convert reduce-args to a simplifier

- convert reduce-args to a simplifier. Currently exposed as reduce-args2 tactic until the old tactic code gets removed.
- bug fixes in model_reconstruction trail
  - allow multiple defs to be added with same pool of removed formulas
  - fix tracking of function symbols instead of expressions to filter replay
- add nla_divisions to track (cheap) divisibility lemmas.
-

src/math/lp/nla_divisions.cpp

@@ -0,0 +1,65 @@
+/*++
+Copyright (c) 2017 Microsoft Corporation
+
+Module Name:
+
+  nla_divisions.cpp
+
+Author:
+  Lev Nachmanson (levnach)
+  Nikolaj Bjorner (nbjorner)
+
+Description:
+
+  Check divisions
+
+--*/
+#include "math/lp/nla_core.h"
+
+namespace nla {
+
+    void divisions::add_idivision(lpvar r, lpvar x, lpvar y) {
+        m_idivisions.push_back({r, x, y});
+        m_core.trail().push(push_back_vector(m_idivisions));
+    }
+
+    typedef lp::lar_term term;
+    
+    // y1 >= y2 > 0 & x1 <= x2 => x1/y1 <= x2/y2
+    // y2 <= y1 < 0 & x1 >= x2 => x1/y1 <= x2/y2
+    void divisions::check(vector<lemma>& lemmas) {
+        core& c = m_core;        
+        if (c.use_nra_model()) 
+            return;
+
+        for (auto const & [r, x, y] : m_idivisions) {
+            auto xval = c.val(x);
+            auto yval = c.val(y);
+            auto rval = c.val(r);
+            if (!c.var_is_int(x)) 
+                continue;
+            if (yval == 0)
+                continue;
+            // idiv semantics
+            if (rval == div(xval, yval))
+                continue;
+            for (auto const& [r2, x2, y2] : m_idivisions) {
+                if (r2 == r)
+                    continue;
+                auto x2val = c.val(x2);
+                auto y2val = c.val(y2);
+                auto r2val = c.val(r2);
+                if (yval >= y2val && y2val > 0 && xval <= x2val && rval > r2val) {
+                    new_lemma lemma(c, "y1 >= y2 > 0 & x1 <= x2 => x1/y1 <= x2/y2");
+                    lemma |= ineq(term(y, rational(-1), y2), llc::LT, rational::zero());
+                    lemma |= ineq(y2, llc::LE, rational::zero());
+                    lemma |= ineq(term(x, rational(-1), x2), llc::GT, rational::zero());
+                    lemma |= ineq(term(r, rational(-1), r2), llc::LE, rational::zero());
+                    return;
+                }
+            }
+        }
+        
+    }
+    
+}