diff --git a/document/core/valid/matching.rst b/document/core/valid/matching.rst
index 440e3d2b9c..f245bec6cd 100644
--- a/document/core/valid/matching.rst
+++ b/document/core/valid/matching.rst
@@ -76,7 +76,9 @@ A :ref:`heap type <syntax-heaptype>` :math:`\heaptype_1` matches a :ref:`heap ty
 
 * Or :math:`\heaptype_1` is :math:`\NOFUNC` and :math:`\heaptype_2` :ref:`matches <match-heaptype>` :math:`\FUNC`.
 
-* Or :math:`\heaptype_1` is :math:`\NOEXTERN` and :math:`\heaptype_2` :ref:`matches <match-heaptype>` :math:`\EXTERN`.
+* Or :math:`\heaptype_1` is :math:`\NOEXN` and :math:`\heaptype_2` is :math:`\EXN`.
+
+* Or :math:`\heaptype_1` is :math:`\NOEXTERN` and :math:`\heaptype_2` is :math:`\EXTERN`.
 
 * Or :math:`\heaptype_1` is :math:`\BOTH`.
 
@@ -168,9 +170,13 @@ A :ref:`heap type <syntax-heaptype>` :math:`\heaptype_1` matches a :ref:`heap ty
    }
    \qquad
    \frac{
-     C \vdashheaptypematch \X{ht} \matchesheaptype \EXTERN
    }{
-     C \vdashheaptypematch \NOEXTERN \matchesheaptype \X{ht}
+     C \vdashheaptypematch \NOEXN \matchesheaptype \EXN
+   }
+   \qquad
+   \frac{
+   }{
+     C \vdashheaptypematch \NOEXTERN \matchesheaptype \EXTERN
    }
 
 .. math::