\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{t3\_conmetr (TMKiM1MpitnoZS7APimuRZT5vbZtMjHdryL)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analmetr : {{\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 $ v4\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r10\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r7\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r4\_analmetr : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v2\_analmetr : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_analmetr : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_analoaf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analmetr~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((r7\_analmetr~\\
X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
((X3{\unicdcdgdad}X4){\unicdcdcdhd}((X5{\unicdcdgdad}X6){\unicdcdcdhd}((X1=k4\_analmetr~X0~X3~X4){\unicdcdcdhd}((X2=k4\_analmetr~\\
X0~X5~X6){\unicdcdcdhd}(r4\_analmetr~X0~X3~X4~X5~X6))))))))))))\end{array}
\label{hyp:ehedfdpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~(k3\_analmetr~X0))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~\\
(u1\_struct\_0~(k3\_analmetr~X0))){\unicdbdjdcd}(((X1=X3){\unicdcdcdhd}(X2=X4)){\unicdbdjdcd}(k4\_analmetr~\\
X0~X1~X2=k2\_aff\_1~(k3\_analmetr~X0)~X3~X4))))))\end{array}
\label{hyp:ehedbdpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analmetr~X0)){\unicdbdjdcd}((v3\_analmetr~\\
X0){\unicdbdjded}((\preoh {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(X1=X2))){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X7 .  (m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~\\
X8~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X2~X1){\unicdcdcdhd}((r2\_analoaf~\\
X0~X1~X2~X3~X3){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X1~X2~X5~X6){\unicdcdcdhd}((r2\_analoaf~X0~X1~X2~\\
X7~X8){\unicdcdcdhd}((\preoh r2\_analoaf~X0~X5~X6~X7~X8){\unicdcdcdhd}(X1{\unicdcdgdad}X2)))){\unicdcdcdhd}(((r2\_analoaf~\\
X0~X1~X2~X1~X3){\unicdbdjdcd}(r2\_analoaf~X0~X2~X1~X2~X3)){\unicdcdcdhd}(({\unicdcdaddd} X9 .  (m1\_subset\_1~\\
X9~(u1\_struct\_0~X0)){\unicdcdcdhd}((r2\_analoaf~X0~X1~X2~X3~X9){\unicdcdcdhd}(r2\_analoaf~X0~\\
X1~X3~X2~X9))){\unicdcdcdhd}((\preoh {\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X10 .  (m1\_subset\_1~X10~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X11 .  \\
(m1\_subset\_1~X11~(u1\_struct\_0~X0)){\unicdbdjdcd}(r2\_analoaf~X0~X9~X10~X9~X11)))){\unicdcdcdhd}\\
(({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdcdcdhd}((r2\_analoaf~\\
X0~X1~X2~X3~X9){\unicdcdcdhd}(X3{\unicdcdgdad}X9))){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X1~X2~X2~X4){\unicdcdcdhd}((X2{\unicdcdgdad}X1){\unicdcdcdhd}\\
({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (r2\_analoaf~\\
X0~X3~X2~X2~X9){\unicdcdcdhd}(r2\_analoaf~X0~X3~X1~X4~X9))))){\unicdcdcdhd}(((r4\_analmetr~X0~\\
X1~X2~X1~X2){\unicdbdjdcd}(X1=X2)){\unicdcdcdhd}((r4\_analmetr~X0~X1~X2~X3~X3){\unicdcdcdhd}(((r4\_analmetr~\\
X0~X1~X2~X3~X4){\unicdbdjdcd}((r4\_analmetr~X0~X1~X2~X4~X3){\unicdcdcdhd}(r4\_analmetr~X0~X3~X4~\\
X1~X2))){\unicdcdcdhd}((\preoh (r4\_analmetr~X0~X1~X2~X5~X6){\unicdcdcdhd}((r2\_analoaf~X0~X1~X2~X7~\\
X8){\unicdcdcdhd}((\preoh r4\_analmetr~X0~X5~X6~X7~X8){\unicdcdcdhd}(X1{\unicdcdgdad}X2)))){\unicdcdcdhd}((\preoh (r4\_analmetr~\\
X0~X1~X2~X5~X6){\unicdcdcdhd}((r4\_analmetr~X0~X1~X2~X7~X8){\unicdcdcdhd}((\preoh r2\_analoaf~X0~X5~X6~\\
X7~X8){\unicdcdcdhd}(X1{\unicdcdgdad}X2)))){\unicdcdcdhd}(({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}((r4\_analmetr~X0~X1~X2~X3~X9){\unicdcdcdhd}(X3{\unicdcdgdad}X9))){\unicdcdcdhd}(\preoh (\preoh r2\_analoaf~X0~\\
X1~X2~X3~X4){\unicdcdcdhd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (\\
r2\_analoaf~X0~X1~X2~X1~X9){\unicdcdcdhd}(r2\_analoaf~X0~X3~X4~X3~X9))))))))))))))))))))))))))))\end{array}
\label{hyp:ehddjdpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analmetr~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjded}(m1\_subset\_1~X1~(u1\_struct\_0~\\
(k3\_analmetr~X0))))\end{array}
\label{hyp:ehddfdpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1 \in k2\_aff\_1~X0~X1~X2){\unicdcdcdhd}(X2 \in k2\_aff\_1~X0~X1~\\
X2))))\end{array}
\label{hyp:ehbdfdpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_analmetr~\\
X0){\unicdcdcdhd}(l1\_analmetr~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))){\unicdbdjdcd}((r10\_analmetr~\\
X0~X1~X2){\unicdbdjded}(r7\_analmetr~X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchbdadpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}((\preoh v7\_struct\_0~(k3\_analmetr~X0)){\unicdcdcdhd}((v1\_analoaf~(k3\_analmetr~\\
X0)){\unicdcdcdhd}((v1\_diraf~(k3\_analmetr~X0)){\unicdcdcdhd}(v2\_diraf~(k3\_analmetr~X0)))))\end{array}
\label{hyp:ggdgedpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k4\_analmetr~X0~X1~X2)~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))\end{array}
\label{hyp:egehpflgedpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analmetr~X0)){\unicdbdjdcd}((v1\_analoaf~\\
(k3\_analmetr~X0)){\unicdcdcdhd}(l1\_analoaf~(k3\_analmetr~X0)))\end{array}
\label{hyp:egehpflgddpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analmetr~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v4\_analmetr~\\
X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}(X1=k4\_analmetr~\\
X0~X2~X3))))))\end{array}
\label{hyp:egbdcdpfbgogbgmgngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~\\
X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k2\_aff\_1~X0~X1~X2=k2\_aff\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_analmetr~X0){\unicdbdjdcd}(((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v3\_analmetr~\\
X0)){\unicdbdjdcd}((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(v2\_analmetr~X0)))\end{array}
\label{hyp:dgdgbdpfbgogbgmgngfgehch}
\end{equation}
\begin{theorem}\label{thm:ehddpfdgpgogngfgehch}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_analmetr~X0){\unicdcdcdhd}(l1\_analmetr~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (v4\_analmetr~\\
X1~X0){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(\preoh (X2 \in X3){\unicdcdcdhd}(r10\_analmetr~X0~X1~X3))))))\end{array}$$
\end{theorem}
\end{document}
