\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{t40\_convex4 (TMciiLKmG8nsXXqqLF9pDJZ2HhHAWQ6yRDN)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_convex4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rlvect\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_complex1 : {\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 $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xcmplx\_0 : {\iota}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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}((v2\_clvect\_1~X0){\unicdcdcdhd}\\
((v3\_clvect\_1~X0){\unicdcdcdhd}((v4\_clvect\_1~X0){\unicdcdcdhd}((v5\_clvect\_1~X0){\unicdcdcdhd}(l1\_clvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(k4\_algstr\_0~X0~X1=k1\_clvect\_1~X0~X1~(k10\_complex1~k6\_complex1)))\end{array}
\label{hyp:ehddpfdgmgghfgdgehpfbd}
\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 .  \\
(v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_convex4~X2~X0){\unicdbdjdcd}(k1\_clvect\_1~\\
(k15\_convex4~X0)~(k1\_rlvect\_2~(k15\_convex4~X0)~X2)~X1=k7\_convex4~\\
X0~X1~X2)))\end{array}
\label{hyp:ehddjdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
{{{{k3\_xcmplx\_0}~{k1\_xcmplx\_0}}~{k1\_xcmplx\_0}}={{k4\_xcmplx\_0}~{np\_\_1}}}\label{hyp:chbhcffgbgmgnefhmgehpfpflgddpfihdgngahmgihpfadpfpfdgchbdchadpfdgchbdchadpfchngbd}
\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 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
v1\_xcmplx\_0~(k3\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgddpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xcmplx\_0}~{k1\_xcmplx\_0}}\label{hyp:ggdgbdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgcdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_clvect\_1}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k6\_complex1}}~{k2\_numbers}}\label{hyp:egehpflggdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (l1\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k1\_rlvect\_2~\\
X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgbdpfchmgghfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k15\_convex4~X0)){\unicdcdcdhd}((v13\_algstr\_0~(k15\_convex4~X0)){\unicdcdcdhd}((v2\_rlvect\_1~\\
(k15\_convex4~X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k15\_convex4~X0)){\unicdcdcdhd}((v4\_rlvect\_1~\\
(k15\_convex4~X0)){\unicdcdcdhd}((v2\_clvect\_1~(k15\_convex4~X0)){\unicdcdcdhd}((v3\_clvect\_1~\\
(k15\_convex4~X0)){\unicdcdcdhd}((v4\_clvect\_1~(k15\_convex4~X0)){\unicdcdcdhd}((v5\_clvect\_1~\\
(k15\_convex4~X0)){\unicdcdcdhd}(l1\_clvect\_1~(k15\_convex4~X0)))))))))))\end{array}
\label{hyp:egehpflgbdfdpfdgpgogghfgihed}
\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}(k8\_convex4~X0~X1=k7\_convex4~X0~(k10\_complex1~\\
k6\_complex1)~X1))\end{array}
\label{hyp:egbdadpfdgpgogghfgihed}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdgpgogghfgihed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_convex4~X1~X0){\unicdbdjdcd}(k4\_algstr\_0~(k15\_convex4~X0)~(k1\_rlvect\_2~\\
(k15\_convex4~X0)~X1)=k8\_convex4~X0~X1))\end{array}$$
\end{theorem}
\end{document}
