Changer rang numérotation théorèmes dans box

\newboxedtheorem[thcounter=section]{theorem}{Théorème}{theorem}
\newboxedtheorem[thcounter=section, background=yellow!20,
                 titlebackground=black!10,
                 titlecolor=blue!60]{lemma}{Lemme}{lemma}
\renewcommand{\thetheorem}{\thesection.\arabic{theorem}}
\renewcommand{\thelemma}{\thesection.\arabic{lemma}}

\documentclass{article}
\usepackage{amsmath}
\makeatletter
%%%%%%%%%%%%%%%%%%% debut fichier boiboites.sty %%%%%%%%%%%%%%%%%%%%%%
\RequirePackage{xkeyval}
\RequirePackage{tikz}
\RequirePackage{amssymb}

\define@key{boxedtheorem}{titlecolor}{\def\titlecolor{#1}}
\define@key{boxedtheorem}{titlebackground}{\def\titlebackground{#1}}
\define@key{boxedtheorem}{background}{\def\background{#1}}
\define@key{boxedtheorem}{titleboxcolor}{\def\titleboxcolor{#1}}
\define@key{boxedtheorem}{boxcolor}{\def\boxcolor{#1}}
\define@key{boxedtheorem}{thcounter}{\def\thcounter{#1}}
\define@key{boxedtheorem}{size}{\def\size{#1}}
\presetkeys{boxedtheorem}{titlecolor = black, titlebackground = white, background = white,%
                         titleboxcolor = black, boxcolor = black, thcounter=, size = .9\textwidth}{}

\newcommand{\couleurs}[1][]{%
    \setkeys{boxedtheorem}{#1}
    \tikzstyle{fancytitle} =[draw=\titleboxcolor, rounded corners, fill=\titlebackground,
                            text= \titlecolor]
    \tikzstyle{mybox} = [draw=\boxcolor, fill=\background, very thick,
                        rectangle, rounded corners, inner sep=10pt, inner ysep=20pt]
}


%Commande generique pour faire un joli encadre
\newsavebox{\boiboite}
\newcommand{\titre}{Titre}
\newenvironment{boite}[2][]%
    {%
    \renewcommand{\titre}{#2}
    \couleurs[#1]
    \begin{lrbox}{\boiboite}%
     \begin{minipage}[!h]{\size}
    }%
    {%
     \end{minipage}
    \end{lrbox}
    \begin{center}
    \begin{tikzpicture}
    \node [mybox] (box){\usebox{\boiboite}};
    \node[fancytitle, right=10pt] at (box.north west) {\titre};
    \end{tikzpicture}
    \end{center}
    }

\newcommand{\newboxedtheorem}[4][]{%
    \couleurs[#1]
    \@ifnotempty{#4}{%
      \@ifundefined{the#4}{\@ifundefined{\thcounter}{\newcounter{#4}}{%
      \newcounter{#4}[\thcounter ] } } { }%
    }
    \newenvironment{#2}[1][]{%
    \@ifnotempty{#4}{\refstepcounter{#4}}
    \begin{boite}[#1]{\textbf{#3\@ifnotempty{#4}{ \csname the#4\endcsname}}\@ifnotempty{##1}{
    (##1)}}
    }%
    {%
    \end{boite}
    }
}
%%%%%%%%%%%%%%%%%%%% end fichier boiboites.sty %%%%%%%%%%%%%%%%%%%%%%
\makeatother

\newboxedtheorem[thcounter=section]{theorem}{Théorème}{theorem}
\newboxedtheorem[thcounter=section, background=yellow!20,
                 titlebackground=black!10,
                 titlecolor=blue!60]{lemma}{Lemme}{lemma}
\renewcommand{\thetheorem}{\thesection.\arabic{theorem}}
\renewcommand{\thelemma}{\thesection.\arabic{lemma}}

\begin{document}

\section{Une section}

\begin{theorem}
Bla bla bla bla.
\end{theorem}

\begin{lemma}
  Pouet.
\end{lemma}

\begin{theorem}
  Blob.
\end{theorem}

\section{Une autre section}

\begin{theorem}
  Et un.
\end{theorem}

\begin{lemma}
  Et deux.
\end{lemma}

\begin{lemma}
  Et trois.
\end{lemma}

\begin{theorem}
  Foo.
\end{theorem}

\end{document}

\documentclass{article}
\usepackage{amsthm}
\usepackage{varwidth}
\usepackage{tcolorbox}
\tcbuselibrary{skins, theorems}

\tcbset{
  my box/.style={
    enhanced,
    before skip=2mm, after skip=2mm,
    colbacktitle=black!10,
    colback=black!5, colframe=black!70, boxrule=0.2mm,
    attach boxed title to top left={
      xshift=10pt, yshift*=\dimexpr -\tcboxedtitleheight/2\relax},
    boxed title style={arc=1ex, boxrule=0.5pt},
    varwidth boxed title*=-3cm,
    fonttitle=\bfseries,
    #1,
  },
}

\tcbset{
  separator sign none,
  description delimiters parenthesis,
  label separator=-,
}

\newtcbtheorem[number within=section]{theorem}{Théorème}
  {my box={colbacktitle=blue!30}}
  {th}
\newtcbtheorem[number within=section]{lemma}{Lemme}
  {my box={colback=yellow!20, coltitle=blue!60, colbacktitle=black!10}}
  {lemme}

\begin{document}

\section{Première section}

\begin{lemma}{}{technique}
Petit lemme.
\end{lemma}

\begin{proof}
  Facile. Je l'ai écrite dans la marge d'un cahier ; hélas, je n'arrive plus à
  mettre la main dessus...
\end{proof}

\begin{theorem}{Théorème de Pat}{pat}
Ce théorème est le numéro~\ref{th-pat}, il se trouve page~\pageref{th-pat} et
s'appuie sur le lemme~\ref{lemme-technique}.
\end{theorem}

Une conséquence immédiate de ce résultat est le théorème~\ref{th-compl-foo}.

\begin{theorem}{Foo}{compl-foo}
Conséquence triviale du théorème~\ref{th-pat}.
\end{theorem}

\begin{theorem}{}{}
Théorème sans nom.
\end{theorem}

\begin{theorem*}{non numéroté}
Bla bla.
\end{theorem*}

\section{Deuxième section}

\begin{theorem}{}{}
Théorème sans nom.
\end{theorem}

\begin{lemma}{}{}
Un lemme.
\end{lemma}

\begin{lemma}{}{}
Un autre lemme.
\end{lemma}

\begin{theorem}{Bar}{bar}
Résultat très important.
\end{theorem}

\end{document}

En plus, l'idéal serait d'avoir les preuves légèrement plus petites (paramétrables pour ce qui est de la taille).

\usepackage{xpatch}
\xpatchcmd{\proof}{\normalfont}{\normalfont\small}{}{\ERROR}