\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{t1\_afvect01 (TMbtag7seJTwmewAVM8cfeDe916yTxJSSXp)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_afvect01 : {{\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 $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_analoaf}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfbgogbgmgpgbggg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_analoaf~X0)){\unicdbdjdcd}((v1\_afvect01~\\
X0){\unicdbdjded}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(r2\_analoaf~X0~X1~X2~X2~X1))){\unicdcdcdhd}\\
(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((r2\_analoaf~X0~X1~X2~X1~X1){\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}(((r2\_analoaf~X0~X1~X2~X5~X6){\unicdcdcdhd}(r2\_analoaf~\\
X0~X3~X4~X5~X6)){\unicdbdjdcd}(r2\_analoaf~X0~X1~X2~X3~X4)))))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(r2\_analoaf~X0~X1~X3~X3~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}\\
(((r2\_analoaf~X0~X5~X1~X5~X2){\unicdcdcdhd}(r2\_analoaf~X0~X5~X3~X5~X4)){\unicdbdjdcd}((X1=X2){\unicdcdcdid}\\
((X3=X4){\unicdcdcdid}(r2\_analoaf~X0~X1~X3~X2~X4))))))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}X2){\unicdcdcdhd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((\preoh (X1{\unicdcdgdad}X3){\unicdcdcdhd}(r2\_analoaf~X0~X1~X2~X2~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(\preoh (X4{\unicdcdgdad}X5){\unicdcdcdhd}((r2\_analoaf~X0~X1~X2~X4~X5){\unicdcdcdhd}((r2\_analoaf~X0~X1~\\
X4~X4~X2){\unicdcdcdhd}(r2\_analoaf~X0~X1~X5~X5~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}\\
(((r2\_analoaf~X0~X1~X2~X2~X6){\unicdcdcdhd}((r2\_analoaf~X0~X2~X3~X4~X5){\unicdcdcdhd}((r2\_analoaf~\\
X0~X2~X4~X4~X3){\unicdcdcdhd}(r2\_analoaf~X0~X2~X5~X5~X3)))){\unicdbdjdcd}(r2\_analoaf~X0~X1~X3~\\
X3~X6)))))))){\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}(\preoh (X1{\unicdcdgdad}X4){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}((r2\_analoaf~X0~X1~X2~X2~X4){\unicdcdcdhd}((r2\_analoaf~\\
X0~X1~X3~X3~X4){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}(\\
{\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (X5{\unicdcdgdad}X6){\unicdcdcdhd}((r2\_analoaf~\\
X0~X2~X3~X5~X6){\unicdcdcdhd}((r2\_analoaf~X0~X2~X5~X5~X3){\unicdcdcdhd}(r2\_analoaf~X0~X2~X6~X6~\\
X3)))))))))))))){\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}(\preoh (r2\_analoaf~X0~X1~X2~X4~X5){\unicdcdcdhd}((r2\_analoaf~X0~\\
X1~X3~X6~X7){\unicdcdcdhd}((r2\_analoaf~X0~X1~X4~X4~X2){\unicdcdcdhd}((r2\_analoaf~X0~X1~X6~X6~X3){\unicdcdcdhd}\\
((r2\_analoaf~X0~X1~X5~X5~X2){\unicdcdcdhd}((r2\_analoaf~X0~X1~X7~X7~X3){\unicdcdcdhd}({\unicdcdadad} X8 .  \\
(m1\_subset\_1~X8~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X9 .  (m1\_subset\_1~X9~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (r2\_analoaf~X0~X2~X3~X8~X9){\unicdcdcdhd}((r2\_analoaf~X0~\\
X2~X8~X8~X3){\unicdcdcdhd}(r2\_analoaf~X0~X2~X9~X9~X3)))))))))))))))))))))))))))\end{array}
\label{hyp:egbdpfbgggghfgdgehadbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{({\preoh{{{v7\_struct\_0}~{X0}}}})}{\unicdbdjdcd}{({\preoh{{{v2\_struct\_0}~{X0}}}})}})}}}\label{hyp:dgdgbdhdpfdhehchfhdgehpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdpfbgggghfgdgehadbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_afvect01~X0){\unicdcdcdhd}(l1\_analoaf~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(r2\_analoaf~X0~X1~X2~X1~X2)))\end{array}$$
\end{theorem}
\end{document}
