Update 0-introduction.tex

blueprint/src/chapters/0-introduction.tex

@@ -473,16 +473,18 @@ \chapter{Introduction}
     $$(\lambda \divides x) \lor (\lambda \divides x-1) \lor (\lambda \divides x+1).$$
     We proceed by analysing each case:
     \begin{itemize}
-        \item Case $\lambda \divides x$. By properties of divisibility
+        \item Case $\lambda \divides x$. \\
+              By properties of divisibility, we have that
               $\lambda \divides x(x - 1)(x - (\eta + 1))$.
-        \item Case $\lambda \divides x-1$. By properties of divisibility
+        \item Case $\lambda \divides x-1$. \\
+              By properties of divisibility, we have that
               $\lambda \divides x(x - 1)(x - (\eta + 1))$.
         \item Case $\lambda \divides x+1$.\\
-              By properties of divisibility it suffices to prove that
+              By properties of divisibility, it suffices to prove that
               $$\lambda \divides x - (\eta + 1) = x + 1 - (\eta - 1 + 3).$$
               By definition of $\lambda$, we have that
               $$x + 1 - (\eta - 1 + 3) = x + 1 - (\lambda + 3).$$
-              By properties of divisibility and \Cref{lmm:lambda_dvd_three},
+              By properties of divisibility and \Cref{lmm:lambda_dvd_three}, we can deduce that
               $\lambda \divides \lambda + 3$.\\
               Therefore, by properties of divisibility, we can conclude that
               $$\lambda \divides x(x - 1)(x - (\eta + 1)).$$