How to write the L-shaped symbol in latex?

The symbol is \rightangle, and is in unicode-math or the legacy packages stix, stix2, mathdesign, fdsymbol, and a few others.

It could be built from \rules.

\documentclass{article}
\usepackage{mathtools}
\usepackage[scr=boondoxupr]{mathalpha}
\newcommand*{\Lcorner}{%
    \mathchoice%
        {\mathrel{\makebox[7pt][c]{\rule{.4pt}{7.5pt}\rule{5pt}{.4pt}}}}%
        {\mathrel{\makebox[7pt][c]{\rule{.4pt}{7.5pt}\rule{5pt}{.4pt}}}}%
        {\mathrel{\makebox[5.5pt][c]{\rule{.4pt}{5.25pt}\rule{3.5pt}{.4pt}}}}%
        {\mathrel{\makebox[4pt][c]{\rule{.4pt}{3.75pt}\rule{2.5pt}{.4pt}}}}%
}
\DeclareMathOperator{\Tan}{Tan}

\begin{document}
\(\displaystyle \Lcorner\)
\(\textstyle \Lcorner\)
\(\scriptstyle \Lcorner\)
\(\scriptscriptstyle \Lcorner\)

\(\displaystyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)

\(\textstyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)

\(\scriptstyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)

\(\scriptscriptstyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)
\end{document}

Picture mode to the rescue. The symbol correctly changes size in the various math styles as well as in different font sizes.

\documentclass{article}
\usepackage{amsmath,pict2e,mathrsfs}

\makeatletter
\DeclareRobustCommand{\Lcorner}{\mathbin{\mspace{1mu}\text{\L@corner}\mspace{1mu}}}
\newcommand{\L@corner}{%
  \setlength{\unitlength}{\fontcharht\font`T}%
  \begin{picture}(0.8,1)
  \roundcap
  \Line(0,1)(0,0)(0.8,0)
  \end{picture}%
}
\makeatother

\DeclareMathOperator{\Tan}{Tan}

\begin{document}

\(\displaystyle \Lcorner\)
\(\textstyle \Lcorner\)
\(\scriptstyle \Lcorner\)
\(\scriptscriptstyle \Lcorner\)

\(\displaystyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)

\(\textstyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)

\(\scriptstyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)

\(\scriptscriptstyle \Tan^k( \mathscr{H}^k \Lcorner F(E), y ) = DF(x)[\Tan^k( \mathscr{H}^k \Lcorner E, x)]\)

{\Large $A\Lcorner B$} {\footnotesize $A\Lcorner B$}
\end{document}

I reused the code by Vincent.