diff --git a/src/util/lp/nla_solver.cpp b/src/util/lp/nla_solver.cpp
index 323d7c00c..73bc26085 100644
--- a/src/util/lp/nla_solver.cpp
+++ b/src/util/lp/nla_solver.cpp
@@ -1107,7 +1107,7 @@ struct solver::imp {
         }
     };
 
-    // we derive a lemma from |x| >= 1 || |y| = 0 => |xy| >= |y|
+    // we derive a lemma from |x| >= 1 || y = 0 => |xy| >= |y|
     bool lemma_for_proportional_factors_on_vars_ge(lpvar i, lpvar j, lpvar k) {
         if (!(abs(vvr(j)) >= rational(1) || vvr(k).is_zero()))
             return false;
@@ -1118,25 +1118,51 @@ struct solver::imp {
         }
         return false;
     }
-
-    // we derive a lemma from |x| <= 1 || |y| = 0 => |xy| <= |y|
-    bool lemma_for_proportional_factors_on_vars_le(lpvar i, lpvar j, lpvar k) {
+    // here xy
+    // we derive a lemma from |x| <= 1 || y = 0 => |xy| <= |y|
+    bool lemma_for_proportional_factors_on_vars_le(lpvar xy, lpvar x, lpvar y) {
         TRACE("nla_solver",
-              tout << "i=";
-              print_var(i, tout);
-              tout << "j=";
-              print_var(j, tout);
-              tout << "k=";
-              print_var(k, tout););
-              
-        if (!(abs(vvr(j)) <= rational(1) || vvr(k).is_zero()))
+              tout << "xy=";
+              print_var(xy, tout);
+              tout << "x=";
+              print_var(x, tout);
+              tout << "y=";
+              print_var(y, tout););
+        const rational & _x = vvr(x);
+        const rational & _y = vvr(y);
+
+        if (!(abs(_x) <= rational(1) || _y.is_zero()))
             return false;
         // the precondition holds
-        if (! (abs(vvr(i)) <= abs(vvr(k)))) {
-            SASSERT(false); // create here
-            return true;
-        }
-        return false;
+        const rational & _xy = vvr(xy);
+        if (abs(_xy) <= abs(_y))
+            return false;
+        // adding x != val(x);
+        lp::lar_term t;
+        t.add_coeff_var(rational(1), x);
+        m_lemma->push_back(ineq(lp::lconstraint_kind::NE, t, _x));
+        
+        t.clear();
+        t.add_coeff_var(rational(1), y);
+        int y_sign;
+        if (_y.is_pos()) {
+            y_sign = 1;
+            m_lemma->push_back(ineq(lp::lconstraint_kind::LE, t, rational::zero()));
+        } else if (_y.is_neg()) {
+            y_sign = -1;
+            m_lemma->push_back(ineq(lp::lconstraint_kind::GE, t, rational::zero()));
+        } else {
+            SASSERT(_y.is_zero());
+            y_sign = 1;
+            m_lemma->push_back(ineq(lp::lconstraint_kind::NE, t, rational::zero()));
+        }            
+        int xy_sign = _xy.is_pos()? 1: -1;
+        t.clear(); // abs(xy) - abs(y) <= 0
+        t.add_coeff_var(rational(xy_sign), xy);
+        t.add_coeff_var(rational(-y_sign), y);
+        m_lemma->push_back(ineq(lp::lconstraint_kind::LE, t, rational::zero()));
+        TRACE("nla_solver", tout<< "lemma: ";print_lemma(*m_lemma, tout););
+        return true;
     }
 
     
@@ -1153,13 +1179,10 @@ struct solver::imp {
               tout << "*";
               print_var(f.m_k, tout);
               );
-        if (lemma_for_proportional_factors_on_vars_ge(var_of_mon, f.m_j, f.m_k)
-            || lemma_for_proportional_factors_on_vars_ge(var_of_mon, f.m_k, f.m_j))
-            return true;
-        if (lemma_for_proportional_factors_on_vars_le(var_of_mon, f.m_j, f.m_k)
-            || lemma_for_proportional_factors_on_vars_le(var_of_mon, f.m_k, f.m_j))
-            return true;
-        return false;
+        return lemma_for_proportional_factors_on_vars_ge(var_of_mon, f.m_j, f.m_k)
+            || lemma_for_proportional_factors_on_vars_ge(var_of_mon, f.m_k, f.m_j)           
+            || lemma_for_proportional_factors_on_vars_le(var_of_mon, f.m_j, f.m_k)
+            || lemma_for_proportional_factors_on_vars_le(var_of_mon, f.m_k, f.m_j);         
     }
     // we derive a lemma from |xy| >= |y| => |x| >= 1 || |y| = 0
     bool basic_lemma_for_mon_proportionality_from_product_to_factors(unsigned i_mon) {