diff --git a/protocol/protocol.tex b/protocol/protocol.tex
index 436c9050..b4e43ad2 100644
--- a/protocol/protocol.tex
+++ b/protocol/protocol.tex
@@ -1223,6 +1223,8 @@ electronic commerce and payment, financial privacy, proof of work, zero knowledg
 \newcommand{\sproutonlypnote}[1]{\notsprout{[\Sprout only]\,\,} \textbf{Note:\,} {#1}}
 \newcommand{\prenuzeropnote}[1]{\notsprout{[Pre-\NUZero]\,\,} \textbf{Note:\,} {#1}}
 \newcommand{\nuzeroonlypnote}[1]{\nuzero{[\NUZero only]\,\,} \textbf{Note:\,} {#1}}
+\newcommand{\fact}[1]{\subparagraph{Fact:}{#1}}
+\newcommand{\facts}[1]{\subparagraph{Facts:}{#1}}
 
 \newcommand{\affiliation}{\hairspace$^\dagger$\;}
 
@@ -4435,7 +4437,7 @@ Let $\ExtractJ \typecolon \GroupJ \rightarrow \GF{\ParamJ{q}}$ be $\Selectu$.
 
 Let $G$ be the subgroup of $\GroupJ$ of order $\ParamJ{r}$ (an odd prime).
 
-Facts: the point $(0, 1) = \ZeroJ$, and the point $(0, -1)$ has order 2 in $\GroupJ$.
+\facts{The point $(0, 1) = \ZeroJ$, and the point $(0, -1)$ has order $2$ in $\GroupJ$.}
 
 % <https://github.com/zcash/zcash/issues/2234#issuecomment-333360977>
 \vspace{2ex}