sumbool; rewrite zle_true by omega.
-    rewrite signed_repr. rewrite zlt_true by omega. apply xor_zero_l.
-    unfold min_signed, max_signed; omega.
+    rewrite zlt_true by lia; auto.
+    symmetry. apply Zmod_unique with (-1); lia.
+  + unfold proj_sumbool; rewrite zle_true by lia.
+    rewrite signed_repr. rewrite zlt_true by lia. apply xor_zero_l.
+    unfold min_signed, max_signed; lia.
 Qed.
 
 Lemma signed_eq:
@@ -3270,10 +3272,10 @@ Lemma not_lt:
 Proof.
   intros. unfold lt. rewrite signed_eq. unfold proj_sumbool.
   destruct (zlt (signed y) (signed x)).
-  rewrite zlt_false. rewrite zeq_false. auto. omega. omega.
+  rewrite zlt_false. rewrite zeq_false. auto. lia. lia.
   destruct (zeq (signed x) (signed y)).
-  rewrite zlt_false. auto. omega.
-  rewrite zlt_true. auto. omega.
+  rewrite zlt_false. auto. lia.
+  rewrite zlt_true. auto. lia.
 Qed.
 
 Lemma lt_not:
@@ -3287,10 +3289,10 @@ Lemma not_ltu:
 Proof.
   intros. unfold ltu, eq.
   destruct (zlt (unsigned y) (unsigned x)).
-  rewrite zlt_false. rewrite zeq_false. auto. omega. omega.
+  rewrite zlt_false. rewrite zeq_false. auto. lia. lia.
   destruct (zeq (unsigned x) (unsigned y)).
-  rewrite zlt_false. auto. omega.
-  rewrite zlt_true. auto. omega.
+  rewrite zlt_false. auto. lia.
+  rewrite zlt_true. auto. lia.
 Qed.
 
 Lemma ltu_not:
@@ -3322,7 +3324,7 @@ Proof.
   clear H3.
   generalize (unsigned_range ofs1) (unsigned_range ofs2). intros P Q.
   generalize (unsigned_add_either base ofs1) (unsigned_add_either base ofs2).
-  intros [C|C] [D|D]; omega.
+  intros [C|C] [D|D]; lia.
 Qed.
 
 (** ** Size of integers, in bits. *)
@@ -3339,14 +3341,14 @@ Theorem bits_size_1:
 Proof.
   intros. destruct (zeq (unsigned x) 0).
   left. rewrite <- (repr_unsigned x). rewrite e; auto.
-  right. apply Ztestbit_size_1. generalize (unsigned_range x); omega.
+  right. apply Ztestbit_size_1. generalize (unsigned_range x); lia.
 Qed.
 
 Theorem bits_size_2:
   forall x i, size x <= i -> testbit x i = false.
 Proof.
-  intros. apply Ztestbit_size_2. generalize (unsigned_range x); omega.
-  fold (size x); omega.
+  intros. apply Ztestbit_size_2. generalize (unsigned_range x); lia.
+  fold (size x); lia.
 Qed.
 
 Theorem size_range:
@@ -3354,9 +3356,9 @@ Theorem size_range:
 Proof.
   intros; split. apply Zsize_pos.
   destruct (bits_size_1 x).
-  subst x; unfold size; rewrite unsigned_zero; simpl. generalize wordsize_pos; omega.
+  subst x; unfold size; rewrite unsigned_zero; simpl. generalize wordsize_pos; lia.
   destruct (zle (size x) zwordsize); auto.
-  rewrite bits_above in H. congruence. omega.
+  rewrite bits_above in H. congruence. lia.
 Qed.
 
 Theorem bits_size_3:
@@ -3369,7 +3371,7 @@ Proof.
   destruct (bits_size_1 x).
   subst x. unfold size; rewrite unsigned_zero; assumption.
   rewrite (H0 (Z.pred (size x))) in H1. congruence.
-  generalize (size_range x); omega.
+  generalize (size_range x); lia.
 Qed.
 
 Theorem bits_size_4:
@@ -3383,14 +3385,14 @@ Proof.
   assert (size x <= n).
     apply bits_size_3; auto.
   destruct (zlt (size x) n).
-  rewrite bits_size_2 in H0. congruence. omega.
-  omega.
+  rewrite bits_size_2 in H0. congruence. lia.
+  lia.
 Qed.
 
 Theorem size_interval_1:
   forall x, 0 <= unsigned x < two_p (size x).
 Proof.
-  intros; apply Zsize_interval_1. generalize (unsigned_range x); omega.
+  intros; apply Zsize_interval_1. generalize (unsigned_range x); lia.
 Qed.
 
 Theorem size_interval_2:
@@ -3404,9 +3406,9 @@ Theorem size_and:
 Proof.
   intros.
   assert (0 <= Z.min (size a) (size b)).
-    generalize (size_range a) (size_range b). zify; omega.
+    generalize (size_range a) (size_range b). zify; lia.
   apply bits_size_3. auto. intros.
-  rewrite bits_and by omega.
+  rewrite bits_and by lia.
   rewrite andb_false_iff.
   generalize (bits_size_2 a i).
   generalize (bits_size_2 b i).
@@ -3419,9 +3421,9 @@ Proof.
   intros.
   generalize (size_interval_1 (and a b)); intros.
   assert (two_p (size (and a b)) <= two_p (Z.min (size a) (size b))).
-  apply two_p_monotone. split. generalize (size_range (and a b)); omega.
+  apply two_p_monotone. split. generalize (size_range (and a b)); lia.
   apply size_and.
-  omega.
+  lia.
 Qed.
 
 Theorem size_or:
@@ -3429,17 +3431,17 @@ Theorem size_or:
 Proof.
   intros. generalize (size_range a) (size_range b); intros.
   destruct (bits_size_1 a).
-  subst a. rewrite size_zero. rewrite or_zero_l. zify; omega.
+  subst a. rewrite size_zero. rewrite or_zero_l. zify; lia.
   destruct (bits_size_1 b).
-  subst b. rewrite size_zero. rewrite or_zero. zify; omega.
+  subst b. rewrite size_zero. rewrite or_zero. zify; lia.
   zify. destruct H3 as [[P Q] | [P Q]]; subst.
   apply bits_size_4. tauto. rewrite bits_or. rewrite H2. apply orb_true_r.
-  omega.
-  intros. rewrite bits_or. rewrite !bits_size_2. auto. omega. omega. omega.
+  lia.
+  intros. rewrite bits_or. rewrite !bits_size_2. auto. lia. lia. lia.
   apply bits_size_4. tauto. rewrite bits_or. rewrite H1. apply orb_true_l.
   destruct (zeq (size a) 0). unfold testbit in H1. rewrite Z.testbit_neg_r in H1.
-  congruence. omega. omega.
-  intros. rewrite bits_or. rewrite !bits_size_2. auto. omega. omega. omega.
+  congruence. lia. lia.
+  intros. rewrite bits_or. rewrite !bits_size_2. auto. lia. lia. lia.
 Qed.
 
 Corollary or_interval:
@@ -3453,12 +3455,12 @@ Theorem size_xor:
 Proof.
   intros.
   assert (0 <= Z.max (size a) (size b)).
-    generalize (size_range a) (size_range b). zify; omega.
+    generalize (size_range a) (size_range b). zify; lia.
   apply bits_size_3. auto. intros.
   rewrite bits_xor. rewrite !bits_size_2. auto.
-  zify; omega.
-  zify; omega.
-  omega.
+  zify; lia.
+  zify; lia.
+  lia.
 Qed.
 
 Corollary xor_interval:
@@ -3467,9 +3469,9 @@ Proof.
   intros.
   generalize (size_interval_1 (xor a b)); intros.
   assert (two_p (size (xor a b)) <= two_p (Z.max (size a) (size b))).
-  apply two_p_monotone. split. generalize (size_range (xor a b)); omega.
+  apply two_p_monotone. split. generalize (size_range (xor a b)); lia.
   apply size_xor.
-  omega.
+  lia.
 Qed.
 
 End Make.
@@ -3549,7 +3551,7 @@ Proof.
   intros. unfold shl'. rewrite testbit_repr; auto.
   destruct (zlt i (Int.unsigned y)).
   apply Z.shiftl_spec_low. auto.
-  apply Z.shiftl_spec_high. omega. omega.
+  apply Z.shiftl_spec_high. lia. lia.
 Qed.
 
 Lemma bits_shru':
@@ -3563,7 +3565,7 @@ Proof.
   destruct (zlt (i + Int.unsigned y) zwordsize).
   auto.
   apply bits_above; auto.
-  omega.
+  lia.
 Qed.
 
 Lemma bits_shr':
@@ -3574,8 +3576,8 @@ Lemma bits_shr':
 Proof.
   intros. unfold shr'. rewrite testbit_repr; auto.
   rewrite Z.shiftr_spec. apply bits_signed.
-  generalize (Int.unsigned_range y); omega.
-  omega.
+  generalize (Int.unsigned_range y); lia.
+  lia.
 Qed.
 
 Lemma shl'_mul_two_p:
@@ -3584,7 +3586,7 @@ Lemma shl'_mul_two_p:
 Proof.
   intros. unfold shl', mul. apply eqm_samerepr.
   rewrite Zshiftl_mul_two_p. apply eqm_mult. apply eqm_refl. apply eqm_unsigned_repr.
-  generalize (Int.unsigned_range y); omega.
+  generalize (Int.unsigned_range y); lia.
 Qed.
 
 Lemma shl'_one_two_p:
@@ -3635,7 +3637,7 @@ Proof.
   intros. apply Int.ltu_inv in H. change (Int.unsigned (Int.repr 63)) with 63 in H.
   set (y1 := Int64.repr (Int.unsigned y)).
   assert (U: unsigned y1 = Int.unsigned y).
-  { apply unsigned_repr. assert (63 < max_unsigned) by reflexivity. omega. }
+  { apply unsigned_repr. assert (63 < max_unsigned) by reflexivity. lia. }
   transitivity (shrx x y1).
 - unfold shrx', shrx, shl', shl. rewrite U; auto.
 - rewrite shrx_carry. 
@@ -3656,20 +3658,20 @@ Proof.
   assert (N1: 63 < max_unsigned) by reflexivity.
   assert (N2: 63 < Int.max_unsigned) by reflexivity.
   assert (A: unsigned z = Int.unsigned y).
-  { unfold z; apply unsigned_repr; omega. }
+  { unfold z; apply unsigned_repr; lia. }
   assert (B: unsigned (sub (repr 64) z) = Int.unsigned (Int.sub (Int.repr 64) y)).
   { unfold z. unfold sub, Int.sub.
     change (unsigned (repr 64)) with 64.
     change (Int.unsigned (Int.repr 64)) with 64.
-    rewrite (unsigned_repr (Int.unsigned y)) by omega.
-    rewrite unsigned_repr, Int.unsigned_repr by omega.
+    rewrite (unsigned_repr (Int.unsigned y)) by lia.
+    rewrite unsigned_repr, Int.unsigned_repr by lia.
     auto. }
   unfold shrx', shr', shru', shl'.
   rewrite <- A.
   change (Int.unsigned (Int.repr 63)) with (unsigned (repr 63)).
   rewrite <- B.
   apply shrx_shr_2.
-  unfold ltu. apply zlt_true. change (unsigned z < 63). rewrite A; omega.
+  unfold ltu. apply zlt_true. change (unsigned z < 63). rewrite A; lia.
 Qed.
 
 Lemma shr'63:
@@ -3677,27 +3679,27 @@ Lemma shr'63:
 Proof.
   intro.
   unfold shr', mone, zero.
-  rewrite Int.unsigned_repr by (change Int.max_unsigned with 4294967295; omega).
+  rewrite Int.unsigned_repr by (change Int.max_unsigned with 4294967295; lia).
   apply same_bits_eq.
   intros i BIT.
   rewrite testbit_repr by assumption.
-  rewrite Z.shiftr_spec by omega.
-  rewrite bits_signed by omega.
+  rewrite Z.shiftr_spec by lia.
+  rewrite bits_signed by lia.
   simpl.
   change zwordsize with 64 in *.
   destruct (zlt _ _) as [LT | GE].
   {
-    replace i with 0 in * by omega.
+    replace i with 0 in * by lia.
     change (0 + 63) with (zwordsize - 1).
     rewrite  sign_bit_of_signed.
     destruct (lt x _).
-    all: rewrite testbit_repr by (change zwordsize with 64 in *; omega).
+    all: rewrite testbit_repr by (change zwordsize with 64 in *; lia).
     all: simpl; reflexivity.
   }
   change (64 - 1) with (zwordsize - 1).
   rewrite  sign_bit_of_signed.
   destruct (lt x _).
-  all: rewrite testbit_repr by (change zwordsize with 64 in *; omega).
+  all: rewrite testbit_repr by (change zwordsize with 64 in *; lia).
   { symmetry.
     apply Ztestbit_m1.
     tauto.
@@ -3711,11 +3713,11 @@ Lemma shru'63:
 Proof.
   intro.
   unfold shru'.
-  rewrite Int.unsigned_repr by (change Int.max_unsigned with 4294967295; omega).
+  rewrite Int.unsigned_repr by (change Int.max_unsigned with 4294967295; lia).
   apply same_bits_eq.
   intros i BIT.
   rewrite testbit_repr by assumption.
-  rewrite Z.shiftr_spec by omega.
+  rewrite Z.shiftr_spec by lia.
   unfold lt.
   rewrite signed_zero.
   unfold one, zero.
@@ -3728,15 +3730,15 @@ Proof.
       rewrite sign_bit_of_signed.
       unfold lt.
       rewrite signed_zero.
-      destruct (zlt _ _); try omega.
+      destruct (zlt _ _); try lia.
       reflexivity.
     }
     change (Z.testbit (unsigned x) (i + 63)) with (testbit x (i+63)).
-    rewrite bits_above by (change zwordsize with 64; omega).
+    rewrite bits_above by (change zwordsize with 64; lia).
     rewrite Ztestbit_1.
     destruct (zeq i 0); trivial.
     subst i.
-    omega.
+    lia.
   }
   destruct (zeq i 0) as [IZERO | INONZERO].
   { subst i.
@@ -3745,14 +3747,13 @@ Proof.
     unfold lt.
     rewrite signed_zero.
     rewrite bits_zero.
-    destruct (zlt _ _); try omega.
-    reflexivity.
+    destruct (zlt _ _); try lia; reflexivity.
   }
   change (Z.testbit (unsigned x) (i + 63)) with (testbit x (i + 63)).
   rewrite bits_zero.
   apply bits_above.
   change zwordsize with 64.
-  omega.
+  lia.
 Qed.
   
 Theorem shrx'1_shr':
@@ -3788,11 +3789,11 @@ Proof.
   change (Int.unsigned iwordsize') with 64 in *.
   assert (128 < max_unsigned) by reflexivity.
   assert (128 < Int.max_unsigned) by reflexivity.
-  assert (Y: unsigned y' = Int.unsigned y) by (apply unsigned_repr; omega).
-  assert (Z: unsigned z' = Int.unsigned z) by (apply unsigned_repr; omega).
+  assert (Y: unsigned y' = Int.unsigned y) by (apply unsigned_repr; lia).
+  assert (Z: unsigned z' = Int.unsigned z) by (apply unsigned_repr; lia).
   assert (P: Int.unsigned (Int.add y z) = unsigned (add y' z')).
-  { unfold Int.add. rewrite Int.unsigned_repr by omega.
-    unfold add. rewrite unsigned_repr by omega. congruence. }
+  { unfold Int.add. rewrite Int.unsigned_repr by lia.
+    unfold add. rewrite unsigned_repr by lia. congruence. }
   intuition auto.
   apply zlt_true. rewrite Y; auto.
   apply zlt_true. rewrite Z; auto.
@@ -3806,7 +3807,7 @@ Theorem or_ror':
   Int.add y z = iwordsize' ->
   ror x (repr (Int.unsigned z)) = or (shl' x y) (shru' x z).
 Proof.
-  intros. destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. rewrite H1; omega.
+  intros. destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. rewrite H1; lia.
   replace (shl' x y) with (shl x (repr (Int.unsigned y))).
   replace (shru' x z) with (shru x (repr (Int.unsigned z))).
   apply or_ror; auto. rewrite F, H1. reflexivity.
@@ -3822,7 +3823,7 @@ Theorem shl'_shl':
   shl' (shl' x y) z = shl' x (Int.add y z).
 Proof.
   intros. apply Int.ltu_inv in H1.
-  destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. omega.
+  destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. lia.
   set (y' := repr (Int.unsigned y)) in *.
   set (z' := repr (Int.unsigned z)) in *.
   replace (shl' x y) with (shl x y').
@@ -3843,7 +3844,7 @@ Theorem shru'_shru':
   shru' (shru' x y) z = shru' x (Int.add y z).
 Proof.
   intros. apply Int.ltu_inv in H1.
-  destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. omega.
+  destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. lia.
   set (y' := repr (Int.unsigned y)) in *.
   set (z' := repr (Int.unsigned z)) in *.
   replace (shru' x y) with (shru x y').
@@ -3864,7 +3865,7 @@ Theorem shr'_shr':
   shr' (shr' x y) z = shr' x (Int.add y z).
 Proof.
   intros. apply Int.ltu_inv in H1.
-  destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. omega.
+  destruct (int_ltu_2_inv y z) as (A & B & C & D & E & F); auto. lia.
   set (y' := repr (Int.unsigned y)) in *.
   set (z' := repr (Int.unsigned z)) in *.
   replace (shr' x y) with (shr x y').
@@ -3889,21 +3890,21 @@ Proof.
   apply same_bits_eq; intros. rewrite bits_shru' by auto. fold Z.
   destruct (zlt Z Y).
 - assert (A: Int.unsigned (Int.sub y z) = Y - Z).
-  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. }
-  symmetry; rewrite bits_shl', A by omega.
+  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. lia. }
+  symmetry; rewrite bits_shl', A by lia.
   destruct (zlt (i + Z) zwordsize).
-+ rewrite bits_shl' by omega. fold Y.
-  destruct (zlt i (Y - Z)); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
-  rewrite bits_zero_ext by omega. rewrite zlt_true by omega. f_equal; omega.
-+ rewrite bits_zero_ext by omega. rewrite ! zlt_false by omega. auto.
++ rewrite bits_shl' by lia. fold Y.
+  destruct (zlt i (Y - Z)); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
+  rewrite bits_zero_ext by lia. rewrite zlt_true by lia. f_equal; lia.
++ rewrite bits_zero_ext by lia. rewrite ! zlt_false by lia. auto.
 - assert (A: Int.unsigned (Int.sub z y) = Z - Y).
-  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. }
-  rewrite bits_zero_ext, bits_shru', A by omega.
-  destruct (zlt (i + Z) zwordsize); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
-  rewrite bits_shl' by omega. fold Y.
+  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. lia. }
+  rewrite bits_zero_ext, bits_shru', A by lia.
+  destruct (zlt (i + Z) zwordsize); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
+  rewrite bits_shl' by lia. fold Y.
   destruct (zlt (i + Z) Y).
-+ rewrite zlt_false by omega. auto.
-+ rewrite zlt_true by omega. f_equal; omega.
++ rewrite zlt_false by lia. auto.
++ rewrite zlt_true by lia. f_equal; lia.
 Qed.
 
 Theorem shr'_shl':
@@ -3916,26 +3917,26 @@ Proof.
   change (Int.unsigned iwordsize') with zwordsize in *.
   unfold Int.ltu. set (Y := Int.unsigned y) in *; set (Z := Int.unsigned z) in *.
   apply same_bits_eq; intros. rewrite bits_shr' by auto. fold Z.
-  rewrite bits_shl' by (destruct (zlt (i + Z) zwordsize); omega). fold Y.
+  rewrite bits_shl' by (destruct (zlt (i + Z) zwordsize); lia). fold Y.
   destruct (zlt Z Y).
 - assert (A: Int.unsigned (Int.sub y z) = Y - Z).
-  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. }
-  rewrite bits_shl', A by omega.
+  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. lia. }
+  rewrite bits_shl', A by lia.
   destruct (zlt i (Y - Z)).
-+ apply zlt_true. destruct (zlt (i + Z) zwordsize); omega.
-+ rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega).
-  rewrite bits_sign_ext by omega. f_equal. 
++ apply zlt_true. destruct (zlt (i + Z) zwordsize); lia.
++ rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); lia).
+  rewrite bits_sign_ext by lia. f_equal. 
   destruct (zlt (i + Z) zwordsize).
-  rewrite zlt_true by omega. omega.
-  rewrite zlt_false by omega. omega.
+  rewrite zlt_true by lia. lia.
+  rewrite zlt_false by lia. lia.
 - assert (A: Int.unsigned (Int.sub z y) = Z - Y).
-  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. omega. }
-  rewrite bits_sign_ext by omega.
-  rewrite bits_shr' by (destruct (zlt i (zwordsize - Z)); omega).
-  rewrite A. rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); omega).
+  { apply Int.unsigned_repr. assert (zwordsize < Int.max_unsigned) by reflexivity. lia. }
+  rewrite bits_sign_ext by lia.
+  rewrite bits_shr' by (destruct (zlt i (zwordsize - Z)); lia).
+  rewrite A. rewrite zlt_false by (destruct (zlt (i + Z) zwordsize); lia).
   f_equal. destruct (zlt i (zwordsize - Z)).
-+ rewrite ! zlt_true by omega. omega.
-+ rewrite ! zlt_false by omega. rewrite zlt_true by omega. omega.
++ rewrite ! zlt_true by lia. lia.
++ rewrite ! zlt_false by lia. rewrite zlt_true by lia. lia.
 Qed.
 
 Lemma shl'_zero_ext:
@@ -3943,11 +3944,11 @@ Lemma shl'_zero_ext:
   shl' (zero_ext n x) m = zero_ext (n + Int.unsigned m) (shl' x m).
 Proof.
   intros. apply same_bits_eq; intros.
-  rewrite bits_zero_ext, ! bits_shl' by omega.
+  rewrite bits_zero_ext, ! bits_shl' by lia.
   destruct (zlt i (Int.unsigned m)).
-- rewrite zlt_true by omega; auto.
-- rewrite bits_zero_ext by omega.
-  destruct (zlt (i - Int.unsigned m) n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
+- rewrite zlt_true by lia; auto.
+- rewrite bits_zero_ext by lia.
+  destruct (zlt (i - Int.unsigned m) n); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
 Qed.
 
 Lemma shl'_sign_ext:
@@ -3956,12 +3957,12 @@ Lemma shl'_sign_ext:
 Proof.
   intros. generalize (Int.unsigned_range m); intros.
   apply same_bits_eq; intros.
-  rewrite bits_sign_ext, ! bits_shl' by omega.
+  rewrite bits_sign_ext, ! bits_shl' by lia.
   destruct (zlt i (n + Int.unsigned m)).
 - rewrite bits_shl' by auto. destruct (zlt i (Int.unsigned m)); auto.
-  rewrite bits_sign_ext by omega. f_equal. apply zlt_true. omega.
-- rewrite zlt_false by omega. rewrite bits_shl' by omega. rewrite zlt_false by omega.
-  rewrite bits_sign_ext by omega. f_equal. rewrite zlt_false by omega. omega.
+  rewrite bits_sign_ext by lia. f_equal. apply zlt_true. lia.
+- rewrite zlt_false by lia. rewrite bits_shl' by lia. rewrite zlt_false by lia.
+  rewrite bits_sign_ext by lia. f_equal. rewrite zlt_false by lia. lia.
 Qed.
 
 Lemma shru'_zero_ext:
@@ -3969,9 +3970,9 @@ Lemma shru'_zero_ext:
   shru' (zero_ext (n + Int.unsigned m) x) m = zero_ext n (shru' x m).
 Proof.
   intros. generalize (Int.unsigned_range m); intros.
-  bit_solve; [|omega]. rewrite bits_shru', bits_zero_ext, bits_shru' by omega.
+  bit_solve; [|lia]. rewrite bits_shru', bits_zero_ext, bits_shru' by lia.
   destruct (zlt (i + Int.unsigned m) zwordsize).
-* destruct (zlt i n); [rewrite zlt_true by omega|rewrite zlt_false by omega]; auto.
+* destruct (zlt i n); [rewrite zlt_true by lia|rewrite zlt_false by lia]; auto.
 * destruct (zlt i n); auto.
 Qed.
 
@@ -3980,9 +3981,9 @@ Lemma shru'_zero_ext_0:
   shru' (zero_ext n x) m = zero.
 Proof.
   intros. generalize (Int.unsigned_range m); intros.
-  bit_solve. rewrite bits_shru', bits_zero_ext by omega.
+  bit_solve. rewrite bits_shru', bits_zero_ext by lia.
   destruct (zlt (i + Int.unsigned m) zwordsize); auto.
-  apply zlt_false. omega.
+  apply zlt_false. lia.
 Qed.
 
 Lemma shr'_sign_ext:
@@ -3995,12 +3996,12 @@ Proof.
   rewrite bits_sign_ext, bits_shr'.
 - f_equal.
   destruct (zlt i n), (zlt (i + Int.unsigned m) zwordsize).
-+ apply zlt_true; omega.
-+ apply zlt_true; omega.
-+ rewrite zlt_false by omega. rewrite zlt_true by omega. omega.
-+ rewrite zlt_false by omega. rewrite zlt_true by omega. omega.
-- destruct (zlt i n); omega.
-- destruct (zlt (i + Int.unsigned m) zwordsize); omega.
++ apply zlt_true; lia.
++ apply zlt_true; lia.
++ rewrite zlt_false by lia. rewrite zlt_true by lia. lia.
++ rewrite zlt_false by lia. rewrite zlt_true by lia. lia.
+- destruct (zlt i n); lia.
+- destruct (zlt (i + Int.unsigned m) zwordsize); lia.
 Qed.
 
 Lemma zero_ext_shru'_min:
@@ -4009,10 +4010,10 @@ Lemma zero_ext_shru'_min:
 Proof.
   intros. apply Int.ltu_inv in H. change (Int.unsigned iwordsize') with zwordsize in H.
   apply Z.min_case_strong; intros; auto.
-  bit_solve; try omega. rewrite ! bits_shru' by omega. 
+  bit_solve; try lia. rewrite ! bits_shru' by lia. 
   destruct (zlt i (zwordsize - Int.unsigned n)).
-  rewrite zlt_true by omega. auto.
-  destruct (zlt i s); auto. rewrite zlt_false by omega; auto.
+  rewrite zlt_true by lia. auto.
+  destruct (zlt i s); auto. rewrite zlt_false by lia; auto.
 Qed.
 
 Lemma sign_ext_shr'_min:
@@ -4024,12 +4025,12 @@ Proof.
   destruct (Z.min_spec (zwordsize - Int.unsigned n) s) as [[A B] | [A B]]; rewrite B; auto.
   apply same_bits_eq; intros. rewrite ! bits_sign_ext by auto.
   destruct (zlt i (zwordsize - Int.unsigned n)). 
-  rewrite zlt_true by omega. auto.
+  rewrite zlt_true by lia. auto.
   assert (C: testbit (shr' x n) (zwordsize - Int.unsigned n - 1) = testbit x (zwordsize - 1)).
-  { rewrite bits_shr' by omega. rewrite zlt_true by omega. f_equal; omega. }
-  rewrite C. destruct (zlt i s); rewrite bits_shr' by omega.
-  rewrite zlt_false by omega. auto.
-  rewrite zlt_false by omega. auto.
+  { rewrite bits_shr' by lia. rewrite zlt_true by lia. f_equal; lia. }
+  rewrite C. destruct (zlt i s); rewrite bits_shr' by lia.
+  rewrite zlt_false by lia. auto.
+  rewrite zlt_false by lia. auto.
 Qed.
 
 Lemma shl'_zero_ext_min:
@@ -4040,10 +4041,10 @@ Proof.
   apply Z.min_case_strong; intros; auto.
   apply same_bits_eq; intros. rewrite ! bits_shl' by auto.
   destruct (zlt i (Int.unsigned n)); auto.
-  rewrite ! bits_zero_ext by omega.
+  rewrite ! bits_zero_ext by lia.
   destruct (zlt (i - Int.unsigned n) s).
-  rewrite zlt_true by omega; auto.
-  rewrite zlt_false by omega; auto.
+  rewrite zlt_true by lia; auto.
+  rewrite zlt_false by lia; auto.
 Qed.
 
 Lemma shl'_sign_ext_min:
@@ -4055,10 +4056,10 @@ Proof.
   destruct (Z.min_spec (zwordsize - Int.unsigned n) s) as [[A B] | [A B]]; rewrite B; auto.
   apply same_bits_eq; intros. rewrite ! bits_shl' by auto.
   destruct (zlt i (Int.unsigned n)); auto.
-  rewrite ! bits_sign_ext by omega. f_equal.
+  rewrite ! bits_sign_ext by lia. f_equal.
   destruct (zlt (i - Int.unsigned n) s).
-  rewrite zlt_true by omega; auto.
-  omegaContradiction.
+  rewrite zlt_true by lia; auto.
+  extlia.
 Qed.
 
 (** Powers of two with exponents given as 32-bit ints *)
@@ -4079,8 +4080,8 @@ Proof.
   destruct (list_in_map_inv _ _ _ H) as [i0 [EQ IN]].
   exploit Z_one_bits_range; eauto. fold zwordsize. intros R.
   unfold Int.ltu. rewrite EQ. rewrite Int.unsigned_repr.
-  change (Int.unsigned iwordsize') with zwordsize. apply zlt_true. omega.
-  assert (zwordsize < Int.max_unsigned) by reflexivity. omega.
+  change (Int.unsigned iwordsize') with zwordsize. apply zlt_true. lia.
+  assert (zwordsize < Int.max_unsigned) by reflexivity. lia.
 Qed.
 
 Fixpoint int_of_one_bits' (l: list Int.int) : int :=
@@ -4099,7 +4100,7 @@ Proof.
   - auto.
   - rewrite IHl by eauto. apply eqm_samerepr; apply eqm_add.
   + rewrite shl'_one_two_p. rewrite Int.unsigned_repr. apply eqm_sym; apply eqm_unsigned_repr.
-    exploit (H a). auto. assert (zwordsize < Int.max_unsigned) by reflexivity. omega.
+    exploit (H a). auto. assert (zwordsize < Int.max_unsigned) by reflexivity. lia.
   + apply eqm_sym; apply eqm_unsigned_repr.
   }
   intros. rewrite <- (repr_unsigned x) at 1. unfold one_bits'. rewrite REC.
@@ -4118,7 +4119,7 @@ Proof.
   { apply Z_one_bits_range with (unsigned n). rewrite B; auto with coqlib. }
   rewrite Int.unsigned_repr. auto.
   assert (zwordsize < Int.max_unsigned) by reflexivity.
-  omega.
+  lia.
 Qed.
 
 Theorem is_power2'_range:
@@ -4137,11 +4138,11 @@ Proof.
   unfold is_power2'; intros.
   destruct (Z_one_bits wordsize (unsigned n) 0) as [ | i [ | ? ?]] eqn:B; inv H.
   rewrite (Z_one_bits_powerserie wordsize (unsigned n)) by (apply unsigned_range).
-  rewrite Int.unsigned_repr. rewrite B; simpl. omega.
+  rewrite Int.unsigned_repr. rewrite B; simpl. lia.
   assert (0 <= i < zwordsize).
   { apply Z_one_bits_range with (unsigned n). rewrite B; auto with coqlib. }
   assert (zwordsize < Int.max_unsigned) by reflexivity.
-  omega.
+  lia.
 Qed.
 
 Theorem mul_pow2':
@@ -4185,7 +4186,7 @@ Proof.
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
   fold (testbit (shru n (repr Int.zwordsize)) i). rewrite bits_shru.
   change (unsigned (repr Int.zwordsize)) with Int.zwordsize.
-  apply zlt_true. omega. omega.
+  apply zlt_true. lia. lia.
 Qed.
 
 Lemma bits_ofwords:
@@ -4200,15 +4201,15 @@ Proof.
   rewrite testbit_repr; auto.
   rewrite !testbit_repr; auto.
   fold (Int.testbit lo i). rewrite Int.bits_above. apply orb_false_r. auto.
-  omega.
+  lia.
 Qed.
 
 Lemma lo_ofwords:
   forall hi lo, loword (ofwords hi lo) = lo.
 Proof.
   intros. apply Int.same_bits_eq; intros.
-  rewrite bits_loword; auto. rewrite bits_ofwords. apply zlt_true. omega.
-  assert (zwordsize = 2 * Int.zwordsize) by reflexivity. omega.
+  rewrite bits_loword; auto. rewrite bits_ofwords. apply zlt_true. lia.
+  assert (zwordsize = 2 * Int.zwordsize) by reflexivity. lia.
 Qed.
 
 Lemma hi_ofwords:
@@ -4216,8 +4217,8 @@ Lemma hi_ofwords:
 Proof.
   intros. apply Int.same_bits_eq; intros.
   rewrite bits_hiword; auto. rewrite bits_ofwords.
-  rewrite zlt_false. f_equal. omega. omega.
-  assert (zwordsize = 2 * Int.zwordsize) by reflexivity. omega.
+  rewrite zlt_false. f_equal. lia. lia.
+  assert (zwordsize = 2 * Int.zwordsize) by reflexivity. lia.
 Qed.
 
 Lemma ofwords_recompose:
@@ -4225,9 +4226,9 @@ Lemma ofwords_recompose:
 Proof.
   intros. apply same_bits_eq; intros. rewrite bits_ofwords; auto.
   destruct (zlt i Int.zwordsize).
-  apply bits_loword. omega.
-  rewrite bits_hiword. f_equal. omega.
-  assert (zwordsize = 2 * Int.zwordsize) by reflexivity. omega.
+  apply bits_loword. lia.
+  rewrite bits_hiword. f_equal. lia.
+  assert (zwordsize = 2 * Int.zwordsize) by reflexivity. lia.
 Qed.
 
 Lemma ofwords_add:
@@ -4238,10 +4239,10 @@ Proof.
   apply eqm_sym; apply eqm_unsigned_repr.
   apply eqm_refl.
   apply eqm_sym; apply eqm_unsigned_repr.
-  change Int.zwordsize with 32; change zwordsize with 64; omega.
+  change Int.zwordsize with 32; change zwordsize with 64; lia.
   rewrite unsigned_repr. generalize (Int.unsigned_range lo). intros [A B]. exact B.
   assert (Int.max_unsigned < max_unsigned) by (compute; auto).
-  generalize (Int.unsigned_range_2 lo); omega.
+  generalize (Int.unsigned_range_2 lo); lia.
 Qed.
 
 Lemma ofwords_add':
@@ -4252,7 +4253,7 @@ Proof.
   change (two_p 32) with Int.modulus.
   change Int.modulus with 4294967296.
   change max_unsigned with 18446744073709551615.
-  omega.
+  lia.
 Qed.
 
 Remark eqm_mul_2p32:
@@ -4276,7 +4277,7 @@ Proof.
   change min_signed with (Int.min_signed * Int.modulus).
   change max_signed with (Int.max_signed * Int.modulus + Int.modulus - 1).
   change Int.modulus with 4294967296.
-  omega.
+  lia.
   apply eqm_samerepr. apply eqm_add. apply eqm_mul_2p32. apply Int.eqm_signed_unsigned. apply eqm_refl.
 Qed.
 
@@ -4291,7 +4292,7 @@ Proof.
   intros. apply Int64.same_bits_eq; intros.
   rewrite H by auto. rewrite ! bits_ofwords by auto.
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
-  destruct (zlt i Int.zwordsize); rewrite H0 by omega; auto.
+  destruct (zlt i Int.zwordsize); rewrite H0 by lia; auto.
 Qed.
 
 Lemma decompose_and:
@@ -4336,21 +4337,21 @@ Proof.
   intros.
   assert (Int.unsigned (Int.sub Int.iwordsize y) = Int.zwordsize - Int.unsigned y).
   { unfold Int.sub. rewrite Int.unsigned_repr. auto.
-    rewrite Int.unsigned_repr_wordsize. generalize Int.wordsize_max_unsigned; omega. }
+    rewrite Int.unsigned_repr_wordsize. generalize Int.wordsize_max_unsigned; lia. }
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
   apply Int64.same_bits_eq; intros.
   rewrite bits_shl' by auto. symmetry. rewrite bits_ofwords by auto.
-  destruct (zlt i Int.zwordsize). rewrite Int.bits_shl by omega.
+  destruct (zlt i Int.zwordsize). rewrite Int.bits_shl by lia.
   destruct (zlt i (Int.unsigned y)). auto.
-  rewrite bits_ofwords by omega. rewrite zlt_true by omega. auto.
-  rewrite zlt_false by omega. rewrite bits_ofwords by omega.
-  rewrite Int.bits_or by omega. rewrite Int.bits_shl by omega.
-  rewrite Int.bits_shru by omega. rewrite H0.
+  rewrite bits_ofwords by lia. rewrite zlt_true by lia. auto.
+  rewrite zlt_false by lia. rewrite bits_ofwords by lia.
+  rewrite Int.bits_or by lia. rewrite Int.bits_shl by lia.
+  rewrite Int.bits_shru by lia. rewrite H0.
   destruct (zlt (i - Int.unsigned y) (Int.zwordsize)).
-  rewrite zlt_true by omega. rewrite zlt_true by omega.
-  rewrite orb_false_l. f_equal. omega.
-  rewrite zlt_false by omega. rewrite zlt_false by omega.
-  rewrite orb_false_r. f_equal. omega.
+  rewrite zlt_true by lia. rewrite zlt_true by lia.
+  rewrite orb_false_l. f_equal. lia.
+  rewrite zlt_false by lia. rewrite zlt_false by lia.
+  rewrite orb_false_r. f_equal. lia.
 Qed.
 
 Lemma decompose_shl_2:
@@ -4363,15 +4364,15 @@ Proof.
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
   assert (Int.unsigned (Int.sub y Int.iwordsize) = Int.unsigned y - Int.zwordsize).
   { unfold Int.sub. rewrite Int.unsigned_repr. auto.
-    rewrite Int.unsigned_repr_wordsize. generalize (Int.unsigned_range_2 y). omega. }
+    rewrite Int.unsigned_repr_wordsize. generalize (Int.unsigned_range_2 y). lia. }
   apply Int64.same_bits_eq; intros.
   rewrite bits_shl' by auto. symmetry. rewrite bits_ofwords by auto.
-  destruct (zlt i Int.zwordsize). rewrite zlt_true by omega. apply Int.bits_zero.
-  rewrite Int.bits_shl by omega.
+  destruct (zlt i Int.zwordsize). rewrite zlt_true by lia. apply Int.bits_zero.
+  rewrite Int.bits_shl by lia.
   destruct (zlt i (Int.unsigned y)).
-  rewrite zlt_true by omega. auto.
-  rewrite zlt_false by omega.
-  rewrite bits_ofwords by omega. rewrite zlt_true by omega. f_equal. omega.
+  rewrite zlt_true by lia. auto.
+  rewrite zlt_false by lia.
+  rewrite bits_ofwords by lia. rewrite zlt_true by lia. f_equal. lia.
 Qed.
 
 Lemma decompose_shru_1:
@@ -4384,25 +4385,25 @@ Proof.
   intros.
   assert (Int.unsigned (Int.sub Int.iwordsize y) = Int.zwordsize - Int.unsigned y).
   { unfold Int.sub. rewrite Int.unsigned_repr. auto.
-    rewrite Int.unsigned_repr_wordsize. generalize Int.wordsize_max_unsigned; omega. }
+    rewrite Int.unsigned_repr_wordsize. generalize Int.wordsize_max_unsigned; lia. }
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
   apply Int64.same_bits_eq; intros.
   rewrite bits_shru' by auto. symmetry. rewrite bits_ofwords by auto.
   destruct (zlt i Int.zwordsize).
-  rewrite zlt_true by omega.
-  rewrite bits_ofwords by omega.
-  rewrite Int.bits_or by omega. rewrite Int.bits_shl by omega.
-  rewrite Int.bits_shru by omega. rewrite H0.
+  rewrite zlt_true by lia.
+  rewrite bits_ofwords by lia.
+  rewrite Int.bits_or by lia. rewrite Int.bits_shl by lia.
+  rewrite Int.bits_shru by lia. rewrite H0.
   destruct (zlt (i + Int.unsigned y) (Int.zwordsize)).
-  rewrite zlt_true by omega.
+  rewrite zlt_true by lia.
   rewrite orb_false_r. auto.
-  rewrite zlt_false by omega.
-  rewrite orb_false_l. f_equal. omega.
-  rewrite Int.bits_shru by omega.
+  rewrite zlt_false by lia.
+  rewrite orb_false_l. f_equal. lia.
+  rewrite Int.bits_shru by lia.
   destruct (zlt (i + Int.unsigned y) zwordsize).
-  rewrite bits_ofwords by omega.
-  rewrite zlt_true by omega. rewrite zlt_false by omega. f_equal. omega.
-  rewrite zlt_false by omega. auto.
+  rewrite bits_ofwords by lia.
+  rewrite zlt_true by lia. rewrite zlt_false by lia. f_equal. lia.
+  rewrite zlt_false by lia. auto.
 Qed.
 
 Lemma decompose_shru_2:
@@ -4415,16 +4416,16 @@ Proof.
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
   assert (Int.unsigned (Int.sub y Int.iwordsize) = Int.unsigned y - Int.zwordsize).
   { unfold Int.sub. rewrite Int.unsigned_repr. auto.
-    rewrite Int.unsigned_repr_wordsize. generalize (Int.unsigned_range_2 y). omega. }
+    rewrite Int.unsigned_repr_wordsize. generalize (Int.unsigned_range_2 y). lia. }
   apply Int64.same_bits_eq; intros.
   rewrite bits_shru' by auto. symmetry. rewrite bits_ofwords by auto.
   destruct (zlt i Int.zwordsize).
-  rewrite Int.bits_shru by omega. rewrite H1.
+  rewrite Int.bits_shru by lia. rewrite H1.
   destruct (zlt (i + Int.unsigned y) zwordsize).
-  rewrite zlt_true by omega. rewrite bits_ofwords by omega.
-  rewrite zlt_false by omega. f_equal; omega.
-  rewrite zlt_false by omega. auto.
-  rewrite zlt_false by omega. apply Int.bits_zero.
+  rewrite zlt_true by lia. rewrite bits_ofwords by lia.
+  rewrite zlt_false by lia. f_equal; lia.
+  rewrite zlt_false by lia. auto.
+  rewrite zlt_false by lia. apply Int.bits_zero.
 Qed.
 
 Lemma decompose_shr_1:
@@ -4437,26 +4438,26 @@ Proof.
   intros.
   assert (Int.unsigned (Int.sub Int.iwordsize y) = Int.zwordsize - Int.unsigned y).
   { unfold Int.sub. rewrite Int.unsigned_repr. auto.
-    rewrite Int.unsigned_repr_wordsize. generalize Int.wordsize_max_unsigned; omega. }
+    rewrite Int.unsigned_repr_wordsize. generalize Int.wordsize_max_unsigned; lia. }
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
   apply Int64.same_bits_eq; intros.
   rewrite bits_shr' by auto. symmetry. rewrite bits_ofwords by auto.
   destruct (zlt i Int.zwordsize).
-  rewrite zlt_true by omega.
-  rewrite bits_ofwords by omega.
-  rewrite Int.bits_or by omega. rewrite Int.bits_shl by omega.
-  rewrite Int.bits_shru by omega. rewrite H0.
+  rewrite zlt_true by lia.
+  rewrite bits_ofwords by lia.
+  rewrite Int.bits_or by lia. rewrite Int.bits_shl by lia.
+  rewrite Int.bits_shru by lia. rewrite H0.
   destruct (zlt (i + Int.unsigned y) (Int.zwordsize)).
-  rewrite zlt_true by omega.
+  rewrite zlt_true by lia.
   rewrite orb_false_r. auto.
-  rewrite zlt_false by omega.
-  rewrite orb_false_l. f_equal. omega.
-  rewrite Int.bits_shr by omega.
+  rewrite zlt_false by lia.
+  rewrite orb_false_l. f_equal. lia.
+  rewrite Int.bits_shr by lia.
   destruct (zlt (i + Int.unsigned y) zwordsize).
-  rewrite bits_ofwords by omega.
-  rewrite zlt_true by omega. rewrite zlt_false by omega. f_equal. omega.
-  rewrite zlt_false by omega. rewrite bits_ofwords by omega.
-  rewrite zlt_false by omega. f_equal.
+  rewrite bits_ofwords by lia.
+  rewrite zlt_true by lia. rewrite zlt_false by lia. f_equal. lia.
+  rewrite zlt_false by lia. rewrite bits_ofwords by lia.
+  rewrite zlt_false by lia. f_equal.
 Qed.
 
 Lemma decompose_shr_2:
@@ -4470,24 +4471,24 @@ Proof.
   assert (zwordsize = 2 * Int.zwordsize) by reflexivity.
   assert (Int.unsigned (Int.sub y Int.iwordsize) = Int.unsigned y - Int.zwordsize).
   { unfold Int.sub. rewrite Int.unsigned_repr. auto.
-    rewrite Int.unsigned_repr_wordsize. generalize (Int.unsigned_range_2 y). omega. }
+    rewrite Int.unsigned_repr_wordsize. generalize (Int.unsigned_range_2 y). lia. }
   apply Int64.same_bits_eq; intros.
   rewrite bits_shr' by auto. symmetry. rewrite bits_ofwords by auto.
   destruct (zlt i Int.zwordsize).
-  rewrite Int.bits_shr by omega. rewrite H1.
+  rewrite Int.bits_shr by lia. rewrite H1.
   destruct (zlt (i + Int.unsigned y) zwordsize).
-  rewrite zlt_true by omega. rewrite bits_ofwords by omega.
-  rewrite zlt_false by omega. f_equal; omega.
-  rewrite zlt_false by omega. rewrite bits_ofwords by omega.
-  rewrite zlt_false by omega. auto.
-  rewrite Int.bits_shr by omega.
+  rewrite zlt_true by lia. rewrite bits_ofwords by lia.
+  rewrite zlt_false by lia. f_equal; lia.
+  rewrite zlt_false by lia. rewrite bits_ofwords by lia.
+  rewrite zlt_false by lia. auto.
+  rewrite Int.bits_shr by lia.
   change (Int.unsigned (Int.sub Int.iwordsize Int.one)) with (Int.zwordsize - 1).
   destruct (zlt (i + Int.unsigned y) zwordsize);
-  rewrite bits_ofwords by omega.
-  symmetry. rewrite zlt_false by omega. f_equal.
-  destruct (zlt (i - Int.zwordsize + (Int.zwordsize - 1)) Int.zwordsize); omega.
-  symmetry. rewrite zlt_false by omega. f_equal.
-  destruct (zlt (i - Int.zwordsize + (Int.zwordsize - 1)) Int.zwordsize); omega.
+  rewrite bits_ofwords by lia.
+  symmetry. rewrite zlt_false by lia. f_equal.
+  destruct (zlt (i - Int.zwordsize + (Int.zwordsize - 1)) Int.zwordsize); lia.
+  symmetry. rewrite zlt_false by lia. f_equal.
+  destruct (zlt (i - Int.zwordsize + (Int.zwordsize - 1)) Int.zwordsize); lia.
 Qed.
 
 Lemma decompose_add:
@@ -4624,14 +4625,14 @@ Proof.
   intros. unfold ltu. rewrite ! ofwords_add'. unfold Int.ltu, Int.eq.
   destruct (zeq (Int.unsigned xh) (Int.unsigned yh)).
   rewrite e. destruct (zlt (Int.unsigned xl) (Int.unsigned yl)).
-  apply zlt_true; omega.
-  apply zlt_false; omega.
+  apply zlt_true; lia.
+  apply zlt_false; lia.
   change (two_p 32) with Int.modulus.
   generalize (Int.unsigned_range xl) (Int.unsigned_range yl).
   change Int.modulus with 4294967296. intros.
   destruct (zlt (Int.unsigned xh) (Int.unsigned yh)).
-  apply zlt_true; omega.
-  apply zlt_false; omega.
+  apply zlt_true; lia.
+  apply zlt_false; lia.
 Qed.
 
 Lemma decompose_leu:
@@ -4643,8 +4644,8 @@ Proof.
   unfold Int.eq. destruct (zeq (Int.unsigned xh) (Int.unsigned yh)).
   auto.
   unfold Int.ltu. destruct (zlt (Int.unsigned xh) (Int.unsigned yh)).
-  rewrite zlt_false by omega; auto.
-  rewrite zlt_true by omega; auto.
+  rewrite zlt_false by lia; auto.
+  rewrite zlt_true by lia; auto.
 Qed.
 
 Lemma decompose_lt:
@@ -4654,14 +4655,14 @@ Proof.
   intros. unfold lt. rewrite ! ofwords_add''. rewrite Int.eq_signed.
   destruct (zeq (Int.signed xh) (Int.signed yh)).
   rewrite e. unfold Int.ltu. destruct (zlt (Int.unsigned xl) (Int.unsigned yl)).
-  apply zlt_true; omega.
-  apply zlt_false; omega.
+  apply zlt_true; lia.
+  apply zlt_false; lia.
   change (two_p 32) with Int.modulus.
   generalize (Int.unsigned_range xl) (Int.unsigned_range yl).
   change Int.modulus with 4294967296. intros.
   unfold Int.lt. destruct (zlt (Int.signed xh) (Int.signed yh)).
-  apply zlt_true; omega.
-  apply zlt_false; omega.
+  apply zlt_true; lia.
+  apply zlt_false; lia.
 Qed.
 
 Lemma decompose_le:
@@ -4673,8 +4674,8 @@ Proof.
   rewrite Int.eq_signed. destruct (zeq (Int.signed xh) (Int.signed yh)).
   auto.
   unfold Int.lt. destruct (zlt (Int.signed xh) (Int.signed yh)).
-  rewrite zlt_false by omega; auto.
-  rewrite zlt_true by omega; auto.
+  rewrite zlt_false by lia; auto.
+  rewrite zlt_true by lia; auto.
 Qed.
 
 (** Utility proofs for mixed 32bit and 64bit arithmetic *)
@@ -4689,7 +4690,7 @@ Proof.
   change (wordsize) with  64%nat in *.
   change (Int.wordsize) with 32%nat in *.
   unfold two_power_nat. simpl.
-  omega.
+  lia.
 Qed.
 
 Remark int_unsigned_repr:
@@ -4709,9 +4710,9 @@ Proof.
   rewrite unsigned_repr by apply int_unsigned_range. rewrite int_unsigned_repr. reflexivity.
   rewrite unsigned_repr by apply int_unsigned_range.
   rewrite int_unsigned_repr. generalize (int_unsigned_range y).
-  omega.
+  lia.
   generalize (Int.sub_ltu x y H). intros.
-  generalize (Int.unsigned_range_2 y). intros. omega.
+  generalize (Int.unsigned_range_2 y). intros. lia.
 Qed.
 
 End Int64.
@@ -4887,7 +4888,7 @@ Lemma to_int_of_int:
   forall n, to_int (of_int n) = n.
 Proof.
   intros; unfold of_int, to_int. rewrite unsigned_repr. apply Int.repr_unsigned.
-  unfold max_unsigned. rewrite modulus_eq32. destruct (Int.unsigned_range n); omega.
+  unfold max_unsigned. rewrite modulus_eq32. destruct (Int.unsigned_range n); lia.
 Qed.
 
 End AGREE32.
@@ -4997,12 +4998,12 @@ Lemma to_int64_of_int64:
   forall n, to_int64 (of_int64 n) = n.
 Proof.
   intros; unfold of_int64, to_int64. rewrite unsigned_repr. apply Int64.repr_unsigned.
-  unfold max_unsigned. rewrite  modulus_eq64. destruct (Int64.unsigned_range n); omega.
+  unfold max_unsigned. rewrite  modulus_eq64. destruct (Int64.unsigned_range n); lia.
 Qed.
 
 End AGREE64.
 
-Hint Resolve
+Global Hint Resolve
   agree32_repr agree32_of_int agree32_of_ints agree32_of_int_eq agree32_of_ints_eq
   agree32_to_int agree32_to_int_eq agree32_neg agree32_add agree32_sub agree32_mul agree32_divs
   agree64_repr agree64_of_int agree64_of_int_eq
@@ -5025,19 +5026,22 @@ Qed.
 
 Global Opaque Ptrofs.repr.
 
-Hint Resolve Int.modulus_pos Int.eqm_refl Int.eqm_refl2 Int.eqm_sym Int.eqm_trans
+Global Hint Resolve
+  Int.modulus_pos Int.eqm_refl Int.eqm_refl2 Int.eqm_sym Int.eqm_trans
   Int.eqm_small_eq Int.eqm_add Int.eqm_neg Int.eqm_sub Int.eqm_mult
   Int.eqm_unsigned_repr Int.eqm_unsigned_repr_l Int.eqm_unsigned_repr_r
   Int.unsigned_range Int.unsigned_range_2
   Int.repr_unsigned Int.repr_signed Int.unsigned_repr : ints.
 
-Hint Resolve Int64.modulus_pos Int64.eqm_refl Int64.eqm_refl2 Int64.eqm_sym Int64.eqm_trans
+Global Hint Resolve
+  Int64.modulus_pos Int64.eqm_refl Int64.eqm_refl2 Int64.eqm_sym Int64.eqm_trans
   Int64.eqm_small_eq Int64.eqm_add Int64.eqm_neg Int64.eqm_sub Int64.eqm_mult
   Int64.eqm_unsigned_repr Int64.eqm_unsigned_repr_l Int64.eqm_unsigned_repr_r
   Int64.unsigned_range Int64.unsigned_range_2
   Int64.repr_unsigned Int64.repr_signed Int64.unsigned_repr : ints.
 
-Hint Resolve Ptrofs.modulus_pos Ptrofs.eqm_refl Ptrofs.eqm_refl2 Ptrofs.eqm_sym Ptrofs.eqm_trans
+Global Hint Resolve
+  Ptrofs.modulus_pos Ptrofs.eqm_refl Ptrofs.eqm_refl2 Ptrofs.eqm_sym Ptrofs.eqm_trans
   Ptrofs.eqm_small_eq Ptrofs.eqm_add Ptrofs.eqm_neg Ptrofs.eqm_sub Ptrofs.eqm_mult
   Ptrofs.eqm_unsigned_repr Ptrofs.eqm_unsigned_repr_l Ptrofs.eqm_unsigned_repr_r
   Ptrofs.unsigned_range Ptrofs.unsigned_range_2
diff --git a/lib/Intv.v b/lib/Intv.v
index a11e619b..4b5ed77d 100644
--- a/lib/Intv.v
+++ b/lib/Intv.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -41,14 +42,14 @@ Lemma notin_range:
   forall x i,
   x < fst i \/ x >= snd i -> ~In x i.
 Proof.
-  unfold In; intros; omega.
+  unfold In; intros; lia.
 Qed.
 
 Lemma range_notin:
   forall x i,
   ~In x i -> fst i < snd i -> x < fst i \/ x >= snd i.
 Proof.
-  unfold In; intros; omega.
+  unfold In; intros; lia.
 Qed.
 
 (** * Emptyness *)
@@ -60,26 +61,26 @@ Lemma empty_dec:
 Proof.
   unfold empty; intros.
   case (zle (snd i) (fst i)); intros.
-  left; omega.
-  right; omega.
+  left; lia.
+  right; lia.
 Qed.
 
 Lemma is_notempty:
   forall i, fst i < snd i -> ~empty i.
 Proof.
-  unfold empty; intros; omega.
+  unfold empty; intros; lia.
 Qed.
 
 Lemma empty_notin:
   forall x i, empty i -> ~In x i.
 Proof.
-  unfold empty, In; intros. omega.
+  unfold empty, In; intros. lia.
 Qed.
 
 Lemma in_notempty:
   forall x i, In x i -> ~empty i.
 Proof.
-  unfold empty, In; intros. omega.
+  unfold empty, In; intros. lia.
 Qed.
 
 (** * Disjointness *)
@@ -109,7 +110,7 @@ Lemma disjoint_range:
   forall i j,
   snd i <= fst j \/ snd j <= fst i -> disjoint i j.
 Proof.
-  unfold disjoint, In; intros. omega.
+  unfold disjoint, In; intros. lia.
 Qed.
 
 Lemma range_disjoint:
@@ -127,13 +128,13 @@ Proof.
 (* Case 1.1: i ends to the left of j, OK *)
   auto.
 (* Case 1.2: i ends to the right of j's start, not disjoint. *)
-  elim (H (fst j)). red; omega. red; omega.
+  elim (H (fst j)). red; lia. red; lia.
 (* Case 2: j starts to the left of i *)
   destruct (zle (snd j) (fst i)).
 (* Case 2.1: j ends to the left of i, OK *)
   auto.
 (* Case 2.2: j ends to the right of i's start, not disjoint. *)
-  elim (H (fst i)). red; omega. red; omega.
+  elim (H (fst i)). red; lia. red; lia.
 Qed.
 
 Lemma range_disjoint':
@@ -141,7 +142,7 @@ Lemma range_disjoint':
   disjoint i j -> fst i < snd i -> fst j < snd j ->
   snd i <= fst j \/ snd j <= fst i.
 Proof.
-  intros. exploit range_disjoint; eauto. unfold empty; intuition omega.
+  intros. exploit range_disjoint; eauto. unfold empty; intuition lia.
 Qed.
 
 Lemma disjoint_dec:
@@ -163,14 +164,14 @@ Lemma in_shift:
   forall x i delta,
   In x i -> In (x + delta) (shift i delta).
 Proof.
-  unfold shift, In; intros. simpl. omega.
+  unfold shift, In; intros. simpl. lia.
 Qed.
 
 Lemma in_shift_inv:
   forall x i delta,
   In x (shift i delta) -> In (x - delta) i.
 Proof.
-  unfold shift, In; simpl; intros. omega.
+  unfold shift, In; simpl; intros. lia.
 Qed.
 
 (** * Enumerating the elements of an interval *)
@@ -182,7 +183,7 @@ Variable lo: Z.
 Function elements_rec (hi: Z) {wf (Zwf lo) hi} : list Z :=
   if zlt lo hi then (hi-1) :: elements_rec (hi-1) else nil.
 Proof.
-  intros. red. omega.
+  intros. red. lia.
   apply Zwf_well_founded.
 Qed.
 
@@ -192,8 +193,8 @@ Lemma In_elements_rec:
 Proof.
   intros. functional induction (elements_rec hi).
   simpl; split; intros.
-  destruct H. clear IHl. omega. rewrite IHl in H. clear IHl. omega.
-  destruct (zeq (hi - 1) x); auto. right. rewrite IHl. clear IHl. omega.
+  destruct H. clear IHl. lia. rewrite IHl in H. clear IHl. lia.
+  destruct (zeq (hi - 1) x); auto. right. rewrite IHl. clear IHl. lia.
   simpl; intuition.
 Qed.
 
@@ -241,20 +242,20 @@ Program Fixpoint forall_rec (hi: Z) {wf (Zwf lo) hi}:
     left _ _
 .
 Next Obligation.
-  red. omega.
+  red. lia.
 Qed.
 Next Obligation.
-  assert (x = hi - 1 \/ x < hi - 1) by omega.
+  assert (x = hi - 1 \/ x < hi - 1) by lia.
   destruct H2. congruence. auto.
 Qed.
 Next Obligation.
-  exists wildcard'; split; auto. omega.
+  exists wildcard'; split; auto. lia.
 Qed.
 Next Obligation.
-  exists (hi - 1); split; auto. omega.
+  exists (hi - 1); split; auto. lia.
 Qed.
 Next Obligation.
-  omegaContradiction.
+  extlia.
 Defined.
 
 End FORALL.
@@ -276,7 +277,7 @@ Variable a: A.
 Function fold_rec (hi: Z) {wf (Zwf lo) hi} : A :=
   if zlt lo hi then f (hi - 1) (fold_rec (hi - 1)) else a.
 Proof.
-  intros. red. omega.
+  intros. red. lia.
   apply Zwf_well_founded.
 Qed.
 
@@ -303,7 +304,7 @@ Qed.
 
 (** Hints *)
 
-Hint Resolve
+Global Hint Resolve
   notin_range range_notin
   is_notempty empty_notin in_notempty
   disjoint_sym empty_disjoint_r empty_disjoint_l
diff --git a/lib/IntvSets.v b/lib/IntvSets.v
index b97d9882..c3fda5f7 100644
--- a/lib/IntvSets.v
+++ b/lib/IntvSets.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -59,7 +60,7 @@ Proof.
 + destruct (zle l x); simpl.
   * tauto.
   * split; intros. congruence.
-    exfalso. destruct H0. omega. exploit BELOW; eauto. omega.
+    exfalso. destruct H0. lia. exploit BELOW; eauto. lia.
 + rewrite IHok. intuition.
 Qed.
 
@@ -74,14 +75,14 @@ Lemma contains_In:
   (contains l0 h0 s = true <-> (forall x, l0 <= x < h0 -> In x s)).
 Proof.
   induction 2; simpl.
-- intuition. elim (H0 l0); omega.
+- intuition. elim (H0 l0); lia.
 - destruct (zle h0 h); simpl.
   destruct (zle l l0); simpl.
   intuition.
   rewrite IHok. intuition. destruct (H3 x); auto. exfalso.
-  destruct (H3 l0). omega. omega. exploit BELOW; eauto. omega.
+  destruct (H3 l0). lia. lia. exploit BELOW; eauto. lia.
   rewrite IHok. intuition. destruct (H3 x); auto. exfalso.
-  destruct (H3 h). omega. omega. exploit BELOW; eauto. omega.
+  destruct (H3 h). lia. lia. exploit BELOW; eauto. lia.
 Qed.
 
 Fixpoint add (L H: Z) (s: t) {struct s} : t :=
@@ -103,9 +104,9 @@ Proof.
   destruct (zlt h0 l).
   simpl. tauto.
   rewrite IHok. intuition idtac.
-  assert (l0 <= x < h0 \/ l <= x < h) by xomega. tauto.
-  left; xomega.
-  left; xomega.
+  assert (l0 <= x < h0 \/ l <= x < h) by extlia. tauto.
+  left; extlia.
+  left; extlia.
 Qed.
 
 Lemma add_ok:
@@ -115,11 +116,11 @@ Proof.
   constructor. auto. intros. inv H0. constructor.
   destruct (zlt h l0).
   constructor; auto. intros. rewrite In_add in H1; auto.
-  destruct H1. omega. auto.
+  destruct H1. lia. auto.
   destruct (zlt h0 l).
-  constructor. auto. simpl; intros. destruct H1. omega. exploit BELOW; eauto. omega.
-  constructor. omega. auto. auto.
-  apply IHok. xomega.
+  constructor. auto. simpl; intros. destruct H1. lia. exploit BELOW; eauto. lia.
+  constructor. lia. auto. auto.
+  apply IHok. extlia.
 Qed.
 
 Fixpoint remove (L H: Z) (s: t) {struct s} : t :=
@@ -141,22 +142,22 @@ Proof.
   induction 1; simpl.
   tauto.
   destruct (zlt h l0).
-  simpl. rewrite IHok. intuition omega.
+  simpl. rewrite IHok. intuition lia.
   destruct (zlt h0 l).
-  simpl. intuition. exploit BELOW; eauto. omega.
+  simpl. intuition. exploit BELOW; eauto. lia.
   destruct (zlt l l0).
   destruct (zlt h0 h); simpl. clear IHok. split.
   intros [A | [A | A]].
-  split. omega. left; omega.
-  split. omega. left; omega.
-  split. exploit BELOW; eauto. omega. auto.
+  split. lia. left; lia.
+  split. lia. left; lia.
+  split. exploit BELOW; eauto. lia. auto.
   intros [A [B | B]].
-  destruct (zlt x l0). left; omega. right; left; omega.
+  destruct (zlt x l0). left; lia. right; left; lia.
   auto.
-  intuition omega.
+  intuition lia.
   destruct (zlt h0 h); simpl.
-  intuition. exploit BELOW; eauto. omega.
-  rewrite IHok. intuition. omegaContradiction.
+  intuition. exploit BELOW; eauto. lia.
+  rewrite IHok. intuition. extlia.
 Qed.
 
 Lemma remove_ok:
@@ -170,9 +171,9 @@ Proof.
   constructor; auto.
   destruct (zlt l l0).
   destruct (zlt h0 h).
-  constructor. omega. intros. inv H1. omega. exploit BELOW; eauto. omega.
-  constructor. omega. auto. auto.
-  constructor; auto. intros. rewrite In_remove in H1 by auto. destruct H1. exploit BELOW; eauto. omega.
+  constructor. lia. intros. inv H1. lia. exploit BELOW; eauto. lia.
+  constructor. lia. auto. auto.
+  constructor; auto. intros. rewrite In_remove in H1 by auto. destruct H1. exploit BELOW; eauto. lia.
   destruct (zlt h0 h).
   constructor; auto.
   auto.
@@ -204,19 +205,19 @@ Proof.
   tauto.
   assert (ok (Cons l0 h0 s0)) by (constructor; auto).
   destruct (zle h l0).
-  rewrite IHok; auto. simpl. intuition. omegaContradiction.
-  exploit BELOW0; eauto. intros. omegaContradiction.
+  rewrite IHok; auto. simpl. intuition. extlia.
+  exploit BELOW0; eauto. intros. extlia.
   destruct (zle h0 l).
-  simpl in IHok0; rewrite IHok0. intuition. omegaContradiction.
-  exploit BELOW; eauto. intros; omegaContradiction.
+  simpl in IHok0; rewrite IHok0. intuition. extlia.
+  exploit BELOW; eauto. intros; extlia.
   destruct (zle l l0).
   destruct (zle h0 h).
   simpl. simpl in IHok0; rewrite IHok0. intuition.
-  simpl. rewrite IHok; auto. simpl. intuition.  exploit BELOW0; eauto. intros; omegaContradiction.
+  simpl. rewrite IHok; auto. simpl. intuition.  exploit BELOW0; eauto. intros; extlia.
   destruct (zle h h0).
   simpl. rewrite IHok; auto. simpl. intuition.
   simpl. simpl in IHok0; rewrite IHok0. intuition.
-  exploit BELOW; eauto. intros; omegaContradiction.
+  exploit BELOW; eauto. intros; extlia.
 Qed.
 
 Lemma inter_ok:
@@ -237,12 +238,12 @@ Proof.
   constructor; auto. intros.
   assert (In x (inter (Cons l h s) s0)) by exact H3.
   rewrite In_inter in H4; auto. apply BELOW0. tauto.
-  constructor. omega. intros. rewrite In_inter in H3; auto. apply BELOW. tauto.
+  constructor. lia. intros. rewrite In_inter in H3; auto. apply BELOW. tauto.
   auto.
   destruct (zle h h0).
-  constructor. omega. intros. rewrite In_inter in H3; auto. apply BELOW. tauto.
+  constructor. lia. intros. rewrite In_inter in H3; auto. apply BELOW. tauto.
   auto.
-  constructor. omega. intros.
+  constructor. lia. intros.
   assert (In x (inter (Cons l h s) s0)) by exact H3.
   rewrite In_inter in H4; auto. apply BELOW0. tauto.
   auto.
@@ -281,20 +282,20 @@ Lemma beq_spec:
 Proof.
   induction 1; destruct 1; simpl.
 - tauto.
-- split; intros. discriminate. exfalso. apply (H0 l). left; omega.
-- split; intros. discriminate. exfalso. apply (H0 l). left; omega.
+- split; intros. discriminate. exfalso. apply (H0 l). left; lia.
+- split; intros. discriminate. exfalso. apply (H0 l). left; lia.
 - split; intros.
 + InvBooleans. subst. rewrite IHok in H3 by auto. rewrite H3. tauto.
 + destruct (zeq l l0). destruct (zeq h h0). simpl. subst.
   apply IHok. auto. intros; split; intros.
-  destruct (proj1 (H1 x)); auto. exfalso. exploit BELOW; eauto. omega.
-  destruct (proj2 (H1 x)); auto. exfalso. exploit BELOW0; eauto. omega.
+  destruct (proj1 (H1 x)); auto. exfalso. exploit BELOW; eauto. lia.
+  destruct (proj2 (H1 x)); auto. exfalso. exploit BELOW0; eauto. lia.
   exfalso. subst l0. destruct (zlt h h0).
-  destruct (proj2 (H1 h)). left; omega. omega. exploit BELOW; eauto. omega.
-  destruct (proj1 (H1 h0)). left; omega. omega. exploit BELOW0; eauto. omega.
+  destruct (proj2 (H1 h)). left; lia. lia. exploit BELOW; eauto. lia.
+  destruct (proj1 (H1 h0)). left; lia. lia. exploit BELOW0; eauto. lia.
   exfalso. destruct (zlt l l0).
-  destruct (proj1 (H1 l)). left; omega. omega. exploit BELOW0; eauto. omega.
-  destruct (proj2 (H1 l0)). left; omega. omega. exploit BELOW; eauto. omega.
+  destruct (proj1 (H1 l)). left; lia. lia. exploit BELOW0; eauto. lia.
+  destruct (proj2 (H1 l0)). left; lia. lia. exploit BELOW; eauto. lia.
 Qed.
 
 End R.
@@ -340,7 +341,7 @@ Proof.
   unfold add, In; intros.
   destruct (zlt l h).
   simpl. apply R.In_add. apply proj2_sig.
-  intuition. omegaContradiction.
+  intuition. extlia.
 Qed.
 
 Program Definition remove (l h: Z) (s: t) : t :=
@@ -392,7 +393,7 @@ Theorem contains_spec:
 Proof.
   unfold contains, In; intros. destruct (zlt l h).
   apply R.contains_In. auto. apply proj2_sig.
-  split; intros. omegaContradiction. auto.
+  split; intros. extlia. auto.
 Qed.
 
 Program Definition beq (s1 s2: t) : bool := R.beq s1 s2.
diff --git a/lib/IterList.v b/lib/IterList.v
index bde47068..d28124c7 100644
--- a/lib/IterList.v
+++ b/lib/IterList.v
@@ -1,4 +1,5 @@
 Require Import Coqlib.
+Require Import Lia.
 
 (** TODO: are these def and lemma already defined in the standard library ?
 
@@ -55,17 +56,17 @@ Qed.
 Lemma length_iter_tail {A} (n:nat): forall (l: list A), (n <= List.length l)%nat -> (List.length l = n + List.length (iter_tail n l))%nat.
 Proof.
   unfold iter_tail; induction n; auto.
-  intros l; destruct l. { simpl; omega. }
+  intros l; destruct l. { simpl; lia. }
   intros; simpl. erewrite IHn; eauto.
-  simpl in *; omega.
+  simpl in *; lia.
 Qed.
 
 Lemma iter_tail_S_ex {A} (n:nat): forall (l: list A), (n < length l)%nat -> exists x, iter_tail n l = x::(iter_tail (S n) l).
 Proof.
   unfold iter_tail; induction n; simpl.
-  - intros l; destruct l; simpl; omega || eauto.
+  - intros l; destruct l; simpl; lia || eauto.
   - intros l H; destruct (IHn (tl l)) as (x & H1).
-    + destruct l; simpl in *; try omega.
+    + destruct l; simpl in *; try lia.
     + rewrite H1; eauto.
 Qed.
 
@@ -74,20 +75,20 @@ Proof.
   intros H1 H2 EQ; exploit (length_iter_tail n1 l); eauto.
   rewrite EQ.
   rewrite (length_iter_tail n2 l); eauto.
-  omega.
+  lia.
 Qed.
 
 Lemma iter_tail_nil_inject {A} (n:nat) (l: list A): iter_tail n l = nil -> (List.length l <= n)%nat.
 Proof.
-  destruct (le_lt_dec n (List.length l)); try omega.
-  intros; exploit (iter_tail_inject1 n (length l) l); try omega.
+  destruct (le_lt_dec n (List.length l)); try lia.
+  intros; exploit (iter_tail_inject1 n (length l) l); try lia.
   rewrite iter_tail_reach_nil. auto.
 Qed.
 
 Lemma list_length_z_nat (A: Type) (l: list A): list_length_z l = Z.of_nat (length l).
 Proof.
   induction l; auto.
-  rewrite list_length_z_cons. simpl. rewrite Zpos_P_of_succ_nat. omega.
+  rewrite list_length_z_cons. simpl. rewrite Zpos_P_of_succ_nat. lia.
 Qed.
 
 Lemma list_length_nat_z (A: Type) (l: list A): length l = Z.to_nat (list_length_z l).
@@ -99,13 +100,13 @@ Lemma is_tail_list_nth_z A (l1 l2: list A):
   is_tail l1 l2 -> list_nth_z l2 ((list_length_z l2) - (list_length_z l1)) = list_nth_z l1 0.
 Proof.
   induction 1; simpl.
-  - replace (list_length_z c - list_length_z c) with 0; omega || auto.
+  - replace (list_length_z c - list_length_z c) with 0; lia || auto.
   - assert (X: list_length_z (i :: c2) > list_length_z c1).
     { rewrite !list_length_z_nat, <- Nat2Z.inj_gt.
       exploit is_tail_bound; simpl; eauto.
-      omega. }
-    destruct (zeq (list_length_z (i :: c2) - list_length_z c1) 0) as [Y|Y]; try omega.
+      lia. }
+    destruct (zeq (list_length_z (i :: c2) - list_length_z c1) 0) as [Y|Y]; try lia.
     replace (Z.pred (list_length_z (i :: c2) - list_length_z c1)) with (list_length_z c2 - list_length_z c1); auto.
     rewrite list_length_z_cons.
-    omega.
+    lia.
 Qed.
diff --git a/lib/Iteration.v b/lib/Iteration.v
index 6a9d3253..82110bff 100644
--- a/lib/Iteration.v
+++ b/lib/Iteration.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -237,8 +238,8 @@ Lemma iter_monot:
 Proof.
   induction p; intros.
   simpl. red; intros; red; auto.
-  destruct q. elimtype False; omega.
-  simpl. apply F_iter_monot. apply IHp. omega.
+  destruct q. elimtype False; lia.
+  simpl. apply F_iter_monot. apply IHp. lia.
 Qed.
 
 Lemma iter_either:
diff --git a/lib/Lattice.v b/lib/Lattice.v
index 8ea736ad..016dad75 100644
--- a/lib/Lattice.v
+++ b/lib/Lattice.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Maps.v b/lib/Maps.v
index 8de3c892..456a1a9a 100644
--- a/lib/Maps.v
+++ b/lib/Maps.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -1442,102 +1443,121 @@ Module ZTree := ITree(ZIndexed).
 
 Module Tree_Properties(T: TREE).
 
-(** An induction principle over [fold]. *)
+(** Two induction principles over [fold]. *)
 
 Section TREE_FOLD_IND.
 
 Variables V A: Type.
 Variable f: A -> T.elt -> V -> A.
-Variable P: T.t V -> A -> Prop.
+Variable P: T.t V -> A -> Type.
 Variable init: A.
 Variable m_final: T.t V.
 
-Hypothesis P_compat:
-  forall m m' a,
-  (forall x, T.get x m = T.get x m') ->
-  P m a -> P m' a.
-
 Hypothesis H_base:
-  P (T.empty _) init.
+  forall m,
+  (forall k, T.get k m = None) ->
+  P m init.
 
 Hypothesis H_rec:
   forall m a k v,
-  T.get k m = None -> T.get k m_final = Some v -> P m a -> P (T.set k v m) (f a k v).
+  T.get k m = Some v -> T.get k m_final = Some v ->
+  P (T.remove k m) a -> P m (f a k v).
 
-Let f' (a: A) (p : T.elt * V) := f a (fst p) (snd p).
+Let f' (p : T.elt * V) (a: A) := f a (fst p) (snd p).
 
-Let P' (l: list (T.elt * V)) (a: A) : Prop :=
-  forall m, list_equiv l (T.elements m) -> P m a.
+Let P' (l: list (T.elt * V)) (a: A) : Type :=
+  forall m, (forall k v, In (k, v) l <-> T.get k m = Some v) -> P m a.
 
-Remark H_base':
+Let H_base':
   P' nil init.
 Proof.
-  red; intros. apply P_compat with (T.empty _); auto.
-  intros. rewrite T.gempty. symmetry. case_eq (T.get x m); intros; auto.
-  assert (In (x, v) nil). rewrite (H (x, v)). apply T.elements_correct. auto.
-  contradiction.
+  intros m EQV. apply H_base.
+  intros. destruct (T.get k m) as [v|] eqn:G; auto.
+  apply EQV in G. contradiction.
 Qed.
 
-Remark H_rec':
+Let H_rec':
   forall k v l a,
-  ~In k (List.map (@fst T.elt V) l) ->
-  In (k, v) (T.elements m_final) ->
+  ~In k (List.map fst l) ->
+  T.get k m_final = Some v ->
   P' l a ->
-  P' (l ++ (k, v) :: nil) (f a k v).
+  P' ((k, v) :: l) (f a k v).
 Proof.
-  unfold P'; intros.
+  unfold P'; intros k v l a NOTIN FINAL HR m EQV.
   set (m0 := T.remove k m).
-  apply P_compat with (T.set k v m0).
-    intros. unfold m0. rewrite T.gsspec. destruct (T.elt_eq x k).
-    symmetry. apply T.elements_complete. rewrite <- (H2 (x, v)).
-    apply in_or_app. simpl. intuition congruence.
-    apply T.gro. auto.
-  apply H_rec. unfold m0. apply T.grs. apply T.elements_complete. auto.
-  apply H1. red. intros [k' v'].
-  split; intros.
-  apply T.elements_correct. unfold m0. rewrite T.gro. apply T.elements_complete.
-  rewrite <- (H2 (k', v')). apply in_or_app. auto.
-  red; intro; subst k'. elim H. change k with (fst (k, v')). apply in_map. auto.
-  assert (T.get k' m0 = Some v'). apply T.elements_complete. auto.
-  unfold m0 in H4. rewrite T.grspec in H4. destruct (T.elt_eq k' k). congruence.
-  assert (In (k', v') (T.elements m)). apply T.elements_correct; auto.
-  rewrite <- (H2 (k', v')) in H5. destruct (in_app_or _ _ _ H5). auto.
-  simpl in H6. intuition congruence.
+  apply H_rec.
+- apply EQV. simpl; auto.
+- auto.
+- apply HR. intros k' v'. rewrite T.grspec. split; intros; destruct (T.elt_eq k' k).
+  + subst k'. elim NOTIN. change k with (fst (k, v')). apply List.in_map; auto.
+  + apply EQV. simpl; auto.
+  + congruence.
+  + apply EQV in H. simpl in H. intuition congruence.
 Qed.
 
-Lemma fold_rec_aux:
-  forall l1 l2 a,
-  list_equiv (l2 ++ l1) (T.elements m_final) ->
-  list_disjoint (List.map (@fst T.elt V) l1) (List.map (@fst T.elt V) l2) ->
-  list_norepet (List.map (@fst T.elt V) l1) ->
-  P' l2 a -> P' (l2 ++ l1) (List.fold_left f' l1 a).
+Lemma fold_ind_aux:
+  forall l,
+  (forall k v, In (k, v) l -> T.get k m_final = Some v) ->
+  list_norepet (List.map fst l) ->
+  P' l (List.fold_right f' init l).
 Proof.
-  induction l1; intros; simpl.
-  rewrite <- List.app_nil_end. auto.
-  destruct a as [k v]; simpl in *. inv H1.
-  change ((k, v) :: l1) with (((k, v) :: nil) ++ l1). rewrite <- List.app_ass. apply IHl1.
-  rewrite app_ass. auto.
-  red; intros. rewrite map_app in H3. destruct (in_app_or _ _ _ H3). apply H0; auto with coqlib.
-  simpl in H4. intuition congruence.
-  auto.
-  unfold f'. simpl. apply H_rec'; auto. eapply list_disjoint_notin; eauto with coqlib.
-  rewrite <- (H (k, v)). apply in_or_app. simpl. auto.
-Qed.
+  induction l as [ | [k v] l ]; simpl; intros FINAL NOREPET.
+- apply H_base'.
+- apply H_rec'.
+  + inv NOREPET. auto.
+  + apply FINAL. auto.
+  + apply IHl. auto. inv NOREPET; auto.
+Defined.
+
+Theorem fold_ind:
+  P m_final (T.fold f m_final init).
+Proof.
+  intros.
+  set (l' := List.rev (T.elements m_final)).
+  assert (P' l' (List.fold_right f' init l')).
+  { apply fold_ind_aux.
+    intros. apply T.elements_complete. apply List.in_rev. auto.
+    unfold l'; rewrite List.map_rev. apply list_norepet_rev. apply T.elements_keys_norepet. }
+  unfold l', f' in X; rewrite fold_left_rev_right in X.
+  rewrite T.fold_spec. apply X.
+  intros; simpl. rewrite <- List.in_rev.
+  split. apply T.elements_complete. apply T.elements_correct.
+Defined.
+
+End TREE_FOLD_IND.
+
+Section TREE_FOLD_REC.
+
+Variables V A: Type.
+Variable f: A -> T.elt -> V -> A.
+Variable P: T.t V -> A -> Prop.
+Variable init: A.
+Variable m_final: T.t V.
+
+Hypothesis P_compat:
+  forall m m' a,
+  (forall x, T.get x m = T.get x m') ->
+  P m a -> P m' a.
+
+Hypothesis H_base:
+  P (T.empty _) init.
+
+Hypothesis H_rec:
+  forall m a k v,
+  T.get k m = None -> T.get k m_final = Some v -> P m a -> P (T.set k v m) (f a k v).
 
 Theorem fold_rec:
   P m_final (T.fold f m_final init).
 Proof.
-  intros. rewrite T.fold_spec. fold f'.
-  assert (P' (nil ++ T.elements m_final) (List.fold_left f' (T.elements m_final) init)).
-    apply fold_rec_aux.
-    simpl. red; intros; tauto.
-    simpl. red; intros. elim H0.
-    apply T.elements_keys_norepet.
-    apply H_base'.
-  simpl in H. red in H. apply H. red; intros. tauto.
+  apply fold_ind. 
+- intros. apply P_compat with (T.empty V); auto.
+  + intros. rewrite T.gempty. auto.
+- intros. apply P_compat with (T.set k v (T.remove k m)).
+  + intros. rewrite T.gsspec, T.grspec. destruct (T.elt_eq x k); auto. congruence.
+  + apply H_rec; auto. apply T.grs.
 Qed.
 
-End TREE_FOLD_IND.
+End TREE_FOLD_REC.
 
 (** A nonnegative measure over trees *)
 
@@ -1552,7 +1572,7 @@ Theorem cardinal_remove:
 Proof.
   unfold cardinal; intros.
   exploit T.elements_remove; eauto. intros (l1 & l2 & P & Q).
-  rewrite P, Q. rewrite ! app_length. simpl. omega.
+  rewrite P, Q. rewrite ! app_length. simpl. lia.
 Qed.
 
 Theorem cardinal_set:
diff --git a/lib/Ordered.v b/lib/Ordered.v
index 1adbd330..d02892ce 100644
--- a/lib/Ordered.v
+++ b/lib/Ordered.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -70,7 +71,7 @@ Proof (@eq_trans t).
 Lemma lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z.
 Proof Z.lt_trans.
 Lemma lt_not_eq : forall x y : t, lt x y -> ~ eq x y.
-Proof. unfold lt, eq, t; intros. omega. Qed.
+Proof. unfold lt, eq, t; intros. lia. Qed.
 Lemma compare : forall x y : t, Compare lt eq x y.
 Proof.
   intros. destruct (Z.compare x y) as [] eqn:E.
@@ -99,11 +100,11 @@ Lemma eq_trans : forall x y z : t, eq x y -> eq y z -> eq x z.
 Proof (@eq_trans t).
 Lemma lt_trans : forall x y z : t, lt x y -> lt y z -> lt x z.
 Proof.
-  unfold lt; intros. omega.
+  unfold lt; intros. lia.
 Qed.
 Lemma lt_not_eq : forall x y : t, lt x y -> ~ eq x y.
 Proof.
-  unfold lt,eq; intros; red; intros. subst. omega.
+  unfold lt,eq; intros; red; intros. subst. lia.
 Qed.
 Lemma compare : forall x y : t, Compare lt eq x y.
 Proof.
@@ -114,7 +115,7 @@ Proof.
   apply GT.
   assert (Int.unsigned x <> Int.unsigned y).
     red; intros. rewrite <- (Int.repr_unsigned x) in n. rewrite <- (Int.repr_unsigned y) in n. congruence.
-  red. omega.
+  red. lia.
 Defined.
 
 Definition eq_dec : forall x y, { eq x y } + { ~ eq x y } := Int.eq_dec.
diff --git a/lib/Parmov.v b/lib/Parmov.v
index db27e83f..d7cab86a 100644
--- a/lib/Parmov.v
+++ b/lib/Parmov.v
@@ -8,10 +8,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -1106,7 +1107,7 @@ Lemma measure_decreasing_1:
   forall st st',
   dtransition st st' -> measure st' < measure st.
 Proof.
-  induction 1; repeat (simpl; rewrite List.app_length); simpl; omega.
+  induction 1; repeat (simpl; rewrite List.app_length); simpl; lia.
 Qed.
 
 Lemma measure_decreasing_2:
diff --git a/lib/Postorder.v b/lib/Postorder.v
index 3181c4cc..0be7d0b4 100644
--- a/lib/Postorder.v
+++ b/lib/Postorder.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -314,10 +315,10 @@ Proof.
   destruct (wrk s) as [ | [x succs] l].
   discriminate.
   destruct succs as [ | y succs ].
-  inv H. simpl. apply lex_ord_right. omega.
+  inv H. simpl. apply lex_ord_right. lia.
   destruct ((gr s)!y) as [succs'|] eqn:?.
   inv H. simpl. apply lex_ord_left. eapply PTree_Properties.cardinal_remove; eauto.
-  inv H. simpl. apply lex_ord_right. omega.
+  inv H. simpl. apply lex_ord_right. lia.
 Qed.
 
 End POSTORDER.
diff --git a/lib/Printlines.ml b/lib/Printlines.ml
index 453096bc..135672cc 100644
--- a/lib/Printlines.ml
+++ b/lib/Printlines.ml
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Printlines.mli b/lib/Printlines.mli
index 545eb033..ec4a1040 100644
--- a/lib/Printlines.mli
+++ b/lib/Printlines.mli
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Readconfig.mli b/lib/Readconfig.mli
index c81e7786..9e3e03d5 100644
--- a/lib/Readconfig.mli
+++ b/lib/Readconfig.mli
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Readconfig.mll b/lib/Readconfig.mll
index 8abcc407..9d5b692b 100644
--- a/lib/Readconfig.mll
+++ b/lib/Readconfig.mll
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Responsefile.mli b/lib/Responsefile.mli
index ada5a15d..84a58971 100644
--- a/lib/Responsefile.mli
+++ b/lib/Responsefile.mli
@@ -7,10 +7,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Responsefile.mll b/lib/Responsefile.mll
index 35a2dbdb..430c6b4e 100644
--- a/lib/Responsefile.mll
+++ b/lib/Responsefile.mll
@@ -7,10 +7,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Tokenize.mli b/lib/Tokenize.mli
index a9f22c4d..f119dcfa 100644
--- a/lib/Tokenize.mli
+++ b/lib/Tokenize.mli
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Tokenize.mll b/lib/Tokenize.mll
index 70e21d55..bd0f433b 100644
--- a/lib/Tokenize.mll
+++ b/lib/Tokenize.mll
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/UnionFind.v b/lib/UnionFind.v
index bd1b763b..ee24a9a7 100644
--- a/lib/UnionFind.v
+++ b/lib/UnionFind.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -563,10 +564,10 @@ Proof.
     destruct (M.elt_eq x0 (repr uf a)).
     - rewrite e, repr_canonical, dec_eq_true.
       inversion G. subst x'. rewrite dec_eq_false; auto.
-      replace (pathlen uf (repr uf a)) with 0; try omega.
+      replace (pathlen uf (repr uf a)) with 0; try lia.
       symmetry. apply pathlen_none. apply repr_res_none.
     - rewrite (repr_unroll uf x0), (pathlen_unroll uf x0), G.
-      destruct (M.elt_eq (repr uf x') (repr uf a)); omega.
+      destruct (M.elt_eq (repr uf x') (repr uf a)); lia.
   + clear H; simpl in G. rewrite M.gsspec in G. destruct (M.elt_eq x0 (repr uf a)); try discriminate.
     rewrite (repr_none uf x0) by auto. rewrite dec_eq_false; auto.
     symmetry. apply pathlen_zero; auto. apply repr_none; auto.
@@ -595,7 +596,7 @@ Proof.
     - inversion G; clear G. subst.
       rewrite !repr_canonical, dec_eq_true.
       rewrite dec_eq_false; auto.
-      rewrite LENa. rewrite (pathlen_none uf (repr uf b)); try omega.
+      rewrite LENa. rewrite (pathlen_none uf (repr uf b)); try lia.
       apply repr_res_none.
     - rewrite (repr_unroll uf x0), G, ! (pathlen_some _ _ _ G).
       destruct (M.elt_eq _ _); auto.
@@ -613,7 +614,7 @@ Proof.
   intros. repeat rewrite pathlen_merge.
   destruct (M.elt_eq (repr uf a) (repr uf b)). auto.
   rewrite H. destruct (M.elt_eq (repr uf y) (repr uf a)).
-  omega. auto.
+  lia. auto.
 Qed.
 
 (* Path compression *)
diff --git a/lib/Wfsimpl.v b/lib/Wfsimpl.v
index a1e4b4ff..6e52cd36 100644
--- a/lib/Wfsimpl.v
+++ b/lib/Wfsimpl.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
diff --git a/lib/Zbits.v b/lib/Zbits.v
index 6f3acaab..f6dc0c9d 100644
--- a/lib/Zbits.v
+++ b/lib/Zbits.v
@@ -6,10 +6,11 @@
 (*                                                                     *)
 (*  Copyright Institut National de Recherche en Informatique et en     *)
 (*  Automatique.  All rights reserved.  This file is distributed       *)
-(*  under the terms of the GNU General Public License as published by  *)
-(*  the Free Software Foundation, either version 2 of the License, or  *)
-(*  (at your option) any later version.  This file is also distributed *)
-(*  under the terms of the INRIA Non-Commercial License Agreement.     *)
+(*  under the terms of the GNU Lesser General Public License as        *)
+(*  published by the Free Software Foundation, either version 2.1 of   *)
+(*  the License, or  (at your option) any later version.               *)
+(*  This file is also distributed under the terms of the               *)
+(*  INRIA Non-Commercial License Agreement.                            *)
 (*                                                                     *)
 (* *********************************************************************)
 
@@ -33,7 +34,7 @@ Definition eqmod (x y: Z) : Prop := exists k, x = k * modul + y.
 
 Lemma eqmod_refl: forall x, eqmod x x.
 Proof.
-  intros; red. exists 0. omega.
+  intros; red. exists 0. lia.
 Qed.
 
 Lemma eqmod_refl2: forall x y, x = y -> eqmod x y.
@@ -57,7 +58,7 @@ Lemma eqmod_small_eq:
 Proof.
   intros x y [k EQ] I1 I2.
   generalize (Zdiv_unique _ _ _ _ EQ I2). intro.
-  rewrite (Z.div_small x modul I1) in H. subst k. omega.
+  rewrite (Z.div_small x modul I1) in H. subst k. lia.
 Qed.
 
 Lemma eqmod_mod_eq:
@@ -136,11 +137,11 @@ Lemma P_mod_two_p_range:
   forall n p, 0 <= P_mod_two_p p n < two_power_nat n.
 Proof.
   induction n; simpl; intros.
-  - rewrite two_power_nat_O. omega.
+  - rewrite two_power_nat_O. lia.
   - rewrite two_power_nat_S. destruct p.
-    + generalize (IHn p). rewrite Z.succ_double_spec. omega.
-    + generalize (IHn p). rewrite Z.double_spec. omega.
-    + generalize (two_power_nat_pos n). omega.
+    + generalize (IHn p). rewrite Z.succ_double_spec. lia.
+    + generalize (IHn p). rewrite Z.double_spec. lia.
+    + generalize (two_power_nat_pos n). lia.
 Qed.
 
 Lemma P_mod_two_p_eq:
@@ -157,7 +158,7 @@ Proof.
       + destruct (IHn p) as [y EQ]. exists y.
         change (Zpos p~0) with (2 * Zpos p). rewrite EQ.
         rewrite (Z.double_spec (P_mod_two_p p n)). ring.
-      + exists 0; omega.
+      + exists 0; lia.
   }
   intros.
   destruct (H n p) as [y EQ].
@@ -221,8 +222,8 @@ Remark Zshiftin_spec:
   forall b x, Zshiftin b x = 2 * x + (if b then 1 else 0).
 Proof.
   unfold Zshiftin; intros. destruct b.
-  - rewrite Z.succ_double_spec. omega.
-  - rewrite Z.double_spec. omega.
+  - rewrite Z.succ_double_spec. lia.
+  - rewrite Z.double_spec. lia.
 Qed.
 
 Remark Zshiftin_inj:
@@ -231,10 +232,10 @@ Remark Zshiftin_inj:
 Proof.
   intros. rewrite !Zshiftin_spec in H.
   destruct b1; destruct b2.
-  split; [auto|omega].
-  omegaContradiction.
-  omegaContradiction.
-  split; [auto|omega].
+  split; [auto|lia].
+  extlia.
+  extlia.
+  split; [auto|lia].
 Qed.
 
 Remark Zdecomp:
@@ -255,9 +256,9 @@ Proof.
   - subst n. destruct b.
     + apply Z.testbit_odd_0.
     + rewrite Z.add_0_r. apply Z.testbit_even_0.
-  - assert (0 <= Z.pred n) by omega.
+  - assert (0 <= Z.pred n) by lia.
     set (n' := Z.pred n) in *.
-    replace n with (Z.succ n') by (unfold n'; omega).
+    replace n with (Z.succ n') by (unfold n'; lia).
     destruct b.
     + apply Z.testbit_odd_succ; auto.
     + rewrite Z.add_0_r. apply Z.testbit_even_succ; auto.
@@ -273,7 +274,7 @@ Remark Ztestbit_shiftin_succ:
   forall b x n, 0 <= n -> Z.testbit (Zshiftin b x) (Z.succ n) = Z.testbit x n.
 Proof.
   intros. rewrite Ztestbit_shiftin. rewrite zeq_false. rewrite Z.pred_succ. auto.
-  omega. omega.
+  lia. lia.
 Qed.
 
 Lemma Zshiftin_ind:
@@ -287,7 +288,7 @@ Proof.
   - induction p.
     + change (P (Zshiftin true (Z.pos p))). auto.
     + change (P (Zshiftin false (Z.pos p))). auto.
-    + change (P (Zshiftin true 0)). apply H0. omega. auto.
+    + change (P (Zshiftin true 0)). apply H0. lia. auto.
   - compute in H1. intuition congruence.
 Qed.
 
@@ -323,7 +324,7 @@ Remark Ztestbit_succ:
   forall n x, 0 <= n -> Z.testbit x (Z.succ n) = Z.testbit (Z.div2 x) n.
 Proof.
   intros. rewrite Ztestbit_eq. rewrite zeq_false. rewrite Z.pred_succ. auto.
-  omega. omega.
+  lia. lia.
 Qed.
 
 Lemma eqmod_same_bits:
@@ -335,13 +336,13 @@ Proof.
   - change (two_power_nat 0) with 1. exists (x-y); ring.
   - rewrite two_power_nat_S.
     assert (eqmod (two_power_nat n) (Z.div2 x) (Z.div2 y)).
-      apply IHn. intros. rewrite <- !Ztestbit_succ. apply H. rewrite Nat2Z.inj_succ; omega.
-      omega. omega.
+      apply IHn. intros. rewrite <- !Ztestbit_succ. apply H. rewrite Nat2Z.inj_succ; lia.
+      lia. lia.
   destruct H0 as [k EQ].
   exists k. rewrite (Zdecomp x). rewrite (Zdecomp y).
   replace (Z.odd y) with (Z.odd x).
   rewrite EQ. rewrite !Zshiftin_spec. ring.
-  exploit (H 0). rewrite Nat2Z.inj_succ; omega.
+  exploit (H 0). rewrite Nat2Z.inj_succ; lia.
   rewrite !Ztestbit_base. auto.
 Qed.
 
@@ -351,7 +352,7 @@ Lemma same_bits_eqmod:
   Z.testbit x i = Z.testbit y i.
 Proof.
   induction n; intros.
-  - simpl in H0. omegaContradiction.
+  - simpl in H0. extlia.
   - rewrite Nat2Z.inj_succ in H0. rewrite two_power_nat_S in H.
     rewrite !(Ztestbit_eq i); intuition.
     destruct H as [k EQ].
@@ -364,7 +365,7 @@ Proof.
     exploit Zshiftin_inj; eauto. intros [A B].
     destruct (zeq i 0).
     + auto.
-    + apply IHn. exists k; auto. omega.
+    + apply IHn. exists k; auto. lia.
 Qed.
 
 Lemma equal_same_bits:
@@ -383,7 +384,7 @@ Proof.
   replace (- Zshiftin (Z.odd x) y - 1)
      with (Zshiftin (negb (Z.odd x)) (- y - 1)).
   rewrite !Ztestbit_shiftin; auto.
-  destruct (zeq i 0). auto. apply IND. omega.
+  destruct (zeq i 0). auto. apply IND. lia.
   rewrite !Zshiftin_spec. destruct (Z.odd x); simpl negb; ring.
 Qed.
 
@@ -395,12 +396,12 @@ Lemma Ztestbit_above:
 Proof.
   induction n; intros.
   - change (two_power_nat 0) with 1 in H.
-    replace x with 0 by omega.
+    replace x with 0 by lia.
     apply Z.testbit_0_l.
   - rewrite Nat2Z.inj_succ in H0. rewrite Ztestbit_eq. rewrite zeq_false.
     apply IHn. rewrite two_power_nat_S in H. rewrite (Zdecomp x) in H.
-    rewrite Zshiftin_spec in H. destruct (Z.odd x); omega.
-    omega. omega. omega.
+    rewrite Zshiftin_spec in H. destruct (Z.odd x); lia.
+    lia. lia. lia.
 Qed.
 
 Lemma Ztestbit_above_neg:
@@ -412,10 +413,10 @@ Proof.
   intros. set (y := -x-1).
   assert (Z.testbit y i = false).
     apply Ztestbit_above with n.
-    unfold y; omega. auto.
+    unfold y; lia. auto.
   unfold y in H1. rewrite Z_one_complement in H1.
   change true with (negb false). rewrite <- H1. rewrite negb_involutive; auto.
-  omega.
+  lia.
 Qed.
 
 Lemma Zsign_bit:
@@ -425,16 +426,16 @@ Lemma Zsign_bit:
 Proof.
   induction n; intros.
   - change (two_power_nat 1) with 2 in H.
-    assert (x = 0 \/ x = 1) by omega.
+    assert (x = 0 \/ x = 1) by lia.
     destruct H0; subst x; reflexivity.
   - rewrite Nat2Z.inj_succ. rewrite Ztestbit_eq. rewrite zeq_false. rewrite Z.pred_succ.
     rewrite IHn. rewrite two_power_nat_S.
     destruct (zlt (Z.div2 x) (two_power_nat n)); rewrite (Zdecomp x); rewrite Zshiftin_spec.
-    rewrite zlt_true. auto. destruct (Z.odd x); omega.
-    rewrite zlt_false. auto. destruct (Z.odd x); omega.
+    rewrite zlt_true. auto. destruct (Z.odd x); lia.
+    rewrite zlt_false. auto. destruct (Z.odd x); lia.
     rewrite (Zdecomp x) in H; rewrite Zshiftin_spec in H.
-    rewrite two_power_nat_S in H. destruct (Z.odd x); omega.
-    omega. omega.
+    rewrite two_power_nat_S in H. destruct (Z.odd x); lia.
+    lia. lia.
 Qed.
 
 Lemma Ztestbit_le:
@@ -444,16 +445,16 @@ Lemma Ztestbit_le:
   x <= y.
 Proof.
   intros x y0 POS0; revert x; pattern y0; apply Zshiftin_ind; auto; intros.
-  - replace x with 0. omega. apply equal_same_bits; intros.
+  - replace x with 0. lia. apply equal_same_bits; intros.
     rewrite Ztestbit_0. destruct (Z.testbit x i) as [] eqn:E; auto.
     exploit H; eauto. rewrite Ztestbit_0. auto.
   - assert (Z.div2 x0 <= x).
     { apply H0. intros. exploit (H1 (Z.succ i)).
-        omega. rewrite Ztestbit_succ; auto. rewrite Ztestbit_shiftin_succ; auto.
+        lia. rewrite Ztestbit_succ; auto. rewrite Ztestbit_shiftin_succ; auto.
     }
     rewrite (Zdecomp x0). rewrite !Zshiftin_spec.
-    destruct (Z.odd x0) as [] eqn:E1; destruct b as [] eqn:E2; try omega.
-    exploit (H1 0). omega. rewrite Ztestbit_base; auto.
+    destruct (Z.odd x0) as [] eqn:E1; destruct b as [] eqn:E2; try lia.
+    exploit (H1 0). lia. rewrite Ztestbit_base; auto.
     rewrite Ztestbit_shiftin_base. congruence.
 Qed.
 
@@ -464,16 +465,16 @@ Lemma Ztestbit_mod_two_p:
 Proof.
   intros n0 x i N0POS. revert x i; pattern n0; apply natlike_ind; auto.
   - intros. change (two_p 0) with 1. rewrite Zmod_1_r. rewrite Z.testbit_0_l.
-    rewrite zlt_false; auto. omega.
+    rewrite zlt_false; auto. lia.
   - intros. rewrite two_p_S; auto.
     replace (x0 mod (2 * two_p x))
        with (Zshiftin (Z.odd x0) (Z.div2 x0 mod two_p x)).
     rewrite Ztestbit_shiftin; auto. rewrite (Ztestbit_eq i x0); auto. destruct (zeq i 0).
-    + rewrite zlt_true; auto. omega.
+    + rewrite zlt_true; auto. lia.
     + rewrite H0. destruct (zlt (Z.pred i) x).
-      * rewrite zlt_true; auto. omega.
-      * rewrite zlt_false; auto. omega.
-      * omega.
+      * rewrite zlt_true; auto. lia.
+      * rewrite zlt_false; auto. lia.
+      * lia.
     + rewrite (Zdecomp x0) at 3. set (x1 := Z.div2 x0). symmetry.
       apply Zmod_unique with (x1 / two_p x).
       rewrite !Zshiftin_spec. rewrite Z.add_assoc. f_equal.
@@ -481,7 +482,7 @@ Proof.
       f_equal. apply Z_div_mod_eq. apply two_p_gt_ZERO; auto.
       ring.
       rewrite Zshiftin_spec. exploit (Z_mod_lt x1 (two_p x)). apply two_p_gt_ZERO; auto.
-      destruct (Z.odd x0); omega.
+      destruct (Z.odd x0); lia.
 Qed.
 
 Corollary Ztestbit_two_p_m1:
@@ -491,7 +492,7 @@ Proof.
   intros. replace (two_p n - 1) with ((-1) mod (two_p n)).
   rewrite Ztestbit_mod_two_p; auto. destruct (zlt i n); auto. apply Ztestbit_m1; auto.
   apply Zmod_unique with (-1). ring.
-  exploit (two_p_gt_ZERO n). auto. omega.
+  exploit (two_p_gt_ZERO n). auto. lia.
 Qed.
 
 Corollary Ztestbit_neg_two_p:
@@ -499,7 +500,7 @@ Corollary Ztestbit_neg_two_p:
   Z.testbit (- (two_p n)) i = if zlt i n then false else true.
 Proof.
   intros. 
-  replace (- two_p n) with (- (two_p n - 1) - 1) by omega. 
+  replace (- two_p n) with (- (two_p n - 1) - 1) by lia. 
   rewrite Z_one_complement by auto.
   rewrite Ztestbit_two_p_m1 by auto. 
   destruct (zlt i n); auto.
@@ -516,16 +517,16 @@ Proof.
   rewrite (Zdecomp x) in *. rewrite (Zdecomp y) in *.
   transitivity (Z.testbit (Zshiftin (Z.odd x || Z.odd y) (Z.div2 x + Z.div2 y)) i).
   - f_equal. rewrite !Zshiftin_spec.
-    exploit (EXCL 0). omega. rewrite !Ztestbit_shiftin_base. intros.
+    exploit (EXCL 0). lia. rewrite !Ztestbit_shiftin_base. intros.
 Opaque Z.mul.
     destruct (Z.odd x); destruct (Z.odd y); simpl in *; discriminate || ring.
   - rewrite !Ztestbit_shiftin; auto.
     destruct (zeq i 0).
     + auto.
-    + apply IND. omega. intros.
-      exploit (EXCL (Z.succ j)). omega.
+    + apply IND. lia. intros.
+      exploit (EXCL (Z.succ j)). lia.
       rewrite !Ztestbit_shiftin_succ. auto.
-      omega. omega.
+      lia. lia.
 Qed.
 
 (** ** Zero and sign extensions *)
@@ -583,8 +584,8 @@ Lemma Znatlike_ind:
   forall n, P n.
 Proof.
   intros. destruct (zle 0 n).
-  apply natlike_ind; auto. apply H; omega.
-  apply H. omega.
+  apply natlike_ind; auto. apply H; lia.
+  apply H. lia.
 Qed.
 
 Lemma Zzero_ext_spec:
@@ -593,16 +594,16 @@ Lemma Zzero_ext_spec:
 Proof.
   unfold Zzero_ext. induction n using Znatlike_ind.
   - intros. rewrite Ziter_base; auto.
-    rewrite zlt_false. rewrite Ztestbit_0; auto. omega.
+    rewrite zlt_false. rewrite Ztestbit_0; auto. lia.
   - intros. rewrite Ziter_succ; auto.
     rewrite Ztestbit_shiftin; auto.
     rewrite (Ztestbit_eq i x); auto.
     destruct (zeq i 0).
-    + subst i. rewrite zlt_true; auto. omega.
+    + subst i. rewrite zlt_true; auto. lia.
     + rewrite IHn. destruct (zlt (Z.pred i) n).
-      rewrite zlt_true; auto. omega.
-      rewrite zlt_false; auto. omega.
-      omega.
+      rewrite zlt_true; auto. lia.
+      rewrite zlt_false; auto. lia.
+      lia.
 Qed.
 
 Lemma Zsign_ext_spec:
@@ -611,29 +612,29 @@ Lemma Zsign_ext_spec:
 Proof.
   intros n0 x i I0. unfold Zsign_ext. 
   unfold proj_sumbool; destruct (zlt 0 n0) as [N0|N0]; simpl.
-- revert x i I0. pattern n0. apply Zlt_lower_bound_ind with (z := 1); [ | omega ].
+- revert x i I0. pattern n0. apply Zlt_lower_bound_ind with (z := 1); [ | lia ].
   unfold Zsign_ext. intros.
   destruct (zeq x 1).
   + subst x; simpl.
     replace (if zlt i 1 then i else 0) with 0.
     rewrite Ztestbit_base.
     destruct (Z.odd x0); [ apply Ztestbit_m1; auto | apply Ztestbit_0 ].
-    destruct (zlt i 1); omega.
-  + set (x1 := Z.pred x). replace x1 with (Z.succ (Z.pred x1)) by omega.
-    rewrite Ziter_succ by (unfold x1; omega). rewrite Ztestbit_shiftin by auto.
+    destruct (zlt i 1); lia.
+  + set (x1 := Z.pred x). replace x1 with (Z.succ (Z.pred x1)) by lia.
+    rewrite Ziter_succ by (unfold x1; lia). rewrite Ztestbit_shiftin by auto.
     destruct (zeq i 0).
-    * subst i. rewrite zlt_true. rewrite Ztestbit_base; auto. omega.
-    * rewrite H by (unfold x1; omega).
+    * subst i. rewrite zlt_true. rewrite Ztestbit_base; auto. lia.
+    * rewrite H by (unfold x1; lia).
       unfold x1; destruct (zlt (Z.pred i) (Z.pred x)).
-      ** rewrite zlt_true by omega.
-         rewrite (Ztestbit_eq i x0) by omega.
-         rewrite zeq_false by omega. auto.
-      ** rewrite zlt_false by omega.
-         rewrite (Ztestbit_eq (x - 1) x0) by omega.
-         rewrite zeq_false by omega. auto.
-- rewrite Ziter_base by omega. rewrite andb_false_r. 
+      ** rewrite zlt_true by lia.
+         rewrite (Ztestbit_eq i x0) by lia.
+         rewrite zeq_false by lia. auto.
+      ** rewrite zlt_false by lia.
+         rewrite (Ztestbit_eq (x - 1) x0) by lia.
+         rewrite zeq_false by lia. auto.
+- rewrite Ziter_base by lia. rewrite andb_false_r. 
   rewrite Z.testbit_0_l, Z.testbit_neg_r. auto.
-  destruct (zlt i n0); omega.
+  destruct (zlt i n0); lia.
 Qed.
 
 (** [Zzero_ext n x] is [x modulo 2^n] *)
@@ -650,14 +651,14 @@ Qed.
 Lemma Zzero_ext_range:
   forall n x, 0 <= n -> 0 <= Zzero_ext n x < two_p n.
 Proof.
-  intros. rewrite Zzero_ext_mod; auto. apply Z_mod_lt. apply two_p_gt_ZERO. omega.
+  intros. rewrite Zzero_ext_mod; auto. apply Z_mod_lt. apply two_p_gt_ZERO. lia.
 Qed.
 
 Lemma eqmod_Zzero_ext:
   forall n x, 0 <= n -> eqmod (two_p n) (Zzero_ext n x) x.
 Proof.
   intros. rewrite Zzero_ext_mod; auto. apply eqmod_sym. apply eqmod_mod.
-  apply two_p_gt_ZERO. omega.
+  apply two_p_gt_ZERO. lia.
 Qed.
 
 (** Relation between [Zsign_ext n x] and (Zzero_ext n x] *)
@@ -670,13 +671,13 @@ Proof.
   rewrite Zsign_ext_spec by auto.
   destruct (Z.testbit x (n - 1)) eqn:SIGNBIT.
 - set (n' := - two_p n). 
-  replace (Zzero_ext n x - two_p n) with (Zzero_ext n x + n') by (unfold n'; omega).
+  replace (Zzero_ext n x - two_p n) with (Zzero_ext n x + n') by (unfold n'; lia).
   rewrite Z_add_is_or; auto. 
-  rewrite Zzero_ext_spec by auto. unfold n'; rewrite Ztestbit_neg_two_p by omega.
+  rewrite Zzero_ext_spec by auto. unfold n'; rewrite Ztestbit_neg_two_p by lia.
   destruct (zlt i n). rewrite orb_false_r; auto. auto.
-  intros. rewrite Zzero_ext_spec by omega. unfold n'; rewrite Ztestbit_neg_two_p by omega.
+  intros. rewrite Zzero_ext_spec by lia. unfold n'; rewrite Ztestbit_neg_two_p by lia.
   destruct (zlt j n); auto using andb_false_r.
-- replace (Zzero_ext n x - 0) with (Zzero_ext n x) by omega.
+- replace (Zzero_ext n x - 0) with (Zzero_ext n x) by lia.
   rewrite Zzero_ext_spec by auto.
   destruct (zlt i n); auto.
 Qed.
@@ -688,20 +689,20 @@ Lemma Zsign_ext_range:
   forall n x, 0 < n -> -two_p (n-1) <= Zsign_ext n x < two_p (n-1).
 Proof.
   intros.
-  assert (A: 0 <= Zzero_ext n x < two_p n) by (apply Zzero_ext_range; omega).
+  assert (A: 0 <= Zzero_ext n x < two_p n) by (apply Zzero_ext_range; lia).
   assert (B: Z.testbit (Zzero_ext n x) (n - 1) =
              if zlt (Zzero_ext n x) (two_p (n - 1)) then false else true).
   { set (N := Z.to_nat (n - 1)).
     generalize (Zsign_bit N (Zzero_ext n x)). 
     rewrite ! two_power_nat_two_p.
-    rewrite inj_S.  unfold N; rewrite Z2Nat.id by omega.
-    intros X; apply X.  replace (Z.succ (n - 1)) with n by omega. exact A. 
+    rewrite inj_S.  unfold N; rewrite Z2Nat.id by lia.
+    intros X; apply X.  replace (Z.succ (n - 1)) with n by lia. exact A. 
   }
   assert (C: two_p n = 2 * two_p (n - 1)).
-  { rewrite <- two_p_S by omega. f_equal; omega. }
-  rewrite Zzero_ext_spec, zlt_true in B by omega.
-  rewrite Zsign_ext_zero_ext by omega. rewrite B.
-  destruct (zlt (Zzero_ext n x) (two_p (n - 1))); omega.
+  { rewrite <- two_p_S by lia. f_equal; lia. }
+  rewrite Zzero_ext_spec, zlt_true in B by lia.
+  rewrite Zsign_ext_zero_ext by lia. rewrite B.
+  destruct (zlt (Zzero_ext n x) (two_p (n - 1))); lia.
 Qed.
 
 Lemma eqmod_Zsign_ext:
@@ -711,9 +712,9 @@ Proof.
   intros. rewrite Zsign_ext_zero_ext by auto. 
   apply eqmod_trans with (x - 0). 
   apply eqmod_sub. 
-  apply eqmod_Zzero_ext; omega.
+  apply eqmod_Zzero_ext; lia.
   exists (if Z.testbit x (n - 1) then 1 else 0). destruct (Z.testbit x (n - 1)); ring.
-  apply eqmod_refl2; omega.
+  apply eqmod_refl2; lia.
 Qed.
 
 (** ** Decomposition of a number as a sum of powers of two. *)
@@ -743,19 +744,19 @@ Proof.
   {
   induction n; intros.
   simpl. rewrite two_power_nat_O in H0.
-  assert (x = 0) by omega. subst x. omega.
+  assert (x = 0) by lia. subst x. lia.
   rewrite two_power_nat_S in H0. simpl Z_one_bits.
   rewrite (Zdecomp x) in H0. rewrite Zshiftin_spec in H0.
   assert (EQ: Z.div2 x * two_p (i + 1) = powerserie (Z_one_bits n (Z.div2 x) (i + 1))).
-    apply IHn. omega.
-    destruct (Z.odd x); omega.
+    apply IHn. lia.
+    destruct (Z.odd x); lia.
   rewrite two_p_is_exp in EQ. change (two_p 1) with 2 in EQ.
   rewrite (Zdecomp x) at 1. rewrite Zshiftin_spec.
   destruct (Z.odd x); simpl powerserie; rewrite <- EQ; ring.
-  omega. omega.
+  lia. lia.
   }
-  intros. rewrite <- H. change (two_p 0) with 1. omega.
-  omega. exact H0.
+  intros. rewrite <- H. change (two_p 0) with 1. lia.
+  lia. exact H0.
 Qed.
 
 Lemma Z_one_bits_range:
@@ -768,12 +769,12 @@ Proof.
   tauto.
   intros x i j. rewrite Nat2Z.inj_succ.
   assert (In j (Z_one_bits n (Z.div2 x) (i + 1)) -> i <= j < i + Z.succ (Z.of_nat n)).
-    intros. exploit IHn; eauto. omega.
+    intros. exploit IHn; eauto. lia.
   destruct (Z.odd x); simpl.
-  intros [A|B]. subst j. omega. auto.
+  intros [A|B]. subst j. lia. auto.
   auto.
   }
-  intros. generalize (H n x 0 i H0). omega.
+  intros. generalize (H n x 0 i H0). lia.
 Qed.
 
 Remark Z_one_bits_zero:
@@ -787,15 +788,15 @@ Remark Z_one_bits_two_p:
   0 <= x < Z.of_nat n ->
   Z_one_bits n (two_p x) i = (i + x) :: nil.
 Proof.
-  induction n; intros; simpl. simpl in H. omegaContradiction.
+  induction n; intros; simpl. simpl in H. extlia.
   rewrite Nat2Z.inj_succ in H.
-  assert (x = 0 \/ 0 < x) by omega. destruct H0.
-  subst x; simpl. decEq. omega. apply Z_one_bits_zero.
+  assert (x = 0 \/ 0 < x) by lia. destruct H0.
+  subst x; simpl. decEq. lia. apply Z_one_bits_zero.
   assert (Z.odd (two_p x) = false /\ Z.div2 (two_p x) = two_p (x-1)).
     apply Zshiftin_inj. rewrite <- Zdecomp. rewrite !Zshiftin_spec.
-    rewrite <- two_p_S. rewrite Z.add_0_r. f_equal; omega. omega.
+    rewrite <- two_p_S. rewrite Z.add_0_r. f_equal; lia. lia.
   destruct H1 as [A B]; rewrite A; rewrite B.
-  rewrite IHn. f_equal; omega. omega.
+  rewrite IHn. f_equal; lia. lia.
 Qed.
 
 (** ** Recognition of powers of two *)
@@ -820,7 +821,7 @@ Proof.
   induction p; simpl P_is_power2; intros.
 - discriminate.
 - change (Z.pos p~0) with (2 * Z.pos p).  apply IHp in H.
-  rewrite Z.log2_double by xomega. rewrite two_p_S.  congruence.
+  rewrite Z.log2_double by extlia. rewrite two_p_S.  congruence.
   apply Z.log2_nonneg.
 - reflexivity.
 Qed.
@@ -848,7 +849,7 @@ Proof.
   intros.
   assert (x <> 0) by (red; intros; subst x; discriminate).
   apply Z_is_power2_sound in H1. destruct H1 as [P Q]. subst i.
-  split. apply Z.log2_nonneg. apply Z.log2_lt_pow2. omega. rewrite <- two_p_equiv; tauto.
+  split. apply Z.log2_nonneg. apply Z.log2_lt_pow2. lia. rewrite <- two_p_equiv; tauto.
 Qed.
 
 Lemma Z_is_power2_complete:
@@ -858,11 +859,11 @@ Opaque Z.log2.
   assert (A: forall x i, Z_is_power2 x = Some i -> Z_is_power2 (2 * x) = Some (Z.succ i)).
   { destruct x; simpl; intros; try discriminate.
     change (2 * Z.pos p) with (Z.pos (xO p)); simpl.
-    destruct (P_is_power2 p); inv H. rewrite <- Z.log2_double by xomega. auto.
+    destruct (P_is_power2 p); inv H. rewrite <- Z.log2_double by extlia. auto.
   }
   induction i using Znatlike_ind; intros.
-- replace i with 0 by omega. reflexivity.
-- rewrite two_p_S by omega. apply A. apply IHi; omega.
+- replace i with 0 by lia. reflexivity.
+- rewrite two_p_S by lia. apply A. apply IHi; lia.
 Qed.
 
 Definition Z_is_power2m1 (x: Z) : option Z := Z_is_power2 (Z.succ x).
@@ -876,13 +877,13 @@ Qed.
 Lemma Z_is_power2m1_sound:
   forall x i, Z_is_power2m1 x = Some i -> x = two_p i - 1.
 Proof.
-  unfold Z_is_power2m1; intros. apply Z_is_power2_sound in H. omega.
+  unfold Z_is_power2m1; intros. apply Z_is_power2_sound in H. lia.
 Qed.
 
 Lemma Z_is_power2m1_complete:
   forall i, 0 <= i -> Z_is_power2m1 (two_p i - 1) = Some i.
 Proof.
-  intros. unfold Z_is_power2m1. replace (Z.succ (two_p i - 1)) with (two_p i) by omega.
+  intros. unfold Z_is_power2m1. replace (Z.succ (two_p i - 1)) with (two_p i) by lia.
   apply Z_is_power2_complete; auto.
 Qed.
 
@@ -891,8 +892,8 @@ Lemma Z_is_power2m1_range:
   0 <= n -> 0 <= x < two_p n -> Z_is_power2m1 x = Some i -> 0 <= i <= n.
 Proof.
   intros. destruct (zeq x (two_p n - 1)).
-- subst x. rewrite Z_is_power2m1_complete in H1 by auto. inv H1; omega.
-- unfold Z_is_power2m1 in H1. apply (Z_is_power2_range n (Z.succ x) i) in H1; omega.
+- subst x. rewrite Z_is_power2m1_complete in H1 by auto. inv H1; lia.
+- unfold Z_is_power2m1 in H1. apply (Z_is_power2_range n (Z.succ x) i) in H1; lia.
 Qed.
 
 (** ** Relation between bitwise operations and multiplications / divisions by powers of 2 *)
@@ -903,7 +904,7 @@ Lemma Zshiftl_mul_two_p:
   forall x n, 0 <= n -> Z.shiftl x n = x * two_p n.
 Proof.
   intros. destruct n; simpl.
-  - omega.
+  - lia.
   - pattern p. apply Pos.peano_ind.
     + change (two_power_pos 1) with 2. simpl. ring.
     + intros. rewrite Pos.iter_succ. rewrite H0.
@@ -925,7 +926,7 @@ Proof.
       rewrite Pplus_one_succ_l. rewrite two_power_pos_is_exp.
       change (two_power_pos 1) with 2.
       rewrite Zdiv2_div. rewrite Z.mul_comm. apply Zdiv_Zdiv.
-      rewrite two_power_pos_nat. apply two_power_nat_pos. omega.
+      rewrite two_power_pos_nat. apply two_power_nat_pos. lia.
   - compute in H. congruence.
 Qed.
 
@@ -938,12 +939,12 @@ Lemma Zquot_Zdiv:
 Proof.
   intros. destruct (zlt x 0).
   - symmetry. apply Zquot_unique_full with ((x + y - 1) mod y - (y - 1)).
-     + red. right; split. omega.
+     + red. right; split. lia.
        exploit (Z_mod_lt (x + y - 1) y); auto.
-       rewrite Z.abs_eq. omega. omega.
+       rewrite Z.abs_eq. lia. lia.
      + transitivity ((y * ((x + y - 1) / y) + (x + y - 1) mod y) - (y-1)).
        rewrite <- Z_div_mod_eq. ring. auto. ring.
-  - apply Zquot_Zdiv_pos; omega.
+  - apply Zquot_Zdiv_pos; lia.
 Qed.
 
 Lemma Zdiv_shift:
@@ -953,8 +954,8 @@ Proof.
   intros. generalize (Z_div_mod_eq x y H). generalize (Z_mod_lt x y H).
   set (q := x / y). set (r := x mod y). intros.
   destruct (zeq r 0).
-  apply Zdiv_unique with (y - 1). rewrite H1. rewrite e. ring. omega.
-  apply Zdiv_unique with (r - 1). rewrite H1. ring. omega.
+  apply Zdiv_unique with (y - 1). rewrite H1. rewrite e. ring. lia.
+  apply Zdiv_unique with (r - 1). rewrite H1. ring. lia.
 Qed.
 
 (** ** Size of integers, in bits. *)
@@ -967,7 +968,7 @@ Definition Zsize (x: Z) : Z :=
 
 Remark Zsize_pos: forall x, 0 <= Zsize x.
 Proof.
-  destruct x; simpl. omega. compute; intuition congruence. omega.
+  destruct x; simpl. lia. compute; intuition congruence. lia.
 Qed.
 
 Remark Zsize_pos': forall x, 0 < x -> 0 < Zsize x.
@@ -991,8 +992,8 @@ Lemma Ztestbit_size_1:
 Proof.
   intros x0 POS0; pattern x0; apply Zshiftin_pos_ind; auto.
   intros. rewrite Zsize_shiftin; auto.
-  replace (Z.pred (Z.succ (Zsize x))) with (Z.succ (Z.pred (Zsize x))) by omega.
-  rewrite Ztestbit_shiftin_succ. auto. generalize (Zsize_pos' x H); omega.
+  replace (Z.pred (Z.succ (Zsize x))) with (Z.succ (Z.pred (Zsize x))) by lia.
+  rewrite Ztestbit_shiftin_succ. auto. generalize (Zsize_pos' x H); lia.
 Qed.
 
 Lemma Ztestbit_size_2:
@@ -1002,12 +1003,12 @@ Proof.
   - subst x0; intros. apply Ztestbit_0.
   - pattern x0; apply Zshiftin_pos_ind.
     + simpl. intros. change 1 with (Zshiftin true 0). rewrite Ztestbit_shiftin.
-      rewrite zeq_false. apply Ztestbit_0. omega. omega.
+      rewrite zeq_false. apply Ztestbit_0. lia. lia.
     + intros. rewrite Zsize_shiftin in H1; auto.
       generalize (Zsize_pos' _ H); intros.
-      rewrite Ztestbit_shiftin. rewrite zeq_false. apply H0. omega.
-      omega. omega.
-    + omega.
+      rewrite Ztestbit_shiftin. rewrite zeq_false. apply H0. lia.
+      lia. lia.
+    + lia.
 Qed.
 
 Lemma Zsize_interval_1:
@@ -1029,18 +1030,18 @@ Proof.
   assert (Z.of_nat N = n) by (apply Z2Nat.id; auto).
   rewrite <- H1 in H0. rewrite <- two_power_nat_two_p in H0.
   destruct (zeq x 0).
-  subst x; simpl; omega.
+  subst x; simpl; lia.
   destruct (zlt n (Zsize x)); auto.
-  exploit (Ztestbit_above N x (Z.pred (Zsize x))). auto. omega.
-  rewrite Ztestbit_size_1. congruence. omega.
+  exploit (Ztestbit_above N x (Z.pred (Zsize x))). auto. lia.
+  rewrite Ztestbit_size_1. congruence. lia.
 Qed.
 
 Lemma Zsize_monotone:
   forall x y, 0 <= x <= y -> Zsize x <= Zsize y.
 Proof.
   intros. apply Z.ge_le. apply Zsize_interval_2. apply Zsize_pos.
-  exploit (Zsize_interval_1 y). omega.
-  omega.
+  exploit (Zsize_interval_1 y). lia.
+  lia.
 Qed.
 
 (** ** Bit insertion, bit extraction *)
@@ -1070,7 +1071,7 @@ Lemma Zextract_s_spec:
 Proof.
   unfold Zextract_s; intros. rewrite Zsign_ext_spec by auto. rewrite Z.shiftr_spec.
   rewrite Z.add_comm. auto.
-  destruct (zlt i len); omega.
+  destruct (zlt i len); lia.
 Qed.
 
 (** Insert bits [0...len-1] of [y] into bits [to...to+len-1] of [x] *)
@@ -1092,10 +1093,10 @@ Proof.
   { intros; apply Ztestbit_two_p_m1; auto. }
   rewrite Z.lor_spec, Z.land_spec, Z.ldiff_spec by auto. 
   destruct (zle to i).
-- rewrite ! Z.shiftl_spec by auto. rewrite ! M by omega. 
+- rewrite ! Z.shiftl_spec by auto. rewrite ! M by lia. 
   unfold proj_sumbool; destruct (zlt (i - to) len); simpl;
   rewrite andb_true_r, andb_false_r.
-+ rewrite zlt_true by omega. apply orb_false_r.
-+ rewrite zlt_false by omega; auto.
-- rewrite ! Z.shiftl_spec_low by omega. simpl. apply andb_true_r.
++ rewrite zlt_true by lia. apply orb_false_r.
++ rewrite zlt_false by lia; auto.
+- rewrite ! Z.shiftl_spec_low by lia. simpl. apply andb_true_r.
 Qed.