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I'd like to number theorems as 1.i (2.i) within specified continuous block of paragraphs of a text which is not defined as section or something like that. How to create such theorem numbering?

2
\newcounter{theoremblock}
\renewcommand{\thetheoremblock}{\roman{theoremblock}}
\newtheorem{btheorem}{Theorem}[theoremblock]
\renewcommand{\thebtheorem}{\arabic{btheorem}.\thetheoremblock}
\newenvironment{theoremblock}{\par\refstepcounter{theoremblock}}{}

\begin{theoremblock}
The following theorem will be our main premise.
\begin{btheorem}
All men are mortal.
\end{btheorem}
The next theorem is the secondary premise.
\begin{btheorem}
Socrates is a man.
\end{btheorem}
From these we can draw our conclusion.
\begin{btheorem}
Socrates is mortal.
\end{btheorem}
\end{theoremblock}

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