diff --git a/src/opt/opt_solver.cpp b/src/opt/opt_solver.cpp
index 091adb9b0..d6877e5db 100644
--- a/src/opt/opt_solver.cpp
+++ b/src/opt/opt_solver.cpp
@@ -190,15 +190,33 @@ namespace opt {
         return m_objective_values;
     }
 
-    expr_ref opt_solver::block_upper_bound(unsigned var, inf_eps const& val) {
+    expr_ref opt_solver::mk_ge(unsigned var, inf_eps const& val) {
         smt::theory_opt& opt = get_optimizer();
-        SASSERT(typeid(smt::theory_inf_arith) == typeid(opt));
-        smt::theory_inf_arith& th = dynamic_cast<smt::theory_inf_arith&>(opt); 
         smt::theory_var v = m_objective_vars[var];
-        return expr_ref(th.block_upper_bound(v, val), m);
+
+        if (typeid(smt::theory_inf_arith) == typeid(opt)) {
+            smt::theory_inf_arith& th = dynamic_cast<smt::theory_inf_arith&>(opt); 
+            return expr_ref(th.mk_ge(v, val), m);
+        }
+
+        if (typeid(smt::theory_mi_arith) == typeid(opt)) {
+            smt::theory_mi_arith& th = dynamic_cast<smt::theory_mi_arith&>(opt); 
+            SASSERT(val.get_infinity().is_zero());
+            return expr_ref(th.mk_ge(v, val.get_numeral()), m);
+        }
+
+        if (typeid(smt::theory_i_arith) == typeid(opt)) {
+            SASSERT(val.get_infinity().is_zero());
+            SASSERT(val.get_infinitesimal().is_zero());
+            smt::theory_i_arith& th = dynamic_cast<smt::theory_i_arith&>(opt); 
+            return expr_ref(th.mk_ge(v, val.get_rational()), m);
+        }
+
+        // difference logic?
+        return expr_ref(m.mk_true(), m);
     }
  
-    expr_ref opt_solver::block_lower_bound(unsigned var, inf_eps const& val) {
+    expr_ref opt_solver::mk_gt(unsigned var, inf_eps const& val) {
         if (val.get_infinity().is_pos()) {
             return expr_ref(m.mk_false(), m);
         }
@@ -207,7 +225,7 @@ namespace opt {
         }
         else {
             inf_rational n = val.get_numeral();            
-            return expr_ref(get_optimizer().block_lower_bound(m_objective_vars[var], n), m);
+            return expr_ref(get_optimizer().mk_gt(m_objective_vars[var], n), m);
         }
     }
 
diff --git a/src/opt/opt_solver.h b/src/opt/opt_solver.h
index 3be11f4bc..f35a79203 100644
--- a/src/opt/opt_solver.h
+++ b/src/opt/opt_solver.h
@@ -75,8 +75,8 @@ namespace opt {
         void reset_objectives();
 
         vector<inf_eps> const& get_objective_values();
-        expr_ref block_lower_bound(unsigned obj_index, inf_eps const& val);
-        expr_ref block_upper_bound(unsigned obj_index, inf_eps const& val);
+        expr_ref mk_gt(unsigned obj_index, inf_eps const& val);
+        expr_ref mk_ge(unsigned obj_index, inf_eps const& val);
 
         static opt_solver& to_opt(solver& s);
         void set_interim_stats(statistics & st);
diff --git a/src/opt/optsmt.cpp b/src/opt/optsmt.cpp
index 1380080ba..ebad310d3 100644
--- a/src/opt/optsmt.cpp
+++ b/src/opt/optsmt.cpp
@@ -121,7 +121,7 @@ namespace opt {
         
         for (unsigned i = 0; i < m_lower.size(); ++i) {
             inf_eps const& v = m_lower[i];
-            disj.push_back(s->block_lower_bound(i, v));
+            disj.push_back(s->mk_gt(i, v));
         }
         constraint = m.mk_or(disj.size(), disj.c_ptr());
         s->assert_expr(constraint);
@@ -149,7 +149,7 @@ namespace opt {
                 smt::theory_var v = m_vars[i]; 
                 mid.push_back((m_upper[i]+m_lower[i])/rational(2));
                 //mid.push_back(m_upper[i]);
-                bound = th.block_upper_bound(v, mid[i]);
+                bound = th.mk_ge(v, mid[i]);
                 bounds.push_back(bound);
             }
             else {
@@ -273,7 +273,7 @@ namespace opt {
         m_upper[i] = mid;
         TRACE("opt", tout << "set lower bound of "; display_objective(tout, i) << " to: " << mid << "\n";
               tout << get_lower(i) << ":" << get_upper(i) << "\n";);
-        s->assert_expr(s->block_upper_bound(i, mid));
+        s->assert_expr(s->mk_ge(i, mid));
     }
 
     std::ostream& optsmt::display_objective(std::ostream& out, unsigned i) const {
diff --git a/src/smt/theory_arith.h b/src/smt/theory_arith.h
index 7979ffc6e..f0211ca9d 100644
--- a/src/smt/theory_arith.h
+++ b/src/smt/theory_arith.h
@@ -999,8 +999,8 @@ namespace smt {
         // -----------------------------------
         virtual inf_eps_rational<inf_rational> maximize(theory_var v);
         virtual theory_var add_objective(app* term);
-        virtual expr* block_lower_bound(theory_var v, inf_rational const& val);
-        expr* block_upper_bound(theory_var v, inf_numeral const& val);
+        virtual expr* mk_gt(theory_var v, inf_rational const& val);
+        virtual expr* mk_ge(theory_var v, inf_numeral const& val);
         void enable_record_conflict(expr* bound);
         void record_conflict(unsigned num_lits, literal const * lits, 
                           unsigned num_eqs, enode_pair const * eqs,
diff --git a/src/smt/theory_arith_aux.h b/src/smt/theory_arith_aux.h
index 90a6db250..96245165f 100644
--- a/src/smt/theory_arith_aux.h
+++ b/src/smt/theory_arith_aux.h
@@ -1044,7 +1044,7 @@ namespace smt {
        \brief: assert val < v
     */
     template<typename Ext>
-    expr* theory_arith<Ext>::block_lower_bound(theory_var v, inf_rational const& val) {
+    expr* theory_arith<Ext>::mk_gt(theory_var v, inf_rational const& val) {
         ast_manager& m = get_manager();
         expr* obj = get_enode(v)->get_owner();
         expr_ref e(m);
@@ -1062,7 +1062,7 @@ namespace smt {
       \brief assert val <= v
     */
     template<typename Ext>
-    expr* theory_arith<Ext>::block_upper_bound(theory_var v, inf_numeral const& val) {
+    expr* theory_arith<Ext>::mk_ge(theory_var v, inf_numeral const& val) {
         ast_manager& m = get_manager();
         context& ctx = get_context();
         std::ostringstream strm;
diff --git a/src/smt/theory_diff_logic.h b/src/smt/theory_diff_logic.h
index 015144c2a..ed52b76fc 100644
--- a/src/smt/theory_diff_logic.h
+++ b/src/smt/theory_diff_logic.h
@@ -310,7 +310,8 @@ namespace smt {
 
         virtual inf_eps_rational<inf_rational> maximize(theory_var v);
         virtual theory_var add_objective(app* term);
-        virtual expr* block_lower_bound(theory_var v, inf_rational const& val);
+        virtual expr* mk_gt(theory_var v, inf_rational const& val);
+        virtual expr* mk_ge(theory_var v, inf_rational const& val) { return 0; }
 
         bool internalize_objective(expr * n, rational const& m, rational& r, objective_term & objective);
 
diff --git a/src/smt/theory_diff_logic_def.h b/src/smt/theory_diff_logic_def.h
index 4202b86a3..1982f2eb7 100644
--- a/src/smt/theory_diff_logic_def.h
+++ b/src/smt/theory_diff_logic_def.h
@@ -1146,7 +1146,7 @@ expr* theory_diff_logic<Ext>::block_objective(theory_var v, inf_rational const&
 }
 
 template<typename Ext>
-expr* theory_diff_logic<Ext>::block_lower_bound(theory_var v, inf_rational const& val) {
+expr* theory_diff_logic<Ext>::mk_gt(theory_var v, inf_rational const& val) {
     expr * o = block_objective(v, val);
     context & ctx = get_context();
     model_ref mdl;
diff --git a/src/smt/theory_opt.h b/src/smt/theory_opt.h
index 774e4abd1..208330bfb 100644
--- a/src/smt/theory_opt.h
+++ b/src/smt/theory_opt.h
@@ -28,9 +28,10 @@ namespace smt {
     class theory_opt {
     public:
         typedef inf_eps_rational<inf_rational> inf_eps;
-        virtual inf_eps_rational<inf_rational> maximize(theory_var v) { UNREACHABLE(); return inf_eps::infinity(); }
+        virtual inf_eps maximize(theory_var v) { UNREACHABLE(); return inf_eps::infinity(); }
         virtual theory_var add_objective(app* term) { UNREACHABLE(); return null_theory_var; }
-        virtual expr* block_lower_bound(theory_var v, inf_rational const& val) { return 0; }
+        virtual expr* mk_gt(theory_var v, inf_rational const& val) { UNREACHABLE(); return 0; }
+        virtual expr* mk_ge(theory_var v, inf_eps const& val) { UNREACHABLE(); return 0; }
     };
 }