I am working on this "graph" in tikz, and I would like to know how I can add crossing-out (and not dashed) below the threshold $\mu_A$ (from the beginning of the arrow, until the dot $\mu_A$), such as to explain that $mu$ doesn't go below this threshold.
I put the picture of the code I get, associated with the code, and also a drawing of what I would like to get.

\begin{tikzpicture}[y=1cm, x=1cm, thick, font=\footnotesize]
% axis
\draw [dashed] [line width=1.2pt] (0,0) -- (3,0);
\draw [line width=1.2pt, ->, >=latex'] (3,0) -- coordinate (x axis) (10,0) [solid];
% time points
\draw (3,-4pt) coordinate (Ans) -- (3,4pt) node[anchor=south] {$\mu_A$};
\draw (5,-4pt) coordinate (dev) -- (5,4pt) node[anchor=south] {$\mu_{B}$};
\draw (7,-4pt) coordinate (Re) -- (7,4pt) node[anchor=south] {$\mu_{C}$};
% curly braces
\draw[decorate,decoration={brace,amplitude=3pt,mirror}]
(3,-2.5) coordinate (Ans_unten) -- (5,-2.5) coordinate (dev_unten);
\node at (4,-3){$\triangle^{\text{opt}}$};
\draw[decorate,decoration={brace,amplitude=3pt,mirror}]
(dev_unten) -- (7,-2.5) coordinate (Re_unten);
\node at (6,-3){$\triangle^{\text{impl}}$};
% vertical dotted lines
\draw[dotted] (Ans) -- (Ans_unten);
\draw[dotted] (dev) -- (dev_unten);
\draw[dotted] (Re) -- (Re_unten);
\end{tikzpicture}

