\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{t39\_convex4 (TMT63L2ehzUbdPekAtNH8n6RyQRF9RygGbL)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k7\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ g1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ v1\_clvect\_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 $ 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.
Let $ k2\_convex4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k14\_convex4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_convex4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k13\_convex4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_clvect\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k11\_convex4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X1~\\
X0){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~\\
X0))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k2\_zfmisc\_1~k2\_numbers~\\
X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_numbers~X0)~X0))))))){\unicdbdjdcd}({\unicdcdadad} X4 .  {\unicdcdadad} X5 .  {\unicdcdadad} X6 .  {\unicdcdadad} X7 .  \\
(g1\_clvect\_1~X0~X1~X2~X3=g1\_clvect\_1~X4~X5~X6~X7){\unicdbdjdcd}((X0=X4){\unicdcdcdhd}((X1=\\
X5){\unicdcdcdhd}((X2=X6){\unicdcdcdhd}(X3=X7)))))\end{array}
\label{hyp:ggchfgfgpfhgbdpfdgmgghfgdgehpfbd}
\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}((v1\_clvect\_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)))))))))))\end{array}
\label{hyp:ggdgedpfdgpgogghfgihed}
\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}
\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}(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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k14\_convex4~X0)){\unicdcdcdhd}((v1\_funct\_2~(k14\_convex4~X0)~(k2\_zfmisc\_1~\\
k2\_numbers~(k10\_convex4~X0))~(k10\_convex4~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k14\_convex4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~k2\_numbers~\\
(k10\_convex4~X0))~(k10\_convex4~X0))))))\end{array}
\label{hyp:egehpflgbdedpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k13\_convex4~X0)){\unicdcdcdhd}((v1\_funct\_2~(k13\_convex4~X0)~(k2\_zfmisc\_1~\\
(k10\_convex4~X0)~(k10\_convex4~X0))~(k10\_convex4~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k13\_convex4~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k10\_convex4~\\
X0)~(k10\_convex4~X0))~(k10\_convex4~X0))))))\end{array}
\label{hyp:egehpflgbdddpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdcdcdhd}\\
(m1\_convex4~X1~X0)){\unicdbdjdcd}(m1\_subset\_1~(k12\_convex4~X0~X1)~(k10\_convex4~\\
X0))\end{array}
\label{hyp:egehpflgbdcdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_struct\_0~X0~X1){\unicdbdjded}\\
(X1 \in u1\_struct\_0~X0))\end{array}
\label{hyp:egfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_struct\_0~X0~X1){\unicdbdjdcd}\\
(k1\_rlvect\_2~X0~X1=X1))\end{array}
\label{hyp:egbdpfchmgghfgdgehpfcd}
\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~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xcmplx\_0~X2){\unicdbdjdcd}\\
(k1\_clvect\_1~X0~X1~X2=k1\_funct\_1~(u1\_clvect\_1~X0)~(k4\_tarski~X2~\\
X1))))\end{array}
\label{hyp:egbdpfdgmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}(k15\_convex4~\\
X0=g1\_clvect\_1~(k10\_convex4~X0)~(k12\_convex4~X0~(k2\_convex4~X0))~\\
(k13\_convex4~X0)~(k14\_convex4~X0))\end{array}
\label{hyp:egbdhdpfdgpgogghfgihed}
\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\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~k2\_numbers~(k10\_convex4~\\
X0))~(k10\_convex4~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~k2\_numbers~(k10\_convex4~X0))~(k10\_convex4~X0)))))){\unicdbdjdcd}\\
((X1=k14\_convex4~X0){\unicdbdjded}({\unicdcdadad} X2 .  (v1\_xcmplx\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(k10\_convex4~X0)){\unicdbdjdcd}(k1\_funct\_1~X1~(k4\_tarski~X2~\\
X3)=k7\_convex4~X0~X2~(k11\_convex4~X0~X3))))))\end{array}
\label{hyp:egbdgdpfdgpgogghfgihed}
\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}(k12\_convex4~X0~X1=X1))\end{array}
\label{hyp:egbdedpfdgpgogghfgihed}
\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~(k10\_convex4~X0)){\unicdbdjdcd}(k11\_convex4~X0~X1=X1))\end{array}
\label{hyp:egbdddpfdgpgogghfgihed}
\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 .  \\
(X1=k10\_convex4~X0){\unicdbdjded}({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}(m1\_convex4~X2~X0)))\end{array}
\label{hyp:egbdcdpfdgpgogghfgihed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_clvect\_1~X0){\unicdbdjdcd}((v1\_clvect\_1~X0){\unicdbdjdcd}(X0=g1\_clvect\_1~\\
(u1\_struct\_0~X0)~(u2\_struct\_0~X0)~(u1\_algstr\_0~X0)~(u1\_clvect\_1~\\
X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfdgmgghfgdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfdgpgogghfgihed}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_clvect\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_convex4~X2~X0){\unicdbdjdcd}(k1\_clvect\_1~\\
(k15\_convex4~X0)~(k1\_rlvect\_2~(k15\_convex4~X0)~X2)~X1=k7\_convex4~\\
X0~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
