Background color of the title of a theorem, including its numbering

Question

I am starting with a classical theorem environment from amsthm, it has the numbering I want. What I would like is to color the background of the name of the theorem. I have tried to do a color box in the definition itself, but I only get to color the name, unfortunately without the numbering. Basically, my question is: how to get the numbering to be colored as well?

I am aware of the package thmtools but I am only trying to color the background of the name and numbering, not the whole theorem.

MWE:

\documentclass{article}

\usepackage{amsmath,amsthm}

\usepackage{xcolor}
\usepackage{colortbl}

\definecolor{1}{RGB}{255,200,255}
\newtheorem{prop1}{\colorbox{1}{Proposition}}

\begin{document}

\begin{prop1}
For any information provision policy $A$,
\[
\rho^*_A = 1.
\]
\end{prop1}

\end{document}

Answer 1

You could define your own theorem style:

\documentclass{article}

\usepackage{amsmath,amsthm}

\usepackage{xcolor}
\usepackage{colortbl}

\definecolor{1}{RGB}{255,200,255}
\newtheoremstyle{colth}% 
{}{}% 
{\itshape}{}% 
{}{}% 
{ }% 
{\colorbox{1}{\textbf{\thmname{#1}\thmnumber{ #2}}\thmnote{ (#3)}.}}
\newtheorem{prop}{Proposition}
\theoremstyle{colth}
\newtheorem{prop1}[prop]{Proposition}

\begin{document}
\begin{prop}
An ordinary Proposition
\end{prop}

\begin{prop1}
For any information provision policy $A$,
\[
\rho^*_A = 1.
\]
\end{prop1}

\begin{prop}[With a note]
For any information provision policy $A$,
\[
\rho^*_A = 1.
\]
\end{prop}

\begin{prop1}[With a note]
For any information provision policy $A$,
\[
\rho^*_A = 1.
\]
\end{prop1}

\end{document}