From 9043add656177eeac1491a73d2f3ab92bec0013c Mon Sep 17 00:00:00 2001
From: Benjamin Barenblat <bbaren@debian.org>
Date: Sat, 29 Dec 2018 14:31:27 -0500
Subject: Imported Upstream version 8.8.2

---
 plugins/omega/PreOmega.v | 46 ++++++++++++++++++++++++++++++++--------------
 1 file changed, 32 insertions(+), 14 deletions(-)

(limited to 'plugins/omega/PreOmega.v')

diff --git a/plugins/omega/PreOmega.v b/plugins/omega/PreOmega.v
index 5f5f548f..59fd9b80 100644
--- a/plugins/omega/PreOmega.v
+++ b/plugins/omega/PreOmega.v
@@ -1,9 +1,11 @@
 (************************************************************************)
-(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016     *)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
 (*   \VV/  **************************************************************)
-(*    //   *      This file is distributed under the terms of the       *)
-(*         *       GNU Lesser General Public License Version 2.1        *)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
 (************************************************************************)
 
 Require Import Arith Max Min BinInt BinNat Znat Nnat.
@@ -26,7 +28,7 @@ Local Open Scope Z_scope.
      - on Z: Z.min, Z.max, Z.abs, Z.sgn are translated in term of <= < =
      - on nat: + * - S O pred min max Pos.to_nat N.to_nat Z.abs_nat
      - on positive: Zneg Zpos xI xO xH + * - Pos.succ Pos.pred Pos.min Pos.max Pos.of_succ_nat
-     - on N: N0 Npos + * - N.succ N.min N.max N.of_nat Z.abs_N
+     - on N: N0 Npos + * - N.pred N.succ N.min N.max N.of_nat Z.abs_N
 *)
 
 
@@ -48,10 +50,13 @@ Ltac zify_unop_var_or_term t thm a :=
  (remember a as za; zify_unop_core t thm za).
 
 Ltac zify_unop t thm a :=
- (* if a is a scalar, we can simply reduce the unop *)
+ (* If a is a scalar, we can simply reduce the unop. *)
+ (* Note that simpl wasn't enough to reduce [Z.max 0 0] (#5439) *)
  let isz := isZcst a in
  match isz with
-  | true => simpl (t a) in *
+  | true =>
+    let u := eval compute in (t a) in
+    change (t a) with u in *
   | _ => zify_unop_var_or_term t thm a
  end.
 
@@ -165,21 +170,31 @@ Ltac zify_nat_op :=
         rewrite (Nat2Z.inj_mul a b) in *
 
   (* O -> Z0 *)
-  | H : context [ Z.of_nat O ] |- _ => simpl (Z.of_nat O) in H
-  | |- context [ Z.of_nat O ] => simpl (Z.of_nat O)
+  | H : context [ Z.of_nat O ] |- _ => change (Z.of_nat O) with Z0 in H
+  | |- context [ Z.of_nat O ] => change (Z.of_nat O) with Z0
 
   (* S -> number or Z.succ *)
   | H : context [ Z.of_nat (S ?a) ] |- _ =>
      let isnat := isnatcst a in
      match isnat with
-      | true => simpl (Z.of_nat (S a)) in H
+      | true =>
+        let t := eval compute in (Z.of_nat (S a)) in
+        change (Z.of_nat (S a)) with t in H
       | _ => rewrite (Nat2Z.inj_succ a) in H
+      | _ => (* if the [rewrite] fails (most likely a dependent occurence of [Z.of_nat (S a)]),
+                hide [Z.of_nat (S a)] in this one hypothesis *)
+        change (Z.of_nat (S a)) with (Z_of_nat' (S a)) in H
      end
   | |- context [ Z.of_nat (S ?a) ] =>
      let isnat := isnatcst a in
      match isnat with
-      | true => simpl (Z.of_nat (S a))
+      | true =>
+        let t := eval compute in (Z.of_nat (S a)) in
+        change (Z.of_nat (S a)) with t
       | _ => rewrite (Nat2Z.inj_succ a)
+      | _ => (* if the [rewrite] fails (most likely a dependent occurence of [Z.of_nat (S a)]),
+                hide [Z.of_nat (S a)] in the goal *)
+        change (Z.of_nat (S a)) with (Z_of_nat' (S a))
      end
 
   (* atoms of type nat : we add a positivity condition (if not already there) *)
@@ -258,8 +273,8 @@ Ltac zify_positive_op :=
   | |- context [ Zpos (Pos.max ?a ?b) ] => rewrite (Pos2Z.inj_max a b)
 
   (* Pos.sub -> Z.max 1 (Z.sub ... ...) *)
-  | H : context [ Zpos (Pos.sub ?a ?b) ] |- _ => rewrite (Pos2Z.inj_sub a b) in H
-  | |- context [ Zpos (Pos.sub ?a ?b) ] => rewrite (Pos2Z.inj_sub a b)
+  | H : context [ Zpos (Pos.sub ?a ?b) ] |- _ => rewrite (Pos2Z.inj_sub_max a b) in H
+  | |- context [ Zpos (Pos.sub ?a ?b) ] => rewrite (Pos2Z.inj_sub_max a b)
 
   (* Pos.succ -> Z.succ *)
   | H : context [ Zpos (Pos.succ ?a) ] |- _ => rewrite (Pos2Z.inj_succ a) in H
@@ -378,6 +393,10 @@ Ltac zify_N_op :=
   | H : context [ Z.of_N (N.sub ?a ?b) ] |- _ => rewrite (N2Z.inj_sub_max a b) in H
   | |- context [ Z.of_N (N.sub ?a ?b) ] => rewrite (N2Z.inj_sub_max a b)
 
+  (* pred -> minus ... -1 -> Z.max (Z.sub ... -1) 0 *)
+  | H : context [ Z.of_N (N.pred ?a) ] |- _ => rewrite (N.pred_sub a) in H
+  | |- context [ Z.of_N (N.pred ?a) ] => rewrite (N.pred_sub a)
+
   (* N.succ -> Z.succ *)
   | H : context [ Z.of_N (N.succ ?a) ] |- _ => rewrite (N2Z.inj_succ a) in H
   | |- context [ Z.of_N (N.succ ?a) ] => rewrite (N2Z.inj_succ a)
@@ -401,4 +420,3 @@ Ltac zify_N := repeat zify_N_rel; repeat zify_N_op; unfold Z_of_N' in *.
 (** The complete Z-ification tactic *)
 
 Ltac zify := repeat (zify_nat; zify_positive; zify_N); zify_op.
-
-- 
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