[Tex/LaTex] How to number cases in proof as case 1(a)

Question

How can I show

Theorem 1. Here starts the theorem.
Proof. This starts proof
Claim 1. This claim contains three sub cases.
Case 1(a). This is first claim first case.
Proof. This is proof of case 1(a).
Case 1(b). This is first claim second case.
Proof. This is proof of case 1(b).
Case 1(c). This is first claim third case.
Proof. This is proof of case 1(c).
Claim 2. This claim contains two sub cases.
Case 2(a). This is second claim first case.
Proof. This is proof of case 2(a).
Case 2(b). This is second claim second case.
Proof. This is proof of case 2(b).\qedhere

Here the problem I am facing is inserting case numbered environment inside of claim. This is the code I am using:

\documentclass[12pt]{article}
\usepackage{amssymb,amsmath,amsthm}
\usepackage[colorlinks=true, allcolors=black]{hyperref}
\usepackage[capitalize,nameinlink]{cleveref}
\usepackage{lipsum}

\newtheorem{theo}{Theorem}

\theoremstyle{definition}
\newtheorem{claim}{Claim}[theo]
\renewcommand\theclaim{\arabic{claim}}
\newtheorem{case}{Case}[claim]

\begin{document}
\begin{theo}
Here starts the theorem.
\end{theo}
\begin{proof}
This starts proof
  \begin{claim}
  This claim contains three sub cases.
    \begin{case}\label{c1} %Case 1.1. showing but Case 1(a) needed
    This is first claim first case.
      \begin{proof}[Proof of \cref{c1}]
      This is proof of case 1(a).%qed symbol not needed here
      \end{proof}
    \end{case}
    \begin{case}
    This is first claim second case.
    \end{case}
    \begin{case}
    This is first claim third case.
    \end{case}
  \end{claim}
  \begin{claim}
  This claim contains two sub cases.
    \begin{case}
    This is second claim first case.
    \end{case}
    \begin{case}\label{c2}
    This is second claim second case.
      \begin{proof}[Proof of \cref{c2}]
      This is proof of case 2(b).\qedhere %qed needed here.
      \end{proof}
    \end{case}
  \end{claim}
\end{proof}
\end{document}

The output of this code is:

Please help so that I can create output as I mentioned above with referencing.

Answer 1

Simply add this line:

\renewcommand\thecase{\theclaim(\alph{case})}