Increase spacing in list

So I’ve been trying for a while now on how to replicate this listing below

And so far all I’ve been able to do is get the vertical spacing and custom enumeration right like so

(Ignore the fact that it’s not the same font)

Here’s the code for it so far:

documentclass{article}
usepackage{enumitem}

begin{document}

renewcommand{labelenumi}{}
renewcommand{labelenumii}{roman{enumi}}
begin{enumerate}
setlengthitemsep{0.5em}   
item Proposition 1quad Aliquam viverra molestie purus LAN:
item Proposition 2quad Aliquam viverra molestie purus
    begin{enumerate}
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    end{enumerate}
item Proposition 3 Aliquam viverra molestie purus
item Proposition 4 Aliquam viverra molestie purus
end{enumerate}

end{document}

The quad commands seem to replicate what the first list is looking like so I’ve tried many ways to make the second level items to align vertically with them but never managed to do so.

documentclass{article}
usepackage{enumitem}
usepackage{calc}

begin{document}

begin{enumerate}[label={Proposition arabic*,},labelwidth=widthof{Proposition 9 }, leftmargin =labelwidth+labelsep]
item Aliquam viverra molestie purus LAN:
item Aliquam viverra molestie purus
    begin{enumerate}[label=roman*,leftmargin=widthof{iii, }]
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    end{enumerate}
item Aliquam viverra molestie purus
item Aliquam viverra molestie purus
end{enumerate}


end{document}

begin{enumerate}[align=left, leftmargin=3.5cm]

documentclass{article}
usepackage{enumitem}

begin{document}

renewcommand{labelenumi}{}
%renewcommand{labelenumii}{roman{enumi}}
begin{enumerate}
setlengthitemsep{0.5em}   
item Proposition 1quad Aliquam viverra molestie purus LAN:
item Proposition 2quad Aliquam viverra molestie purus
    begin{enumerate}[label=roman*,align=left, leftmargin=3.5cm]
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    item Aliquam viverra molestie purus
    end{enumerate}
item Proposition 3 Aliquam viverra molestie purus
item Proposition 4 Aliquam viverra molestie purus
end{enumerate}

end{document}