\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{t33\_clopban4 (TMcz6fkz9528FnqwFnmo1ph1gU4ZDStd4gc)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_normsp\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_cfuncdom : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_clopban2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clopban2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_clopban4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_clopban3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_clopban4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_clopban4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\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.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}\\
((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}((v1\_funct\_1~(k6\_clopban4~\\
X0)){\unicdcdcdhd}((v1\_funct\_2~(k6\_clopban4~X0)~(u1\_struct\_0~X0)~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(k6\_clopban4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpflggdpfdgmgpgahcgbgoged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}\\
((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k7\_clopban4~X0~X1=k3\_funct\_2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X0)~(k6\_clopban4~X0)~X1))\end{array}
\label{hyp:eghdpfdgmgpgahcgbgoged}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}\\
((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)))))){\unicdbdjdcd}\\
((X1=k6\_clopban4~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~(u1\_struct\_0~X0)~X1~X2=k1\_clopban3~\\
X0~(k1\_clopban4~X0~X2)))))\end{array}
\label{hyp:eggdpfdgmgpgahcgbgoged}
\end{equation}
\begin{theorem}\label{thm:ehddddpfdgmgpgahcgbgoged}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_normsp\_0~X0){\unicdcdcdhd}\\
((v4\_normsp\_0~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v1\_vectsp\_1~X0){\unicdcdcdhd}((v3\_vectsp\_1~\\
X0){\unicdcdcdhd}((v2\_clvect\_1~X0){\unicdcdcdhd}((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}\\
((v5\_clvect\_1~X0){\unicdcdcdhd}((v8\_clvect\_1~X0){\unicdcdcdhd}((v2\_cfuncdom~X0){\unicdcdcdhd}((v5\_clopban2~\\
X0){\unicdcdcdhd}(l1\_clopban2~X0)))))))))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k7\_clopban4~X0~X1=k1\_clopban3~X0~(k1\_clopban4~\\
X0~X1)))\end{array}$$
\end{theorem}
\end{document}
