diff --git a/src/ast/array_peq.cpp b/src/ast/array_peq.cpp
index 9f4f1b10d..7c2be078d 100644
--- a/src/ast/array_peq.cpp
+++ b/src/ast/array_peq.cpp
@@ -25,9 +25,9 @@ bool is_partial_eq(const func_decl *f) {
     return f->get_name() == PARTIAL_EQ;
 }
 
-bool is_partial_eq(const app *a) {
+bool is_partial_eq(const expr *a) {
     SASSERT(a);
-    return is_partial_eq(a->get_decl());
+    return is_app(a) && is_partial_eq(to_app(a)->get_decl());
 }
 
 app_ref mk_peq(expr *e0, expr *e1, vector<expr_ref_vector> const &indices,
diff --git a/src/ast/array_peq.h b/src/ast/array_peq.h
index 9e71791c1..86a88ad35 100644
--- a/src/ast/array_peq.h
+++ b/src/ast/array_peq.h
@@ -85,7 +85,7 @@ app_ref mk_peq(expr *e0, expr *e1, vector<expr_ref_vector> const &indices,
 
 bool is_partial_eq(const func_decl *f);
 
-bool is_partial_eq(const app *a);
+bool is_partial_eq(const expr *a);
 
 inline bool is_peq(const func_decl *f) { return is_partial_eq(f); }
-inline bool is_peq(const app *a) { return is_partial_eq(a); }
+inline bool is_peq(const expr *a) { return is_partial_eq(a); }
diff --git a/src/qe/mbp/mbp_arrays_tg.cpp b/src/qe/mbp/mbp_arrays_tg.cpp
index da1bb1837..d2744f72a 100644
--- a/src/qe/mbp/mbp_arrays_tg.cpp
+++ b/src/qe/mbp/mbp_arrays_tg.cpp
@@ -63,7 +63,7 @@ struct mbp_array_tg::impl {
     bool is_var(expr *t) { return is_uninterp_const(t) && has_var(t); }
 
     bool is_wr_on_rhs(expr *e) {
-        return is_app(e) && is_partial_eq(to_app(e)) &&
+        return is_partial_eq(e) &&
                is_wr_on_rhs(to_app(e)->get_arg(0), to_app(e)->get_arg(1));
     }
 
@@ -325,7 +325,7 @@ struct mbp_array_tg::impl {
             }
             nt = term;
             is_neg = m.is_not(term, nt);
-            if (is_app(nt) && is_partial_eq(to_app(nt))) {
+            if (is_partial_eq(nt)) {
                 peq p(to_app(nt), m);
                 if (m_use_mdl && is_arr_write(p.lhs())) {
                     mark_seen(nt);
diff --git a/src/qe/mbp/mbp_qel.cpp b/src/qe/mbp/mbp_qel.cpp
index 33fd6cc04..42366b737 100644
--- a/src/qe/mbp/mbp_qel.cpp
+++ b/src/qe/mbp/mbp_qel.cpp
@@ -178,10 +178,9 @@ public:
                tout << "\n";);
 
         std::function<bool(expr *)> non_core = [&](expr *e) {
-            if (is_app(e) && is_partial_eq(to_app(e)))
+            if (is_partial_eq(e))
                 return true;
-            if (m.is_ite(e) || m.is_or(e) || m.is_implies(e) ||
-                m.is_distinct(e))
+            if (m.is_ite(e) || m.is_or(e) || m.is_implies(e) || m.is_distinct(e))
                 return true;
             return red_vars.is_marked(e);
         };
@@ -208,7 +207,7 @@ public:
 
         std::function<bool(expr *)> substituted = [&](expr *e) {
             return
-                (is_app(e) && is_partial_eq(to_app(e))) ||
+                is_partial_eq(e) ||
                 m.is_ite(e) ||
                 red_vars.is_marked(e) ||
                 s_vars.is_marked(e);
diff --git a/src/qe/mbp/mbp_term_graph.cpp b/src/qe/mbp/mbp_term_graph.cpp
index bb8d6028b..6ae669f58 100644
--- a/src/qe/mbp/mbp_term_graph.cpp
+++ b/src/qe/mbp/mbp_term_graph.cpp
@@ -32,7 +32,6 @@ Notes:
 #include "ast/occurs.h"
 #include "ast/rewriter/th_rewriter.h"
 #include "model/model_evaluator.h"
-#include "qe/mbp/mbp_arrays.h"
 #include "util/bit_vector.h"
 #include "util/obj_pair_hashtable.h"
 #include "util/uint_set.h"
@@ -184,7 +183,7 @@ public:
             t->get_root().m_parents.push_back(this);
             m_children.push_back(t);
         }
-        m_is_peq = is_partial_eq(to_app(m_expr));
+        m_is_peq = is_partial_eq(m_expr);
     }
 
     class parents {
@@ -578,7 +577,7 @@ term *term_graph::internalize_term(expr *t) {
     merge_flush();
     SASSERT(res);
     expr* arg = nullptr;
-    if (m.is_not(t, arg) && is_app(arg) && is_partial_eq(to_app(arg))) {
+    if (m.is_not(t, arg) && is_partial_eq(arg)) {
         term* p = get_term(arg);
         SASSERT(p);
         p->set_npeq_child();
@@ -1017,18 +1016,19 @@ void term_graph::to_lits(expr_ref_vector &lits, bool all_equalities,
 // assumes that representatives have already been picked
 void term_graph::to_lits_qe_lite(expr_ref_vector &lits,
                                  std::function<bool(expr *)> *non_core) {
-    DEBUG_CODE(for (auto t : m_terms) SASSERT(t->get_repr()););
-    DEBUG_CODE(for (auto t : m_terms)
-                   SASSERT(!t->is_cgr() || t->get_repr()->is_cgr()););
+    SASSERT(all_of(m_terms, [](term* t) { return !!t->get_repr(); }));
+    SASSERT(all_of(m_terms, [](term* t) { return !t->is_cgr() || t->get_repr()->is_cgr(); }));
     is_non_core not_in_core(non_core);
     check_pred contains_nc(not_in_core, m, false);
     // literals other than eq, neq, distinct
     for (expr *a : m_lits) {
-        if (!is_internalized(a)) continue;
-        if (m_explicit_eq && get_term(a)->is_eq_or_neq()) continue;
-        expr_ref r(m);
-        r = mk_app(a);
-        if (non_core == nullptr || !contains_nc(r)) lits.push_back(r);
+        if (!is_internalized(a)) 
+            continue;
+        if (m_explicit_eq && get_term(a)->is_eq_or_neq()) 
+            continue;
+        expr_ref r(mk_app(a), m);        
+        if (non_core == nullptr || !contains_nc(r)) 
+            lits.push_back(r);
     }
 
     // equalities
@@ -1054,7 +1054,8 @@ void term_graph::to_lits_qe_lite(expr_ref_vector &lits,
             d = mk_app(*(c->get_repr()));
             if (non_core == nullptr || !contains_nc(d)) args.push_back(d);
         }
-        if (args.size() < 2) continue;
+        if (args.size() < 2) 
+            continue;
         if (args.size() == 2)
             distinct = mk_neq(m, args.get(0), args.get(1));
         else
@@ -1600,32 +1601,20 @@ public:
 //  modifies `vars` to keep the variables that could not be eliminated
 void term_graph::qel(app_ref_vector &vars, expr_ref &fml,
                      std::function<bool(expr *)> *non_core) {
-    unsigned i = 0;
-    for (auto v : vars) {
-        if (is_internalized(v)) { vars[i++] = v; }
-    }
-    vars.shrink(i);
+
+    filter(vars, [this](auto v) { return is_internalized(v); });
     pick_repr();
     refine_repr();
 
     expr_ref_vector lits(m);
     to_lits_qe_lite(lits, non_core);
-    if (lits.size() == 0)
-        fml = m.mk_true();
-    else if (lits.size() == 1)
-        fml = lits[0].get();
-    else
-        fml = m.mk_and(lits);
+    fml = mk_and(lits);
 
     // Remove all variables that are do not appear in the formula
     expr_sparse_mark mark;
     mark_all_sub_expr marker(mark);
     quick_for_each_expr(marker, fml);
-    i = 0;
-    for (auto v : vars) {
-        if (mark.is_marked(v)) vars[i++] = v;
-    }
-    vars.shrink(i);
+    filter(vars, [&mark](auto v) { return mark.is_marked(v); });
 }
 
 void term_graph::set_vars(func_decl_ref_vector const &decls, bool exclude) {
diff --git a/src/util/util.h b/src/util/util.h
index 104617e4f..0fed4a13b 100644
--- a/src/util/util.h
+++ b/src/util/util.h
@@ -388,6 +388,14 @@ bool all_of(S const& set, T const& p) {
             return false;
     return true;
 }
+template<typename S, typename T>
+void filter(S& v, T const& p) {
+    unsigned i = 0;
+    for (auto const& e: v)
+        if (p(e))
+            v[i++] = e;
+    v.shrink(i);
+}
 
 template<typename S, typename T>
 bool xor_of(S const& set, T const& p) {