diff --git a/text/main.tex b/text/main.tex
index fe7eab6..aa2358a 100644
--- a/text/main.tex
+++ b/text/main.tex
@@ -10,6 +10,7 @@
 \usepackage[ruled,lined,noend,linesnumbered]{algorithm2e}
 \usepackage{amsmath}
 \usepackage{amssymb}
+\usepackage{amsthm}
 \usepackage[french, english]{babel}
 \usepackage{booktabs}
 \usepackage{caption}
diff --git a/text/problem/thething/problem.tex b/text/problem/thething/problem.tex
index 1ab4717..293279f 100644
--- a/text/problem/thething/problem.tex
+++ b/text/problem/thething/problem.tex
@@ -170,7 +170,33 @@ Theorem~\ref{theor:thething-prv} proposes how to achieve the desired privacy for
 \end{theorem}
 % \mk{To discuss.}
 
-Due to space constraints, we omit the proof of Theorem~\ref{theor:thething-prv} and defer it for a longer version of this paper.
+% Due to space constraints, we omit the proof of Theorem~\ref{theor:thething-prv} and defer it for a longer version of this paper.
+\begin{proof}
+  \label{pf:thething-prv}
+  All mechanisms use independent randomness, and therefore for a series of events $S_T = {D_1, \dots, D_T}$ and outputs $(\pmb{o}_1, \dots, \pmb{o}_T) \in O \subseteq \mathcal{O}$ it holds that
+
+  $$Pr[\mathcal{M}(S_T) = (\pmb{o}_1, \dots, \pmb{o}_T)] = \prod_{i \in [1, T]} Pr[\mathcal{M}_i(D_i) = \pmb{o}_i]$$
+
+  Likewise, for any {\thething}-neighboring series of events $S'_T$ of $S_T$ with the same outputs $(\pmb{o}_1, \dots, \pmb{o}_T) \in O \subseteq \mathcal{O}$
+
+  $$Pr[\mathcal{M}(S'_T) = (\pmb{o}_1, \dots, \pmb{o}_T)] = \prod_{i \in [1, T]} Pr[\mathcal{M}_i(D'_i) = \pmb{o}_i]$$
+
+  Since $S_T$ and $S'_T$ are {\thething}-neighboring, there exists $i \in T$ such that $D_i = D'_i$ for a set of {\thethings} with timestamps $L$.
+  Thus, we get
+
+  $$\frac{Pr[\mathcal{M}(S_T) = (\pmb{o}_1, \dots, \pmb{o}_T)]}{Pr[\mathcal{M}(S'_T) = (\pmb{o}_1, \dots, \pmb{o}_T)]} = \prod_{i \in L \cup \{t\}} \frac{Pr[\mathcal{M}_i(D_i) = \pmb{o}_i]}{Pr[\mathcal{M}_i(D'_i) = \pmb{o}_i]}$$
+
+  $D_i$ and $D'_i$ are neighboring for $i \in L \cup \{t\}$.
+  $\mathcal{M}_i$ is differential private and from Definition~\ref{def:dp} we get that $\frac{Pr[\mathcal{M}_i(D_i) = \pmb{o}_i]}{Pr[\mathcal{M}_i(D'_i) = \pmb{o}_i]} \leq e^{\varepsilon_i}$.
+  Hence, we can write
+
+  $$\frac{Pr[\mathcal{M}(S_T) = (\pmb{o}_1, \dots, \pmb{o}_T)]}{Pr[\mathcal{M}(S'_T) = (\pmb{o}_1, \dots, \pmb{o}_T)]} \leq \prod_{i \in L \cup \{t\}} e^{\varepsilon_i} = e^{\sum_{i \in L \cup \{t\}} \varepsilon_i}$$
+
+  For any $O \in \mathcal{O}$ we get $\frac{Pr[\mathcal{M}(S_T) \in O}{Pr[\mathcal{M}(S'_T) \in O]} \leq e^{\sum_{i \in L \cup \{t\}} \varepsilon_i}$.
+  If the formula of Theorem~\ref{theor:thething-prv} holds, then we get $\frac{Pr[\mathcal{M}(S_T) \in O}{Pr[\mathcal{M}(S'_T) \in O]} \leq e^\varepsilon$.
+  Due to Definition~\ref{def:thething-prv} this concludes our proof.
+\end{proof}
+
 
 \subsubsection{{\Thething} privacy mechanisms}
 \label{subsec:lmdk-mechs}