diff --git a/source/algorithms.tex b/source/algorithms.tex
index ff4c3b38ed..0b447937dd 100644
--- a/source/algorithms.tex
+++ b/source/algorithms.tex
@@ -335,7 +335,7 @@
 another function invocation is specified to synchronize with it,
 and if it is not a memory allocation or deallocation function.
 \begin{note}
-Implementations must ensure that internal synchronization
+Implementations ensure that internal synchronization
 inside standard library functions does not prevent forward progress
 when those functions are executed by threads of execution
 with weakly parallel forward progress guarantees.
diff --git a/source/templates.tex b/source/templates.tex
index 5c6c3bde0a..65b4fb5e03 100644
--- a/source/templates.tex
+++ b/source/templates.tex
@@ -138,7 +138,8 @@
 \begin{note}
 Default arguments for function templates and for member functions of
 class templates are considered definitions for the purpose of template
-instantiation\iref{temp.decls} and must obey the one-definition rule\iref{basic.def.odr}.
+instantiation\iref{temp.decls},
+and thus the one-definition rule\iref{basic.def.odr} applies.
 \end{note}
 
 \pnum