Commit 94ab527c authored by Ralf Jung's avatar Ralf Jung

add an omega auto database

parent a3d083c7
......@@ -100,7 +100,7 @@ Lemma wp_le_true E n1 n2 Q :
Q LitTrueV wp E (Le (LitNat n1) (LitNat n2)) Q.
Proof.
intros; rewrite -(wp_lift_pure_det_step (Le _ _) LitTrue None) ?right_id //;
last by intros; inv_step; eauto with lia.
last by intros; inv_step; eauto with omega.
by rewrite -wp_value'.
Qed.
......@@ -109,7 +109,7 @@ Lemma wp_le_false E n1 n2 Q :
Q LitFalseV wp E (Le (LitNat n1) (LitNat n2)) Q.
Proof.
intros; rewrite -(wp_lift_pure_det_step (Le _ _) LitFalse None) ?right_id //;
last by intros; inv_step; eauto with lia.
last by intros; inv_step; eauto with omega.
by rewrite -wp_value'.
Qed.
......@@ -155,7 +155,7 @@ Lemma wp_le E n1 n2 P Q :
Proof.
intros; destruct (decide (n1 n2)).
* rewrite -wp_le_true; auto.
* rewrite -wp_le_false; auto with lia.
* rewrite -wp_le_false; auto with omega.
Qed.
End lifting.
......@@ -90,7 +90,7 @@ Module LiftingTests.
* rewrite -wp_case_inr //.
rewrite -!later_intro -wp_value' //.
rewrite and_elim_r. apply const_elim_l=>Hle.
by replace n1 with (pred n2) by lia.
by replace n1 with (pred n2) by omega.
Qed.
Lemma Pred_spec n E Q :
......@@ -101,10 +101,10 @@ Module LiftingTests.
apply later_mono, wp_le=> Hn.
- rewrite -wp_case_inl //.
rewrite -!later_intro -wp_value' //.
by replace n with 0 by lia.
by replace n with 0 by omega.
- rewrite -wp_case_inr //.
rewrite -!later_intro -FindPred_spec.
auto using and_intro, const_intro with lia.
auto using and_intro, const_intro with omega.
Qed.
Goal E,
......
......@@ -2,6 +2,7 @@
(* This file is distributed under the terms of the BSD license. *)
(** This file collects general purpose tactics that are used throughout
the development. *)
Require Import Omega.
Require Export Psatz.
Require Export prelude.base.
......@@ -24,6 +25,7 @@ to be combined in combination with other hint database. *)
Hint Extern 998 (_ = _) => f_equal : f_equal.
Hint Extern 999 => congruence : congruence.
Hint Extern 1000 => lia : lia.
Hint Extern 1000 => omega : omega.
(** The tactic [intuition] expands to [intuition auto with *] by default. This
is rather efficient when having big hint databases, or expensive [Hint Extern]
......
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