\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{t29\_descip\_1 (TMThQXFpmyKLjcyBuebisiy2SqF9FFjKKVp)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_16 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ np\_\_6 : {\iota}$ be given.
Let $ np\_\_7 : {\iota}$ be given.
Let $ np\_\_8 : {\iota}$ be given.
Let $ np\_\_9 : {\iota}$ be given.
Let $ np\_\_10 : {\iota}$ be given.
Let $ np\_\_11 : {\iota}$ be given.
Let $ np\_\_12 : {\iota}$ be given.
Let $ np\_\_13 : {\iota}$ be given.
Let $ np\_\_14 : {\iota}$ be given.
Let $ np\_\_15 : {\iota}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X0){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~X0){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X0){\unicdbdjdcd}({\unicdcdaddd} X9 .  (m2\_finseq\_1~X9~X0){\unicdcdcdhd}\\
((v3\_card\_1~X9~np\_\_8){\unicdcdcdhd}((k1\_funct\_1~X9~np\_\_1=X1){\unicdcdcdhd}((k1\_funct\_1~\\
X9~np\_\_2=X2){\unicdcdcdhd}((k1\_funct\_1~X9~np\_\_3=X3){\unicdcdcdhd}((k1\_funct\_1~X9~np\_\_4=\\
X4){\unicdcdcdhd}((k1\_funct\_1~X9~np\_\_5=X5){\unicdcdcdhd}((k1\_funct\_1~X9~np\_\_6=X6){\unicdcdcdhd}((k1\_funct\_1~\\
X9~np\_\_7=X7){\unicdcdcdhd}(k1\_funct\_1~X9~np\_\_8=X8))))))))))))))))))\end{array}
\label{hyp:ehcdidpfegfgdhdgjgahpfbd}
\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 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}(((v3\_card\_1~X1~np\_\_8){\unicdcdcdhd}(v3\_card\_1~\\
X2~np\_\_8)){\unicdbdjdcd}((v3\_card\_1~(k8\_finseq\_1~X0~X1~X2)~np\_\_16){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_1=k1\_funct\_1~X1~np\_\_1){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_2=k1\_funct\_1~X1~np\_\_2){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_3=k1\_funct\_1~X1~np\_\_3){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_4=k1\_funct\_1~X1~np\_\_4){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_5=k1\_funct\_1~X1~np\_\_5){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_6=k1\_funct\_1~X1~np\_\_6){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_7=k1\_funct\_1~X1~np\_\_7){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_8=k1\_funct\_1~X1~np\_\_8){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_9=k1\_funct\_1~X2~np\_\_1){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_10=k1\_funct\_1~X2~np\_\_2){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_11=k1\_funct\_1~X2~np\_\_3){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_12=k1\_funct\_1~X2~np\_\_4){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_13=k1\_funct\_1~X2~np\_\_5){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_14=k1\_funct\_1~X2~np\_\_6){\unicdcdcdhd}((k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_15=k1\_funct\_1~X2~np\_\_7){\unicdcdcdhd}(k1\_funct\_1~\\
(k8\_finseq\_1~X0~X1~X2)~np\_\_16=k1\_funct\_1~X2~np\_\_8))))))))))))))))))))\end{array}
\label{hyp:mgedcdpfegfgdhdgjgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_finseq\_1~X1~X0){\unicdcdcdhd}(m1\_finseq\_1~\\
X2~X0)){\unicdbdjdcd}(m2\_finseq\_1~(k8\_finseq\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgidpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfegfgdhdgjgahpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~X0){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~X0){\unicdbdjdcd}\\
({\unicdcdadad} X6 .  (m1\_subset\_1~X6~X0){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~X0){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~X0){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~X0){\unicdbdjdcd}\\
({\unicdcdadad} X10 .  (m1\_subset\_1~X10~X0){\unicdbdjdcd}({\unicdcdadad} X11 .  (m1\_subset\_1~\\
X11~X0){\unicdbdjdcd}({\unicdcdadad} X12 .  (m1\_subset\_1~X12~X0){\unicdbdjdcd}({\unicdcdadad} X13 .  (m1\_subset\_1~\\
X13~X0){\unicdbdjdcd}({\unicdcdadad} X14 .  (m1\_subset\_1~X14~X0){\unicdbdjdcd}({\unicdcdadad} X15 .  (m1\_subset\_1~\\
X15~X0){\unicdbdjdcd}({\unicdcdadad} X16 .  (m1\_subset\_1~X16~X0){\unicdbdjdcd}({\unicdcdaddd} X17 .  (m2\_finseq\_1~\\
X17~X0){\unicdcdcdhd}((v3\_card\_1~X17~np\_\_16){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_1=X1){\unicdcdcdhd}(\\
(k1\_funct\_1~X17~np\_\_2=X2){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_3=X3){\unicdcdcdhd}((k1\_funct\_1~\\
X17~np\_\_4=X4){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_5=X5){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_6=\\
X6){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_7=X7){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_8=X8){\unicdcdcdhd}(\\
(k1\_funct\_1~X17~np\_\_9=X9){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_10=X10){\unicdcdcdhd}((k1\_funct\_1~\\
X17~np\_\_11=X11){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_12=X12){\unicdcdcdhd}((k1\_funct\_1~X17~\\
np\_\_13=X13){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_14=X14){\unicdcdcdhd}((k1\_funct\_1~X17~np\_\_15=\\
X15){\unicdcdcdhd}(k1\_funct\_1~X17~np\_\_16=X16))))))))))))))))))))))))))))))))))\end{array}$$
\end{theorem}
\end{document}
