\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{t23\_group\_7 (TMLj4kaNG7u6rEfhmpk3PhMVr7ShNEMnwMb)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_enumset1 : {{\iota}{\unicdbdjdcd}{{\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 $ v1\_funct\_1 : {{\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 $ v2\_group\_7 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finseq\_1~X3))){\unicdbdjdcd}((X3=k11\_finseq\_1~X0~X1~\\
X2){\unicdbdjded}((k3\_finseq\_1~X3=np\_\_3){\unicdcdcdhd}((k1\_funct\_1~X3~np\_\_1=X0){\unicdcdcdhd}((k1\_funct\_1~\\
X3~np\_\_2=X1){\unicdcdcdhd}(k1\_funct\_1~X3~np\_\_3=X2)))))\end{array}
\label{hyp:ehedfdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l3\_algstr\_0~X2)){\unicdbdjdcd}((v1\_relat\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}\\
((v4\_relat\_1~(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}\\
((v1\_funct\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k11\_finseq\_1~\\
X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}(v1\_group\_7~(k11\_finseq\_1~\\
X0~X1~X2))))))))\end{array}
\label{hyp:ehcdcdpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
{{{k2\_finseq\_1}~{np\_\_3}}={{{{k1\_enumset1}~{np\_\_1}}~{np\_\_2}}~{np\_\_3}}}\label{hyp:ehbdpfggjgogdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  k10\_xtuple\_0~(k11\_finseq\_1~\\
X0~X1~X2)=k1\_enumset1~X0~X1~X2\end{array}
\label{hyp:ehbdcdidpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~(k11\_finseq\_1~X0~\\
X1~X2)){\unicdcdcdhd}(v1\_funct\_1~(k11\_finseq\_1~X0~X1~X2))\end{array}
\label{hyp:ggdgjdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0)){\unicdcdcdhd}(((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(l3\_algstr\_0~X1)){\unicdcdcdhd}((\preoh v2\_struct\_0~\\
X2){\unicdcdcdhd}(l3\_algstr\_0~X2)))){\unicdbdjdcd}((v1\_partfun1~(k11\_finseq\_1~X0~X1~X2)~\\
(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}(v1\_group\_7~(k11\_finseq\_1~X0~\\
X1~X2)))\end{array}
\label{hyp:ggdgbdidpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  v1\_finseq\_1~(k11\_finseq\_1~X0~\\
X1~X2)\end{array}
\label{hyp:ggdgbdbdpfggjgogdhfgbhpfbd}
\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}((\\
v2\_group\_7~X1~X0){\unicdbdjded}({\unicdcdadad} X2 .  \preoh (X2 \in X0){\unicdcdcdhd}({\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~\\
X3){\unicdcdcdhd}((v2\_group\_1~X3){\unicdcdcdhd}(l3\_algstr\_0~X3))){\unicdbdjdcd}(X3{\unicdcdgdad}k1\_funct\_1~X1~X2))))\end{array}
\label{hyp:egddpfhgchpgfhahpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (X3=k1\_enumset1~\\
X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}(\preoh (X4{\unicdcdgdad}X0){\unicdcdcdhd}((X4{\unicdcdgdad}X1){\unicdcdcdhd}(X4{\unicdcdgdad}X2))))\end{array}
\label{hyp:egbdpffgogfhngdhfgehbd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfhgchpgfhahpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_group\_1~X0){\unicdcdcdhd}(l3\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_group\_1~X1){\unicdcdcdhd}(l3\_algstr\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v2\_group\_1~X2){\unicdcdcdhd}(l3\_algstr\_0~\\
X2))){\unicdbdjdcd}((v1\_relat\_1~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}((v4\_relat\_1~(k11\_finseq\_1~\\
X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_funct\_1~(k11\_finseq\_1~\\
X0~X1~X2)){\unicdcdcdhd}((v1\_partfun1~(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~\\
np\_\_2~np\_\_3)){\unicdcdcdhd}((v1\_group\_7~(k11\_finseq\_1~X0~X1~X2)){\unicdcdcdhd}(v2\_group\_7~\\
(k11\_finseq\_1~X0~X1~X2)~(k1\_enumset1~np\_\_1~np\_\_2~np\_\_3)))))))))\end{array}$$
\end{theorem}
\end{document}
