Update filter.tex

1 files changed, 10 insertions, 0 deletions

diff --git a/library/set/filter.tex b/library/set/filter.tex
index e196b64..4537b81 100644
--- a/library/set/filter.tex
+++ b/library/set/filter.tex
@@ -69,6 +69,16 @@
     Then $B\in\principalfilter{S}{A}$ iff $A\subseteq B$.
 \end{proposition}
 
+\begin{proposition}\label{principalfilter_bottom}
+    Suppose $A\subseteq S$.
+    Then $A\in\principalfilter{S}{A}$.
+\end{proposition}
+
+\begin{proposition}\label{principalfilter_top}
+    Suppose $A\subseteq S$.
+    Then $S\in\principalfilter{S}{A}$.
+\end{proposition}
+
 \begin{proposition}\label{principalfilter_is_filter}
     Suppose $A\subseteq S$.
     Suppose $A$ is inhabited.