improve zero_bounds tactic

1 files changed, 15 insertions, 3 deletions

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.