\documentclass{article}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\begin{document}
\title{t8\_kolmog01 (TMKqSRb26LHGcHDfxtAf34EBrPWKdTNU6Sp)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_kolmog01 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ m1\_prob\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_prob\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}((r1\_tarski~\\
X3~(k1\_kolmog01~X0~X1~X4~X2)){\unicdbdjded}({\unicdcdadad} X5 .  (m1\_prob\_1~X5~X0~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X6 .  (m1\_prob\_1~X6~X0~X1){\unicdbdjdcd}(((X5 \in X3){\unicdcdcdhd}(X6 \in X4)){\unicdbdjdcd}(r1\_prob\_2~\\
X0~X1~X2~X5~X6)))))))))\end{array}
\label{hyp:ehhdpflgpgmgngpghgadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_prob\_1~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_prob\_1~X4~X0~X1){\unicdbdjdcd}((r1\_prob\_2~\\
X0~X1~X4~X2~X3){\unicdbdjdcd}(r1\_prob\_2~X0~X1~X4~X3~X2))))))\end{array}
\label{hyp:ehbdjdpfahchpgcgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehidpflgpgmgngpghgadbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
((v1\_prob\_1~X1~X0){\unicdcdcdhd}((v4\_prob\_1~X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k1\_zfmisc\_1~X0)))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_prob\_1~X2~X0~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~X1))){\unicdbdjdcd}((r1\_tarski~\\
X3~(k1\_kolmog01~X0~X1~X4~X2)){\unicdbdjdcd}(r1\_tarski~X4~(k1\_kolmog01~X0~X1~X3~\\
X2)))))))\end{array}$$
\end{theorem}
\end{document}
