\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{t39\_group\_7 (TMZX6hVhqmZBnWDwJE2pBJUPVR3DkySt4gf)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_group\_7 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v15\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~(k1\_tarski~np\_\_1)~\\
(k9\_finseq\_1~X0)))){\unicdcdcdhd}((v1\_group\_6~X1~X0~(k2\_group\_7~(k1\_tarski~\\
np\_\_1)~(k9\_finseq\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~(k1\_tarski~np\_\_1)~(\\
k9\_finseq\_1~X0))))))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~(\\
k1\_tarski~np\_\_1)~(k9\_finseq\_1~X0)))~X1~X2=k4\_group\_7~X0~X2)){\unicdbdjdcd}(\\
v3\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~(k1\_tarski~\\
np\_\_1)~(k9\_finseq\_1~X0))))))\end{array}
\label{hyp:ehddidpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~(k1\_tarski~np\_\_1)~\\
(k9\_finseq\_1~X0)))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~(k1\_tarski~np\_\_1)~(\\
k9\_finseq\_1~X0)))))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~(\\
k1\_tarski~np\_\_1)~(k9\_finseq\_1~X0)))~X1~X2=k4\_group\_7~X0~X2)){\unicdbdjdcd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
(k2\_group\_7~(k1\_tarski~np\_\_1)~(k9\_finseq\_1~X0)))){\unicdcdcdhd}((v1\_group\_6~\\
X1~X0~(k2\_group\_7~(k1\_tarski~np\_\_1)~(k9\_finseq\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~(k2\_group\_7~\\
(k1\_tarski~np\_\_1)~(k9\_finseq\_1~X0)))))))))))\end{array}
\label{hyp:ehddhdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdaddd} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~X2~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X2~X1))))){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X2){\unicdbdjdcd}(k3\_funct\_2~X2~X1~X3~\\
X4=X0~X4))\end{array}
\label{hyp:dhedpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_finseq\_1}~{X0}}={{k5\_finseq\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}(v2\_group\_7~(k5\_finseq\_1~X0)~(k1\_tarski~np\_\_1))\end{array}
\label{hyp:ggdgjdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}((v1\_partfun1~\\
(k5\_finseq\_1~X0)~(k1\_tarski~np\_\_1)){\unicdcdcdhd}(v1\_group\_7~(k5\_finseq\_1~\\
X0)))\end{array}
\label{hyp:ggdgidpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}(v4\_relat\_1~\\
(k5\_finseq\_1~X0)~(k1\_tarski~np\_\_1))\end{array}
\label{hyp:ggdghdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_group\_7~X1){\unicdcdcdhd}(v3\_group\_7~\\
X1~X0)))))){\unicdbdjdcd}((v15\_algstr\_0~(k2\_group\_7~X0~X1)){\unicdcdcdhd}(v3\_group\_1~(\\
k2\_group\_7~X0~X1)))\end{array}
\label{hyp:ggdgedpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}((v1\_group\_7~X1){\unicdcdcdhd}(v2\_group\_7~\\
X1~X0)))))){\unicdbdjdcd}((v15\_algstr\_0~(k2\_group\_7~X0~X1)){\unicdcdcdhd}(v2\_group\_1~(\\
k2\_group\_7~X0~X1)))\end{array}
\label{hyp:ggdgddpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_group\_7~X1))))){\unicdbdjdcd}((\\
\preoh v2\_struct\_0~(k2\_group\_7~X0~X1)){\unicdcdcdhd}((v15\_algstr\_0~(k2\_group\_7~\\
X0~X1)){\unicdcdcdhd}(v1\_monoid\_0~(k2\_group\_7~X0~X1))))\end{array}
\label{hyp:ggdgcdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}(v3\_group\_7~(k5\_finseq\_1~X0)~(k1\_tarski~np\_\_1))\end{array}
\label{hyp:ggdgbdadpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~(k9\_finseq\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k9\_finseq\_1~\\
X0))\end{array}
\label{hyp:egehpflgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~X1~X0){\unicdcdcdhd}(v1\_group\_7~X1))))){\unicdbdjdcd}((\\
v15\_algstr\_0~(k2\_group\_7~X0~X1)){\unicdcdcdhd}(l3\_algstr\_0~(k2\_group\_7~X0~\\
X1)))\end{array}
\label{hyp:egehpflgcdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~\\
X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)))){\unicdbdjdcd}((r1\_group\_6~X0~X1){\unicdbdjded}\\
({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(u1\_struct\_0~X0)~\\
(u1\_struct\_0~X1)){\unicdcdcdhd}((v1\_group\_6~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))))){\unicdcdcdhd}(v3\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:egbdbdpfhgchpgfhahpfgd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfhgchpgfhahpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}((v3\_group\_1~\\
X0){\unicdcdcdhd}(l3\_algstr\_0~X0)))){\unicdbdjdcd}(r1\_group\_6~X0~(k2\_group\_7~(k1\_tarski~\\
np\_\_1)~(k9\_finseq\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
