diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/Util/ZUtil.v | 12 |
1 files changed, 10 insertions, 2 deletions
diff --git a/src/Util/ZUtil.v b/src/Util/ZUtil.v index e20ff9010..708eb5417 100644 --- a/src/Util/ZUtil.v +++ b/src/Util/ZUtil.v @@ -22,7 +22,7 @@ Hint Resolve (fun a b H => proj1 (Z.mod_pos_bound a b H)) (fun a b H => proj2 (Z which can reasonably be said to "simplify" the goal, should go in this database. *) Create HintDb zsimplify discriminated. -Hint Rewrite Z.div_1_r Z.mul_1_r Z.mul_1_l Z.sub_diag Z.mul_0_r Z.mul_0_l Z.add_0_l Z.add_0_r Z.opp_involutive Z.sub_0_r Z_mod_same_full : zsimplify. +Hint Rewrite Z.div_1_r Z.mul_1_r Z.mul_1_l Z.sub_diag Z.mul_0_r Z.mul_0_l Z.add_0_l Z.add_0_r Z.opp_involutive Z.sub_0_r Z_mod_same_full Z.sub_simpl_r Z.sub_simpl_l : zsimplify. Hint Rewrite Z.div_mul Z.div_1_l Z.div_same Z.mod_same Z.div_small Z.mod_small Z.div_add Z.div_add_l Z.mod_add Z.div_0_l using lia : zsimplify. (** "push" means transform [-f x] to [f (-x)]; "pull" means go the other way *) @@ -44,7 +44,7 @@ Hint Rewrite <- Z.opp_add_distr : pull_Zopp. Hint Rewrite <- Z.div_opp_l_nz Z.div_opp_l_z using lia : push_Zopp. Hint Rewrite <- Z.mul_opp_l : push_Zopp. Hint Rewrite Z.opp_add_distr : push_Zopp. -Hint Rewrite Z.pow_sub_r Z.pow_div_l using lia : push_Zpow. +Hint Rewrite Z.pow_sub_r Z.pow_div_l Z.pow_twice_r using lia : push_Zpow. Hint Rewrite <- Z.pow_sub_r Z.pow_div_l using lia : pull_Zpow. Hint Rewrite Z.mul_add_distr_l Z.mul_add_distr_r Z.mul_sub_distr_l Z.mul_sub_distr_r : push_Zmul. Hint Rewrite <- Z.mul_add_distr_l Z.mul_add_distr_r Z.mul_sub_distr_l Z.mul_sub_distr_r : pull_Zmul. @@ -1056,6 +1056,14 @@ Module Z. Definition mul_div_le' := fun x y z w p H0 H1 H2 H3 => @Z.le_trans _ _ w (@Z.mul_div_le x y z H0 H1 H2 H3) p. Hint Resolve mul_div_le' : zarith. + + Lemma two_p_two_eq_four : 2^(2) = 4. + Proof. reflexivity. Qed. + Hint Rewrite <- two_p_two_eq_four : push_Zpow. + + Lemma two_sub_sub_inner_sub x y z : 2 * x - y - (x - z) = x - y + z. + Proof. clear; lia. Qed. + Hint Rewrite two_sub_sub_inner_sub : zsimplify. End Z. Module Export BoundsTactics. |