Using cleveref for referencing amsthm objects in beamer

Question

I am a beginner with amsthm, and I'm using cleveref for referencing the theorem s/definitions/lemmas. BTW, all of this is happening in beamer. On using \Cref{label} for definitions, lemmas, and everything else under the sun - I get something of the form Theorem <number>. Everything isn't a theorem! I want Definition <number> and Lemma <number> too. How can I fix this?

I also get this error:

Warning: hyperref package loaded with implicit=false option - disabling cleveref's hyperref support. This situation is not supported by cleveref, and there's no guarantee anything will work. You're on your own! on input line 2370.

\documentclass[aspectratio=169,xcolor=dvipsnames]{beamer}
\setbeamercovered{transparent}
\setbeamertemplate{theorems}[numbered] 
\usetheme{CambridgeUS}
\usepackage{amsmath,amssymb,amsthm,amsfonts,amscd}
\usepackage{cleveref}
\usepackage{tikz}
\usepackage{parskip}
\usepackage{graphicx} % Allows including images
\usepackage{booktabs} % Allows the use of \toprule, \midrule and \bottomrule in tables
\usepackage{hyperref}
\theoremstyle{definition}
\numberwithin{theorem}{section}
\newtheorem{exercise}{Exercise}
\begin{definition}[Program]
\label{prog}
A program is a set of states in a labeled transition system.
\end{definition}
\begin{theorem}
Euler is the best mathematician.
\end{theorem}
\begin{lemma}
\label{xyz}
beamer is amazing.
\end{lemma}
We just saw \Cref{xyz} and \Cref{prog}.

Answer 1

By default, beamer defines the definition to share a counter with the theorem like this:

\newtheorem{definition}[theorem]{\translate{Definition}}

If you want cleveref to distinguish between both environments, you can redefine it without the shared counter:

\documentclass[aspectratio=169,xcolor=dvipsnames]{beamer}
\setbeamercovered{transparent}
\setbeamertemplate{theorems}[numbered] 
\usetheme{CambridgeUS}
\usepackage{cleveref}
\makeatletter
\let\definition@undefined
\makeatother
\newtheorem{definition}{Definition}
\makeatletter
\let\lemma@undefined
\makeatother
\newtheorem{lemma}{Lemma}
\begin{document}
\begin{frame}
\begin{definition}[Program]
\label{prog}
A program is a set of states in a labeled transition system.
\end{definition}
\begin{theorem}
Euler is the best mathematician.
\end{theorem}
\begin{lemma}
\label{xyz}
beamer is amazing.
\end{lemma}
We just saw \Cref{xyz} and \Cref{prog}.
\end{frame}
\end{document}