\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}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t2\_convex4 (TMH84NuVC8kkauTfxV9toHZGSU5voKzoqgv)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k2\_convex4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_complex1 : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_rlvect\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ m1\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_rlvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_rlvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~\\
k1\_numbers~(k4\_rlvect\_2~X0)~X1=k6\_numbers))\end{array}
\label{hyp:ehcdadpfchmgghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_convex4~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((k3\_funct\_2~(u1\_struct\_0~X0)~k2\_numbers~X1~X2=k5\_complex1){\unicdbdjded}\\
(\preoh X2 \in k1\_convex4~X0~X1))))\end{array}
\label{hyp:ehbdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_rlvect\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((k3\_funct\_2~(u1\_struct\_0~X0)~k1\_numbers~X1~X2=k6\_numbers){\unicdbdjded}\\
(\preoh X2 \in k3\_rlvect\_2~X0~X1))))\end{array}
\label{hyp:ehbdjdpfchmgghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}(m1\_rlvect\_2~\\
(k4\_rlvect\_2~X0)~X0)\end{array}
\label{hyp:egehpflgedpfchmgghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}(m1\_convex4~\\
(k2\_convex4~X0)~X0)\end{array}
\label{hyp:egehpflgcdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_rlvect\_2~X1~X0){\unicdbdjdcd}((X1=k4\_rlvect\_2~X0){\unicdbdjded}(k3\_rlvect\_2~X0~X1=\\
k1\_xboole\_0)))\end{array}
\label{hyp:egfdpfchmgghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_convex4~X1~X0){\unicdbdjdcd}((X1=k2\_convex4~X0){\unicdbdjded}(k1\_convex4~X0~X1=k1\_xboole\_0)))\end{array}
\label{hyp:egddpfdgpgogghfgihed}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdgpgogghfgihed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k3\_funct\_2~(u1\_struct\_0~X0)~\\
k2\_numbers~(k2\_convex4~X0)~X1=k5\_complex1))\end{array}$$
\end{theorem}
\end{document}
