\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{t34\_anproj\_2 (TMZc7k2aMBJfm8QdwA7aQCoAR2v7iJCR2Tq)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_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\_numbers : {\iota}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v2\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_collsp : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_anproj\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v7\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_anproj\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}(l1\_rlvect\_1~X0))))))))))){\unicdbdjdcd}(\preoh ({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  \\
(m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X8 .  (m1\_subset\_1~X8~k1\_numbers){\unicdbdjdcd}\\
((k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~(k1\_rlvect\_1~\\
X0~X1~X5)~(k1\_rlvect\_1~X0~X2~X6))~(k1\_rlvect\_1~X0~X3~X7))~(k1\_rlvect\_1~\\
X0~X4~X8)=k4\_struct\_0~X0){\unicdbdjdcd}((X5=k6\_numbers){\unicdcdcdhd}((X6=k6\_numbers){\unicdcdcdhd}\\
((X7=k6\_numbers){\unicdcdcdhd}(X8=k6\_numbers))))))))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_collsp~X1){\unicdcdcdhd}((v3\_collsp~X1){\unicdcdcdhd}((v4\_collsp~\\
X1){\unicdcdcdhd}((v2\_anproj\_2~X1){\unicdcdcdhd}((v3\_anproj\_2~X1){\unicdcdcdhd}(l1\_collsp~X1))))))){\unicdbdjdcd}\\
(\preoh (X1=k5\_anproj\_1~X0){\unicdcdcdhd}(\preoh v7\_anproj\_2~X1))))\end{array}
\label{hyp:ehddddpfbgogahchpgkgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}(l1\_rlvect\_1~X0))))))))))){\unicdbdjdcd}(\preoh ({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}(({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~\\
X8~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~k1\_numbers){\unicdcdcdhd}(X5=\\
k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~\\
X1~X6)~(k1\_rlvect\_1~X0~X2~X7))~(k1\_rlvect\_1~X0~X3~X8))~(k1\_rlvect\_1~\\
X0~X4~X9))))))){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~k1\_numbers){\unicdbdjdcd}((k3\_rlvect\_1~X0~(k3\_rlvect\_1~\\
X0~(k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~X1~X5)~(k1\_rlvect\_1~X0~X2~X6))~\\
(k1\_rlvect\_1~X0~X3~X7))~(k1\_rlvect\_1~X0~X4~X8)=k4\_struct\_0~X0){\unicdbdjdcd}\\
((X5=k6\_numbers){\unicdcdcdhd}((X6=k6\_numbers){\unicdcdcdhd}((X7=k6\_numbers){\unicdcdcdhd}(X8=\\
k6\_numbers)))))))))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(\\
(v2\_collsp~X1){\unicdcdcdhd}((v3\_collsp~X1){\unicdcdcdhd}((v4\_collsp~X1){\unicdcdcdhd}((v2\_anproj\_2~\\
X1){\unicdcdcdhd}((v3\_anproj\_2~X1){\unicdcdcdhd}(l1\_collsp~X1))))))){\unicdbdjdcd}(\preoh (X1=k5\_anproj\_1~\\
X0){\unicdcdcdhd}(v8\_anproj\_2~X1))))\end{array}
\label{hyp:ehddcdpfbgogahchpgkgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfbgogahchpgkgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}(l1\_rlvect\_1~X0))))))))))){\unicdbdjdcd}(\preoh ({\unicdcdaddd} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}(({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~k1\_numbers){\unicdcdcdhd}\\
({\unicdcdaddd} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X8 .  (m1\_subset\_1~\\
X8~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X9 .  (m1\_subset\_1~X9~k1\_numbers){\unicdcdcdhd}(X5=\\
k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~(k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~\\
X1~X6)~(k1\_rlvect\_1~X0~X2~X7))~(k1\_rlvect\_1~X0~X3~X8))~(k1\_rlvect\_1~\\
X0~X4~X9))))))){\unicdcdcdhd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X7 .  (m1\_subset\_1~X7~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X8 .  (m1\_subset\_1~X8~k1\_numbers){\unicdbdjdcd}((k3\_rlvect\_1~X0~(k3\_rlvect\_1~\\
X0~(k3\_rlvect\_1~X0~(k1\_rlvect\_1~X0~X1~X5)~(k1\_rlvect\_1~X0~X2~X6))~\\
(k1\_rlvect\_1~X0~X3~X7))~(k1\_rlvect\_1~X0~X4~X8)=k4\_struct\_0~X0){\unicdbdjdcd}\\
((X5=k6\_numbers){\unicdcdcdhd}((X6=k6\_numbers){\unicdcdcdhd}((X7=k6\_numbers){\unicdcdcdhd}(X8=\\
k6\_numbers)))))))))))))){\unicdcdcdhd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}(\\
(v2\_collsp~X1){\unicdcdcdhd}((v3\_collsp~X1){\unicdcdcdhd}((v4\_collsp~X1){\unicdcdcdhd}((v2\_anproj\_2~\\
X1){\unicdcdcdhd}((v3\_anproj\_2~X1){\unicdcdcdhd}(l1\_collsp~X1))))))){\unicdbdjdcd}(\preoh (X1=k5\_anproj\_1~\\
X0){\unicdcdcdhd}((\preoh v7\_anproj\_2~X1){\unicdcdcdhd}(v8\_anproj\_2~X1)))))\end{array}$$
\end{theorem}
\end{document}
