diff options
Diffstat (limited to 'library/set')
| -rw-r--r-- | library/set/regularity.tex | 9 | ||||
| -rw-r--r-- | library/set/suc.tex | 2 |
2 files changed, 6 insertions, 5 deletions
diff --git a/library/set/regularity.tex b/library/set/regularity.tex index 794d34f..068d6a8 100644 --- a/library/set/regularity.tex +++ b/library/set/regularity.tex @@ -31,7 +31,7 @@ Then there exists a \in-minimal element of $A$. \end{proposition} \begin{proof} - Follows by \cref{regularity_aux,inhabited}. + Follows by \cref{regularity_aux}. \end{proof} @@ -44,10 +44,11 @@ \begin{proof} \begin{byCase} \caseOf{$A = \emptyset$.} - Straightforward. - \caseOf{$A$ is inhabited.} - Take $a$ such that $a$ is a \in-minimal element of $A$. + Follows by assumption. + \caseOf{$A \neq\emptyset$.} + Take $a$ such that $a$ is a \in-minimal element of $A$ by \cref{nonempty_inhabited,regularity}. Then for all $x\in a$ we have $x\notin A$. + Follows by assumption. \end{byCase} \end{proof}. diff --git a/library/set/suc.tex b/library/set/suc.tex index 3776045..ecfa701 100644 --- a/library/set/suc.tex +++ b/library/set/suc.tex @@ -1,7 +1,7 @@ \import{set/cons.tex} \import{set/regularity.tex} -\subsection{Successor} +\subsection{Ordinal successor} \begin{definition}\label{suc} $\suc{x} = \cons{x}{x}$. |