diff --git a/src/ansi-c/c_typecast.cpp b/src/ansi-c/c_typecast.cpp
index 0bb7fa0da08..85541711fab 100644
--- a/src/ansi-c/c_typecast.cpp
+++ b/src/ansi-c/c_typecast.cpp
@@ -13,7 +13,6 @@ Author: Daniel Kroening, kroening@kroening.com
 #include <cassert>
 
 #include <util/arith_tools.h>
-#include <util/base_type.h>
 #include <util/c_types.h>
 #include <util/config.h>
 #include <util/expr_util.h>
@@ -551,7 +550,7 @@ void c_typecastt::implicit_typecast_followed(
         // very generous:
         // between any two function pointers it's ok
       }
-      else if(base_type_eq(src_sub, dest_sub, ns))
+      else if(src_sub == dest_sub)
       {
         // ok
       }
@@ -565,9 +564,9 @@ void c_typecastt::implicit_typecast_followed(
         // Also generous: between any to scalar types it's ok.
         // We should probably check the size.
       }
-      else if(src_sub.id()==ID_array &&
-              dest_sub.id()==ID_array &&
-              base_type_eq(src_sub.subtype(), dest_sub.subtype(), ns))
+      else if(
+        src_sub.id() == ID_array && dest_sub.id() == ID_array &&
+        src_sub.subtype() == dest_sub.subtype())
       {
         // we ignore the size of the top-level array
         // in the case of pointers to arrays
diff --git a/src/ansi-c/c_typecheck_expr.cpp b/src/ansi-c/c_typecheck_expr.cpp
index be6cba22c55..b852bb16100 100644
--- a/src/ansi-c/c_typecheck_expr.cpp
+++ b/src/ansi-c/c_typecheck_expr.cpp
@@ -14,7 +14,6 @@ Author: Daniel Kroening, kroening@kroening.com
 #include <cassert>
 
 #include <util/arith_tools.h>
-#include <util/base_type.h>
 #include <util/c_types.h>
 #include <util/config.h>
 #include <util/cprover_prefix.h>
@@ -1064,9 +1063,9 @@ void c_typecheck_baset::typecheck_expr_typecast(exprt &expr)
 
   const typet expr_type=follow(expr.type());
 
-  if(expr_type.id()==ID_union &&
-     !base_type_eq(expr_type, op.type(), *this) &&
-     op.id()!=ID_initializer_list)
+  if(
+    expr_type.id() == ID_union && expr_type != op.type() &&
+    op.id() != ID_initializer_list)
   {
     // This is a GCC extension. It's either a 'temporary union',
     // where the argument is one of the member types.
@@ -1080,7 +1079,7 @@ void c_typecheck_baset::typecheck_expr_typecast(exprt &expr)
     // we need to find a member with the right type
     for(const auto &c : to_union_type(expr_type).components())
     {
-      if(base_type_eq(c.type(), op.type(), *this))
+      if(c.type() == op.type())
       {
         // found! build union constructor
         union_exprt union_expr(c.get_name(), op, expr.type());
@@ -1131,7 +1130,7 @@ void c_typecheck_baset::typecheck_expr_typecast(exprt &expr)
   const typet op_type = op.type();
 
   // cast to same type?
-  if(base_type_eq(expr_type, op_type, *this))
+  if(expr_type == op_type)
     return; // it's ok
 
   // vectors?
@@ -2516,8 +2515,7 @@ exprt c_typecheck_baset::do_special_functions(
       expr.arguments().front(), expr.arguments().back());
     equality_expr.add_source_location()=source_location;
 
-    if(!base_type_eq(equality_expr.lhs().type(),
-                     equality_expr.rhs().type(), *this))
+    if(equality_expr.lhs().type() != equality_expr.rhs().type())
     {
       error().source_location = f_op.source_location();
       error() << "equal expects two operands of same type" << eom;
diff --git a/src/ansi-c/c_typecheck_initializer.cpp b/src/ansi-c/c_typecheck_initializer.cpp
index 91b79107fb7..bed63ec7de9 100644
--- a/src/ansi-c/c_typecheck_initializer.cpp
+++ b/src/ansi-c/c_typecheck_initializer.cpp
@@ -19,7 +19,6 @@ Author: Daniel Kroening, kroening@kroening.com
 #include <util/simplify_expr.h>
 #include <util/std_types.h>
 #include <util/string_constant.h>
-#include <util/type_eq.h>
 
 #include "anonymous_member.h"
 
diff --git a/src/cpp/cpp_typecheck_expr.cpp b/src/cpp/cpp_typecheck_expr.cpp
index db7ee51e955..3bf0da62939 100644
--- a/src/cpp/cpp_typecheck_expr.cpp
+++ b/src/cpp/cpp_typecheck_expr.cpp
@@ -16,7 +16,6 @@ Author: Daniel Kroening, kroening@cs.cmu.edu
 #endif
 
 #include <util/arith_tools.h>
-#include <util/base_type.h>
 #include <util/c_types.h>
 #include <util/config.h>
 #include <util/expr_initializer.h>
@@ -2373,9 +2372,9 @@ void cpp_typecheckt::typecheck_method_application(
     if(expr.arguments().size()==func_type.parameters().size())
     {
       // this might be set up for base-class initialisation
-      if(!base_type_eq(expr.arguments().front().type(),
-                      func_type.parameters().front().type(),
-                      *this))
+      if(
+        expr.arguments().front().type() !=
+        func_type.parameters().front().type())
       {
         implicit_typecast(expr.arguments().front(), this_type);
         assert(is_reference(expr.arguments().front().type()));