\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{t76\_transgeo (TMVFX2Nbx8LLu9V4CEmw4qPLgVzJnEhUm5E)}
\maketitle
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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_analoaf : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ r1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r1\_aff\_1~\\
X0~X1~X2~X3){\unicdcdcdhd}(r2\_analoaf~X0~X1~X2~X3~X4)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(r1\_aff\_1~X0~X1~\\
X2~X4)))))))\end{array}
\label{hyp:ehjdpfbgggggpfbd}
\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}({\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}(((r1\_aff\_1~X0~X1~X2~X3){\unicdcdcdhd}((r1\_aff\_1~\\
X0~X1~X2~X4){\unicdcdcdhd}(r1\_aff\_1~X0~X1~X2~X5))){\unicdbdjdcd}((X1=X2){\unicdcdcdid}(r1\_aff\_1~X0~X3~X4~\\
X5))))))))\end{array}
\label{hyp:ehidpfbgggggpfbd}
\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}((r1\_aff\_1~X0~X1~X1~X2){\unicdcdcdhd}((r1\_aff\_1~X0~X1~X2~\\
X2){\unicdcdcdhd}(r1\_aff\_1~X0~X1~X2~X1)))))\end{array}
\label{hyp:ehhdpfbgggggpfbd}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_aff\_1~X0~X1~X2~X3){\unicdbdjdcd}((r1\_aff\_1~X0~X1~X3~X2){\unicdcdcdhd}((r1\_aff\_1~\\
X0~X2~X1~X3){\unicdcdcdhd}((r1\_aff\_1~X0~X2~X3~X1){\unicdcdcdhd}((r1\_aff\_1~X0~X3~X1~X2){\unicdcdcdhd}(r1\_aff\_1~\\
X0~X3~X2~X1)))))))))\end{array}
\label{hyp:ehgdpfbgggggpfbd}
\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}({\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}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}((\preoh (\preoh (r2\_analoaf~X0~X1~X2~X3~X4){\unicdcdcdhd}\\
(r2\_analoaf~X0~X1~X2~X5~X6)){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X1~X2~X3~X4){\unicdcdcdhd}(r2\_analoaf~\\
X0~X5~X6~X1~X2)){\unicdcdcdhd}((\preoh (r2\_analoaf~X0~X3~X4~X1~X2){\unicdcdcdhd}(r2\_analoaf~X0~X5~X6~\\
X1~X2)){\unicdcdcdhd}(\preoh (r2\_analoaf~X0~X3~X4~X1~X2){\unicdcdcdhd}(r2\_analoaf~X0~X1~X2~X5~X6))))){\unicdcdcdhd}\\
(\preoh r2\_analoaf~X0~X3~X4~X5~X6)))))))))\end{array}
\label{hyp:ehfdpfbgggggpfbd}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_analoaf~\\
X0~X1~X2~X3~X4){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X4~X3){\unicdcdcdhd}((r2\_analoaf~X0~X2~X1~X3~\\
X4){\unicdcdcdhd}((r2\_analoaf~X0~X2~X1~X4~X3){\unicdcdcdhd}((r2\_analoaf~X0~X3~X4~X1~X2){\unicdcdcdhd}((r2\_analoaf~\\
X0~X3~X4~X2~X1){\unicdcdcdhd}((r2\_analoaf~X0~X4~X3~X1~X2){\unicdcdcdhd}(r2\_analoaf~X0~X4~X3~X2~\\
X1))))))))))))\end{array}
\label{hyp:ehedpfbgggggpfbd}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_aff\_1~X0~X1~X2~X3){\unicdbdjded}(r2\_analoaf~X0~X1~X2~X1~X3)))))\end{array}
\label{hyp:egbdpfbgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdgdpfehchbgogdhhgfgpg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(((r2\_analoaf~X0~X1~X2~X3~X4){\unicdcdcdhd}\\
((r2\_analoaf~X0~X1~X2~X3~X5){\unicdcdcdhd}((r2\_analoaf~X0~X1~X3~X2~X4){\unicdcdcdhd}(r2\_analoaf~\\
X0~X1~X3~X2~X5)))){\unicdbdjdcd}((r1\_aff\_1~X0~X1~X2~X3){\unicdcdcdid}(X4=X5))))))))\end{array}$$
\end{theorem}
\end{document}
