Restore exact cases and contradiction

4 files changed, 67 insertions, 7 deletions

diff --git a/test/phase5/exact-case-failure.tex b/test/phase5/exact-case-failure.tex
new file mode 100644
index 0000000..95530d5
--- /dev/null
+++ b/test/phase5/exact-case-failure.tex
@@ -0,0 +1,14 @@
+\begin{proposition}\label{case_failure_exact}
+    Let $A$ be a set.
+    $A=A$.
+\end{proposition}
+\begin{proof}
+    \begin{byCase}
+    \caseOf{$A=\emptyset$.}
+        Follows.
+    \caseOf{$A=\{A\}$.}
+        Follows.
+    \caseOf{$A=\{\emptyset\}$.}
+        Follows.
+    \end{byCase}
+\end{proof}
diff --git a/test/phase5/exact-cases-contradiction.tex b/test/phase5/exact-cases-contradiction.tex
new file mode 100644
index 0000000..1752139
--- /dev/null
+++ b/test/phase5/exact-cases-contradiction.tex
@@ -0,0 +1,45 @@
+\begin{proposition}\label{cases_exact}
+    Let $A$ be a set.
+    $A=A$.
+\end{proposition}
+\begin{proof}
+    \begin{byCase}
+    \caseOf{$A=\emptyset$.}
+        Follows.
+    \caseOf{$A=\{A\}$.}
+        Follows.
+    \caseOf{$A=A$.}
+        Follows.
+    \end{byCase}
+\end{proof}
+
+\begin{proposition}\label{by_contradiction_exact}
+    Let $A$ be a set.
+    $A=A$.
+\end{proposition}
+\begin{proof}
+    Suppose not.
+    Contradiction.
+\end{proof}
+
+\begin{proposition}\label{arbitrary_contradiction_exact}
+    Let $A$ be a set.
+    Suppose $A\neq A$.
+    Then $A=A$.
+\end{proposition}
+\begin{proof}
+    Contradiction.
+\end{proof}
+
+\begin{proposition}\label{omitted_case_exact}
+    Let $A$ be a set.
+    $A=A$.
+\end{proposition}
+\begin{proof}
+    \begin{byCase}
+    \caseOf{$A=A$.}
+        Omitted.
+    \caseOf{$A\neq A$.}
+        Follows.
+    \end{byCase}
+\end{proof}
diff --git a/test/phase5/exact-contradiction-goal.tex b/test/phase5/exact-contradiction-goal.tex
deleted file mode 100644
index 007683f..0000000
--- a/test/phase5/exact-contradiction-goal.tex
+++ /dev/null
@@ -1,7 +0,0 @@
-\begin{proposition}\label{phase5_invalid_contradiction}
-    For all $A$ we have $A = A$.
-\end{proposition}
-\begin{proof}
-    Fix $A$.
-    Contradiction.
-\end{proof}
diff --git a/test/phase5/exact-direct-contradictory.tex b/test/phase5/exact-direct-contradictory.tex
new file mode 100644
index 0000000..e29498e
--- /dev/null
+++ b/test/phase5/exact-direct-contradictory.tex
@@ -0,0 +1,8 @@
+\begin{proposition}\label{direct_contradictory_exact}
+    Let $A$ be a set.
+    Suppose $A\neq A$.
+    Then $A=A$.
+\end{proposition}
+\begin{proof}
+    Follows.
+\end{proof}