\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{t36\_convex4 (TMUYEdJAveTEGZ5WrV8oQ3KkSQxkjvRJqNu)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k9\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k10\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_complex1 : {\iota}$ be given.
Let $ k8\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_convex4~X3~X0){\unicdbdjdcd}((m2\_convex4~\\
X3~X0~X1){\unicdbdjdcd}(m2\_convex4~(k7\_convex4~X0~X2~X3)~X0~X1)))))\end{array}
\label{hyp:ehcdgdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_convex4~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_convex4~X3~X0){\unicdbdjdcd}(((m2\_convex4~\\
X2~X0~X1){\unicdcdcdhd}(m2\_convex4~X3~X0~X1)){\unicdbdjdcd}(m2\_convex4~(k5\_convex4~X0~X2~X3)~\\
X0~X1)))))\end{array}
\label{hyp:ehcdadpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{np\_\_1}}}}\label{hyp:dhahdgbdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}(k10\_complex1~X0=k4\_xcmplx\_0~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdadpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
(k4\_xcmplx\_0~X0)){\unicdcdcdhd}(v1\_xcmplx\_0~(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ggdggdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~\\
X0)){\unicdcdcdhd}((v1\_xcmplx\_0~X1){\unicdcdcdhd}(m1\_convex4~X2~X0))){\unicdbdjdcd}(m1\_convex4~(k7\_convex4~\\
X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflghdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_complex1}}~{k2\_numbers}}\label{hyp:egehpflggdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_complex1}={np\_\_1}}\label{hyp:egedpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_convex4~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_convex4~X2~X0){\unicdbdjdcd}(k9\_convex4~\\
X0~X1~X2=k5\_convex4~X0~X1~(k8\_convex4~X0~X2))))\end{array}
\label{hyp:egbdbdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_convex4~X1~X0){\unicdbdjdcd}(k8\_convex4~X0~X1=k7\_convex4~X0~(k10\_complex1~\\
k6\_complex1)~X1))\end{array}
\label{hyp:egbdadpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehddgdpfdgpgogghfgihed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_convex4~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_convex4~X3~X0){\unicdbdjdcd}(((m2\_convex4~\\
X2~X0~X1){\unicdcdcdhd}(m2\_convex4~X3~X0~X1)){\unicdbdjdcd}(m2\_convex4~(k9\_convex4~X0~X2~X3)~\\
X0~X1)))))\end{array}$$
\end{theorem}
\end{document}
