Correct references in last 2 commits

main.tex

@@ -697,6 +697,7 @@ conditions. However, these can be reduced down completely to purely numerical
 problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
 
 \begin{lemma}[Numerical Tests for Sufficiently Large `left' Pseudo-walls]
+	\label{lem:num_test_prob1}
 	Given a Chern character $v$ with positive rank and $\Delta(v) \geq 0$,
 	and a choice of point $P$ on $\Theta_v^-$.
 	Solutions $u=(r,c\ell,d\frac{1}{2}\ell^2)$
@@ -726,7 +727,7 @@ problem with the help of lemma \ref{lem:pseudo_wall_numerical_tests}.
 \end{proof}
 
 \begin{corrolary}[Numerical Tests for All `left' Pseudo-walls]
-\label{cor:numerical-test-left-pseudowalls-rational-betamin}
+\label{cor:num_test_prob2}
 	Given a Chern character $v$ with positive rank and $\Delta(v) \geq 0$,
 	such that $\beta_{-}\coloneqq\beta_{-}(v) \in \QQ$.
 	Solutions $u=(r,c\ell,d\frac{1}{2}\ell^2)$
@@ -985,8 +986,8 @@ u = Chern_Char(*var("r c d", domain="real"))
 \end{sagesilent}
 
 Recall from condition \ref{item:chern1bound:lem:num_test_prob1} in
-lemma \ref{lem:pseudo_wall_numerical_tests}
-(or corrolary \ref{cor:numerical-test-left-pseudowalls-rational-betamin})
+lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2})
 that $\chern_1^{\beta}(u)$ has fixed bounds in terms of $\chern_1^{\beta}(v)$,
 and so we can write:
 
@@ -1019,8 +1020,8 @@ and we shall be varying $\chern_0(E) = r$ to see when certain inequalities fail.
 \subsection{Numerical Inequalities}
 
 This section studies the numerical conditions that $u$ must satisfy as per
-lemma \ref{lem:pseudo_wall_numerical_tests}
-(or corrolary \ref{cor:numerical-test-left-pseudowalls-rational-betamin}).
+lemma \ref{lem:num_test_prob1}
+(or corrolary \ref{cor:num_test_prob2})
 
 \subsubsection{Size of pseudo-wall: $\chern_2^P(u)>0$ }
 \label{subsect-d-bound-radiuscond}