Added the homotopic version of Cauchy's theorem.

src/dg/derivative/euclid.tex

@@ -39,7 +39,7 @@
     \frac{f(x + h, y) - f(x, y)}{h} \to \frac{df}{dx}(x, y)
     \]
 
-    as $h \to 0$, uniformly on compact subsets of $(a, b) \times Y$. 
+    as $h \to 0$, uniformly on compacts. 
 \end{proposition}
 \begin{proof}
     Let $[c, d] \subset (a, b)$ and $K \subset Y$ be compact, then by the \hyperref[Mean Value Theorem]{theorem:mean-value-theorem-line}, for any $(x, y) \in [c, d] \times K$ and $h \in \real$ with $x + h$, 

src/dg/derivative/higher.tex

@@ -197,3 +197,5 @@
 
     (2): By (1), $D^n_\sigma f$ is constant. 
 \end{proof}
+
+