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I am making a slide for presentation. This is a part of slide I am making:

\usepackage{amsmath}

\usepackage{amsfonts}

\usepackage{amssymb}

\usepackage{graphicx}

\usepackage{tikz}

\usepackage{tcolorbox}

\setcounter{MaxMatrixCols}{30}

\usetikzlibrary{shapes, decorations.pathreplacing}

\usepackage[utf8]{inputenc}

\usepackage{mathtools}   

\begin{document}

\begin{frame}{Problem 1}

    \begin{tcolorbox}

    \textit{Case 2:} $c_0(\mathbb{R}) \subset X(\mathbb{R})$\\
let 
\begin{center}

\begin{align}

& x_n + i y_n \in c_0(\mathbb{C})\\

& \Rightarrow x_n+iy_n \longrightarrow 0\\

& \Rightarrow x_n \longrightarrow 0, y_n \longrightarrow 0\\

& \Rightarrow (x_n),(y_n) \in c_0(\mathbb{R})\subset X(\mathbb{R})\\

& \Rightarrow x_n + iy_n \in X(\mathbb{C})
\end{align}

\end{center}
$\Rightarrow$ $c_0(\mathbb{C}) \subset X(\mathbb{C})$\\

Hence, if $Spear(X)$ is not compact, $X$ contains a copy of $c_0$ or $l_1$.\\

    \end{tcolorbox}
\end{frame}

\end{document}

There is a huge gap between the word "let" and where the next equation begins in the frame. I am using the command "align" and "center" and yet couldn't fix the gap. How do I fix it?

Thanks for the help!!

1

Based on https://tex.stackexchange.com/a/386266/36296

\documentclass{beamer}

\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
%\usepackage{graphicx}
\usepackage{tcolorbox}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}  
\usepackage{nccmath}

\begin{document}

\begin{frame}{Problem 1}
    \begin{tcolorbox}
        \textit{Case 2:} $c_0(\mathbb{R}) \subset X(\mathbb{R})$

        let 
        \useshortskip
        \begin{align}
            & x_n + i y_n \in c_0(\mathbb{C})\\
            & \Rightarrow x_n+iy_n \longrightarrow 0\\
            & \Rightarrow x_n \longrightarrow 0, y_n \longrightarrow 0\\
            & \Rightarrow (x_n),(y_n) \in c_0(\mathbb{R})\subset X(\mathbb{R})\\
            & \Rightarrow x_n + iy_n \in X(\mathbb{C})
        \end{align}

        $\Rightarrow$ $c_0(\mathbb{C}) \subset X(\mathbb{C})$

        Hence, if $Spear(X)$ is not compact, $X$ contains a copy of $c_0$ or $l_1$.
    \end{tcolorbox}
\end{frame}

\end{document}

enter image description here

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