\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=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
\newcommand\unicdcdcdjd{\cap}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t15\_entropy1 (TMK8uHGQj4suogSSu3FsUZPPCkkoYrjpjFa)}
\maketitle
Let $ v1\_matrprob : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\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 $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ r1\_entropy1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_partfun3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((v4\_partfun3~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((X1 \in k4\_finseq\_1~X0){\unicdcdcdhd}\\
(k1\_seq\_1~X0~X1=k18\_rvsum\_1~X0)){\unicdbdjdcd}(r1\_entropy1~X0~X1))))\end{array}
\label{hyp:ehbdedpffgogehchpgahjhbd}
\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}
\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 .  (m1\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((v1\_matrprob~X0){\unicdbdjdcd}((\\
\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v4\_partfun3~X0)))\end{array}
\label{hyp:dgdgbdpffgogehchpgahjhbd}
\end{equation}
\begin{theorem}\label{thm:ehbdfdpffgogehchpgahjhbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrprob~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k1\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(((X1 \in k4\_finseq\_1~\\
X0){\unicdcdcdhd}(k1\_seq\_1~X0~X1=np\_\_1)){\unicdbdjdcd}(r1\_entropy1~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
