diff --git a/content/shmem_alltoall.tex b/content/shmem_alltoall.tex
index 9b642ddf..8559e788 100644
--- a/content/shmem_alltoall.tex
+++ b/content/shmem_alltoall.tex
@@ -98,7 +98,7 @@
     If \VAR{team} compares equal to \LibConstRef{SHMEM\_TEAM\_INVALID} or is
     otherwise invalid, the behavior is undefined.
 
-    Before any \ac{PE} calls a \FUNC{shmem\_alltoall} routine, the following
+    Before the local \ac{PE} calls a \FUNC{shmem\_alltoall} routine, the following
     conditions must be ensured, otherwise the behavior is undefined:
     \begin{itemize}
         \item The \dest{} array on all \acp{PE} in the team is ready to
diff --git a/content/shmem_broadcast.tex b/content/shmem_broadcast.tex
index b008ac2e..bd66bf8b 100644
--- a/content/shmem_broadcast.tex
+++ b/content/shmem_broadcast.tex
@@ -85,7 +85,7 @@
       the team.
     \end{itemize}
 
-    Before any \ac{PE} calls a broadcast routine, the following conditions
+    Before the local \ac{PE} calls a broadcast routine, the following conditions
     must be ensured, otherwise the behavior is undefined:
     \begin{itemize}
         \item The \dest{} array on all \acp{PE} in the team is ready to
diff --git a/content/shmem_collect.tex b/content/shmem_collect.tex
index 8d973e7b..a658ca93 100644
--- a/content/shmem_collect.tex
+++ b/content/shmem_collect.tex
@@ -88,7 +88,7 @@
     If \VAR{team} compares equal to \LibConstRef{SHMEM\_TEAM\_INVALID} or is
     otherwise invalid, the behavior is undefined.
 
-    Before any \ac{PE} calls a collect routine, the following conditions must
+    Before the local \ac{PE} calls a collect routine, the following conditions must
     be ensured, otherwise the behavior is undefined:
     \begin{itemize}
         \item The \dest{} array on all \acp{PE} in the team is ready to
diff --git a/content/shmem_reductions.tex b/content/shmem_reductions.tex
index cd9e1295..49ebf44f 100644
--- a/content/shmem_reductions.tex
+++ b/content/shmem_reductions.tex
@@ -295,7 +295,7 @@ \subsubsubsection{PROD}
     If \VAR{team} compares equal to \LibConstRef{SHMEM\_TEAM\_INVALID} or is
     otherwise invalid, the behavior is undefined.
 
-    Before any \ac{PE} calls a reduction routine, the following conditions
+    Before the local \ac{PE} calls a reduction routine, the following conditions
     must be ensured, otherwise the behavior is undefined:
     \begin{itemize}
         \item The \dest{} array on all \acp{PE} in the team is ready to
diff --git a/content/shmem_scan.tex b/content/shmem_scan.tex
index 9cd7b201..3e80fa1c 100644
--- a/content/shmem_scan.tex
+++ b/content/shmem_scan.tex
@@ -90,7 +90,7 @@
   \LibConstRef{SHMEM\_TEAM\_INVALID} or is otherwise invalid, the
   behavior is undefined.
 
-  Before any \ac{PE} calls a scan routine, the following conditions must be
+  Before the local \ac{PE} calls a scan routine, the following conditions must be
   ensured, otherwise the behavior is undefined:
   \begin{itemize}
       \item The \dest{} array on all \acp{PE} in the team is ready to accept