\documentclass{article}
\newtheorem{axiom}{Axiom}
\newtheorem{theorem}{Theorem}
\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t44\_entropy1 (TMaefKoZquAbYkBJuZwdQq3Zbowpd299EQJ)}
\maketitle
Let $ v1\_matrix\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v4\_matrprob : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_matrprob : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_entropy1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_matrprob : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_partfun3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_matrprob : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_matrprob : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
((v2\_matrprob~X0){\unicdbdjded}(v4\_partfun3~(k2\_entropy1~k1\_numbers~X0)))\end{array}
\label{hyp:ehedddpffgogehchpgahjhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(k5\_matrprob~X0=k18\_rvsum\_1~(k2\_entropy1~k1\_numbers~X0))\end{array}
\label{hyp:ehedcdpffgogehchpgahjhbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m1\_finseq\_1~X1~(k3\_finseq\_2~X0)))){\unicdbdjdcd}(m2\_finseq\_1~(k2\_entropy1~\\
X0~X1)~X0)\end{array}
\label{hyp:egehpflgcdpffgogehchpgahjhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
((v3\_matrprob~X0){\unicdbdjded}(k5\_matrprob~X0=np\_\_1))\end{array}
\label{hyp:eghdpfngbgehchahchpgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((v1\_matrprob~X0){\unicdbdjded}((\\
{\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X1 \in k4\_finseq\_1~\\
X0){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(k1\_seq\_1~X0~X1)))){\unicdcdcdhd}(k18\_rvsum\_1~\\
X0=np\_\_1)))\end{array}
\label{hyp:egfdpfngbgehchahchpgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((v4\_partfun3~X0){\unicdbdjded}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X1 \in k4\_finseq\_1~X0){\unicdbdjdcd}\\
(r1\_xxreal\_0~k6\_numbers~(k1\_seq\_1~X0~X1)))))\end{array}
\label{hyp:egbdpffgogehchpgahjhbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}(((v1\_matrix\_1~\\
X0){\unicdcdcdhd}((v2\_matrprob~X0){\unicdcdcdhd}(v3\_matrprob~X0))){\unicdbdjdcd}((v1\_matrix\_1~X0){\unicdcdcdhd}\\
(v4\_matrprob~X0)))\end{array}
\label{hyp:dgdgcdpfngbgehchahchpgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}(((v1\_matrix\_1~\\
X0){\unicdcdcdhd}(v4\_matrprob~X0)){\unicdbdjdcd}((v1\_matrix\_1~X0){\unicdcdcdhd}((v2\_matrprob~X0){\unicdcdcdhd}\\
(v3\_matrprob~X0))))\end{array}
\label{hyp:dgdgbdpfngbgehchahchpgcg}
\end{equation}
\begin{theorem}\label{thm:ehededpffgogehchpgahjhbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
((v4\_matrprob~X0){\unicdbdjded}(v1\_matrprob~(k2\_entropy1~k1\_numbers~X0)))\end{array}$$
\end{theorem}
\end{document}
