The answer I gave to Disabling "destination with the same identifier" with package silence doesn't apply here, because the amsart class disables loading amsthm and provides the equivalent code, so it's not possible to apply the method of loading amsthm after hyperref.
Here's a hack that allows loading amsthm in the right position, but that defies the changes amsart makes to the standard theorem styles, so this might be rejected if you want to submit the document to the AMS.
\documentclass{amsart}
% make amsthm.sty loadable
\expandafter\let\csname ver@amsthm.sty\endcsname\relax
% remove the definitions that will be redone by amsthm
\let\theoremstyle\relax
\let\newtheoremstyle\relax
\let\pushQED\relax
\let\popQED\relax
\let\qedhere\relax
\let\mathqed\relax
\let\openbox\relax
\let\proof\relax\let\endproof\relax
\usepackage{hyperref}
\usepackage{amsthm}
\usepackage{cleveref}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}[theorem]{Proposition}
\begin{document}
\begin{proposition}
\end{proposition}
\end{document}
Other hacks are necessary for getting back at least the correct spacings.
\documentclass{amsart}
% make amsthm.sty loadable
\expandafter\let\csname ver@amsthm.sty\endcsname\relax
% remove the definitions that will be redone by amsthm
\let\theoremstyle\relax
\let\newtheoremstyle\relax
\let\pushQED\relax
\let\popQED\relax
\let\qedhere\relax
\let\mathqed\relax
\let\openbox\relax
\let\proof\relax\let\endproof\relax
\usepackage{hyperref}
\usepackage{amsthm}
\usepackage{cleveref}
\makeatletter
\newtheoremstyle{standard}% name
{6\p@\@plus6\p@\relax}% Space above
{6\p@\@plus6\p@\relax}% Space below
{\itshape}% Body font
{}% Indent amount (empty = no indent, \parindent = para indent)
{\bfseries}% Thm head font
{.}% Punctuation after thm head
{ }% Space after thm head: " " = normal interword space;
% \newline = linebreak
{}% Thm head spec (can be left empty, meaning `normal')
\makeatother
\theoremstyle{standard}
\newtheorem{theorem}{Theorem}
\newtheorem{proposition}[theorem]{Proposition}
\newcommand{\testA}{words words and other words }
\newcommand{\testB}{\testA\testA\testA\testA\testA}
\begin{document}
\testB
\begin{proposition}\label{test}
\testA
\end{proposition}
\begin{proof}
\testB
\end{proof}
\testB
\begin{proof}
\testB
\end{proof}
\testB
\cref{test}
\end{document}
articlewe can loadamsthmafterhyperref, withamsartthe code ofamsthmis already in the class and the package is not loaded. – egreg Jun 18 '15 at 08:58amsthmto make the mwe minimal. Is there a better solution than not usingamsartor ignoring the warnings? Is there a chance of misformed links? – ronno Jun 18 '15 at 09:37