\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t42\_entropy1 (TMFRRAsFKSZajV5RaZUsWeuwKdEfB5d6EbN)}
\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 $ k5\_matrprob : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_entropy1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_matrprob : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ 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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{{k18\_rvsum\_1}~{({{k6\_finseq\_1}~{k1\_numbers}})}}={k6\_numbers}}\label{hyp:ehhdcdpfchghdhfhngpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\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}\\
({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k3\_finseq\_2~k1\_numbers)){\unicdbdjdcd}(((k3\_finseq\_1~\\
X1=k3\_finseq\_1~X0){\unicdcdcdhd}((k1\_matrprob~k1\_numbers~X1~np\_\_1=k1\_matrprob~\\
k1\_numbers~X0~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
((r1\_xxreal\_0~np\_\_1~X2){\unicdbdjdcd}((r1\_xxreal\_0~(k3\_finseq\_1~X0)~X2){\unicdcdcdid}(\\
k1\_matrprob~k1\_numbers~X1~(k2\_nat\_1~X2~np\_\_1)=k8\_finseq\_1~k1\_numbers~\\
(k1\_matrprob~k1\_numbers~X1~X2)~(k1\_matrprob~k1\_numbers~X0~(k2\_nat\_1~\\
X2~np\_\_1)))))))){\unicdbdjdcd}(k5\_matrprob~X0=k18\_rvsum\_1~(k1\_matrprob~k1\_numbers~\\
X1~(k3\_finseq\_1~X0)))))\end{array}
\label{hyp:ehddidpffgogehchpgahjhbd}
\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}\\
((k3\_finseq\_1~X0=k6\_numbers){\unicdbdjdcd}(k5\_matrprob~X0=k6\_numbers))\end{array}
\label{hyp:ehcdddpfngbgehchahchpgcg}
\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}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_xboole\_0}~{({{k6\_finseq\_1}~{X0}})}}}\label{hyp:ggdgfdpfggjgogdhfgbhpfbd}
\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 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_matrix\_1~X1){\unicdcdcdhd}\\
(m2\_finseq\_1~X1~(k3\_finseq\_2~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~\\
X2~X0){\unicdbdjdcd}(((k3\_finseq\_1~X1=k6\_numbers){\unicdbdjdcd}((X2=k2\_entropy1~X0~X1){\unicdbdjded}\\
(X2=k1\_xboole\_0))){\unicdcdcdhd}((k3\_finseq\_1~X1{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}((X2=k2\_entropy1~\\
X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  (m2\_finseq\_1~X3~(k3\_finseq\_2~X0)){\unicdcdcdhd}((X2=k1\_matrprob~\\
X0~X3~(k3\_finseq\_1~X1)){\unicdcdcdhd}((k3\_finseq\_1~X3=k3\_finseq\_1~X1){\unicdcdcdhd}((k1\_matrprob~\\
X0~X3~np\_\_1=k1\_matrprob~X0~X1~np\_\_1){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_subset\_1~\\
X4~k1\_numbers~k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~np\_\_1~X4){\unicdbdjdcd}((r1\_xxreal\_0~\\
(k3\_finseq\_1~X1)~X4){\unicdcdcdid}(k1\_matrprob~X0~X3~(k2\_nat\_1~X4~np\_\_1)=k8\_finseq\_1~\\
X0~(k1\_matrprob~X0~X3~X4)~(k1\_matrprob~X0~X1~(k2\_nat\_1~X4~np\_\_1)))))))))))))))\end{array}
\label{hyp:egfdpffgogehchpgahjhbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpffgogehchpgahjhbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_matrix\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~(k3\_finseq\_2~k1\_numbers))){\unicdbdjdcd}\\
(k5\_matrprob~X0=k18\_rvsum\_1~(k2\_entropy1~k1\_numbers~X0))\end{array}$$
\end{theorem}
\end{document}
