diff --git a/main.tex b/main.tex
index 32ac155..0320e0d 100644
--- a/main.tex
+++ b/main.tex
@@ -39,7 +39,6 @@
 \usepackage{amsthm} % For theorem style
 \usepackage{thmtools}
 \usepackage{thm-restate}
-\usepackage[capitalise]{cleveref}
 \usepackage{comment}
 \usepackage{tikz}
 \usetikzlibrary{positioning,patterns,shapes}
@@ -49,6 +48,9 @@
 \declaretheorem[sibling=theorem]{lemma}
 \declaretheorem[numberwithin=chapter,style=definition]{definition}
 
+% References
+\usepackage[capitalise]{cleveref}
+
 \usepackage{pdfpages}
 \usepackage{xspace}
 
diff --git a/sec-lattices.tex b/sec-lattices.tex
index 61edf00..e280bdc 100644
--- a/sec-lattices.tex
+++ b/sec-lattices.tex
@@ -62,7 +62,7 @@ In order to define the $\SIVP$ problem and assumption, let us first define the s
   where $\mathcal B(\mathbf c, r)$ denotes the ball of radius $r$ centered in $\mathbf c$.
 \end{definition}
 
-Which leads us to the $\SIVP$ problem, which is finding a set of sufficiently short linearly independent vectors given a lattice basis.
+This leads us to the $\SIVP$ problem, which is finding a set of sufficiently short linearly independent vectors given a lattice basis.
 
 \begin{definition}[$\SIVP$] \label{de:sivp}
   For a dimension $n$ lattice described by a basis $\mathbf B \in \RR^{n \times m}$, and a parameter $\gamma > 0$, the shortest independent vectors problem is to find $n$ linearly independent vectors $v_1, \ldots, v_n$ such that $\| v_1 \| \leq \| v_2 \| \leq \ldots \leq \| v_n \|$ and $\|v_n\| \leq \gamma \cdot \lambda_n(\mathbf B)$.
@@ -73,10 +73,8 @@ In other words, it means that no polynomial time algorithms can solve those prob
 %As explained before, we will rely on the assumption that both algorithmic problems below are hard. Meaning that no (probabilistic) polynomial time algorithms can solve them with non-negligible probability and non-negligible advantage, respectively.
 
 \begin{definition}[The $\SIS$ problem] \label{de:sis} \index{Lattices!Short Integer Solution}
-  Let~$m,q,\beta$ be functions of~$n \in \mathbb{N}$. The Short Integer
-  Solution problem $\SIS_{n,m,q,\beta}$ is, given~$\mathbf{A} \sample
-  U(\Zq^{n \times m})$, find~$\mathbf{x} \in \Lambda_q^{\perp}(\mathbf{A})$
-  with~$0 < \|\mathbf{x}\| \leq \beta$.
+  Let~$m,q,\beta$ be functions of~$n \in \mathbb{N}$.
+  The Short Integer Solution problem $\SIS_{n,m,q,\beta}$ is, given~$\mathbf{A} \sample U(\Zq^{n \times m})$, find~$\mathbf{x} \in \Lambda_q^{\perp}(\mathbf{A})$ with~$0 < \|\mathbf{x}\| \leq \beta$.
 \end{definition}
 
 If~$q \geq \sqrt{n} \beta$ and~$m,\beta \leq \mathsf{poly}(n)$, then $\SIS_{n,m,q,\beta}$ is at least as hard as