From b18cfd89e1e8760185d9f50dd777c1c8096cf807 Mon Sep 17 00:00:00 2001 From: jadep Date: Tue, 12 Mar 2019 15:53:08 -0400 Subject: improve zero_bounds tactic --- src/Util/ZUtil/Tactics/ZeroBounds.v | 18 +++++++++++++++--- 1 file changed, 15 insertions(+), 3 deletions(-) (limited to 'src/Util') diff --git a/src/Util/ZUtil/Tactics/ZeroBounds.v b/src/Util/ZUtil/Tactics/ZeroBounds.v index 86501d84b..c81343b55 100644 --- a/src/Util/ZUtil/Tactics/ZeroBounds.v +++ b/src/Util/ZUtil/Tactics/ZeroBounds.v @@ -1,11 +1,12 @@ Require Import Coq.ZArith.ZArith Coq.omega.Omega. Require Import Crypto.Util.ZUtil.Tactics.PrimeBound. Require Import Crypto.Util.ZUtil.Div. +Require Import Crypto.Util.ZUtil.Le. Local Open Scope Z_scope. Module Z. (* prove that combinations of known positive/nonnegative numbers are positive/nonnegative *) - Ltac zero_bounds' := + Ltac zero_bounds'' := repeat match goal with | [ |- 0 <= _ + _] => apply Z.add_nonneg_nonneg | [ |- 0 <= _ - _] => apply Z.le_0_sub @@ -14,14 +15,25 @@ Module Z. | [ |- 0 <= _ ^ _ ] => apply Z.pow_nonneg | [ |- 0 <= Z.shiftr _ _] => apply Z.shiftr_nonneg | [ |- 0 <= _ mod _] => apply Z.mod_pos_bound - | [ |- 0 < _ + _] => try solve [apply Z.add_pos_nonneg; zero_bounds']; - try solve [apply Z.add_nonneg_pos; zero_bounds'] + | [ |- 0 < _ + _] => try solve [apply Z.add_pos_nonneg; zero_bounds'']; + try solve [apply Z.add_nonneg_pos; zero_bounds''] | [ |- 0 < _ - _] => apply Z.lt_0_sub | [ |- 0 < _ * _] => apply Z.lt_0_mul; left; split | [ |- 0 < _ / _] => apply Z.div_str_pos | [ |- 0 < _ ^ _ ] => apply Z.pow_pos_nonneg end; try omega; try Z.prime_bound; auto. + Ltac zero_bounds' := + repeat match goal with + | |- ?a <> 0 => apply Z.positive_is_nonzero + | |- ?a > 0 => apply Z.lt_gt + | |- ?a >= 0 => apply Z.le_ge + end; + try match goal with + | |- 0 < ?a => zero_bounds'' + | |- 0 <= ?a => zero_bounds'' + end. + Ltac zero_bounds := try omega; try Z.prime_bound; zero_bounds'. Hint Extern 1 => progress zero_bounds : zero_bounds. -- cgit v1.2.3