\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{t24\_anproj\_1 (TMMi4AgFQZ4RvgtBXKmeVdGS9YxZsMe3tVL)}
\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 $ k3\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_collsp : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_anproj\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_anproj\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v9\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_anproj\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k3\_anproj\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_anproj\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_collsp : {{\iota}{\unicdbdjdcd}{{\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}((u1\_struct\_0~(k5\_anproj\_1~\\
X0)=k3\_anproj\_1~X0){\unicdcdcdhd}(u1\_collsp~(k5\_anproj\_1~X0)=k4\_anproj\_1~\\
X0))\end{array}
\label{hyp:ehcdddpfbgogahchpgkgpfbd}
\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}(m1\_collsp~(k4\_anproj\_1~X0)~\\
(k3\_anproj\_1~X0))\end{array}
\label{hyp:egehpflgedpfbgogahchpgkgpfbd}
\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}({\unicdcdadad} X1 .  (m1\_collsp~X1~(k3\_anproj\_1~\\
X0)){\unicdbdjdcd}((X1=k4\_anproj\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  \\
(k3\_xtuple\_0~X2~X3~X4 \in X1){\unicdbdjded}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}({\unicdcdaddd} X7 .  \\
(m1\_subset\_1~X7~(u1\_struct\_0~X0)){\unicdcdcdhd}((X2=k2\_anproj\_1~X0~X5){\unicdcdcdhd}((\\
X3=k2\_anproj\_1~X0~X6){\unicdcdcdhd}((X4=k2\_anproj\_1~X0~X7){\unicdcdcdhd}((\preoh v9\_struct\_0~\\
X5~X0){\unicdcdcdhd}((\preoh v9\_struct\_0~X6~X0){\unicdcdcdhd}((\preoh v9\_struct\_0~X7~X0){\unicdcdcdhd}(r2\_anproj\_1~\\
X0~X5~X6~X7)))))))))))))\end{array}
\label{hyp:eggdpfbgogahchpgkgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdedpfbgogahchpgkgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v2\_struct\_0~X3){\unicdcdcdhd}\\
((\preoh v7\_struct\_0~X3){\unicdcdcdhd}((v13\_algstr\_0~X3){\unicdcdcdhd}((v2\_rlvect\_1~X3){\unicdcdcdhd}((\\
v3\_rlvect\_1~X3){\unicdcdcdhd}((v4\_rlvect\_1~X3){\unicdcdcdhd}((v5\_rlvect\_1~X3){\unicdcdcdhd}((v6\_rlvect\_1~\\
X3){\unicdcdcdhd}((v7\_rlvect\_1~X3){\unicdcdcdhd}((v8\_rlvect\_1~X3){\unicdcdcdhd}(l1\_rlvect\_1~X3))))))))))){\unicdbdjdcd}\\
(\preoh (k3\_xtuple\_0~X0~X1~X2 \in u1\_collsp~(k5\_anproj\_1~X3)){\unicdcdcdhd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~\\
(u1\_struct\_0~X3)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X3)){\unicdbdjdcd}\\
(\preoh (X0=k2\_anproj\_1~X3~X4){\unicdcdcdhd}((X1=k2\_anproj\_1~X3~X5){\unicdcdcdhd}((X2=k2\_anproj\_1~\\
X3~X6){\unicdcdcdhd}((\preoh v9\_struct\_0~X4~X3){\unicdcdcdhd}((\preoh v9\_struct\_0~X5~X3){\unicdcdcdhd}((\preoh v9\_struct\_0~\\
X6~X3){\unicdcdcdhd}(r2\_anproj\_1~X3~X4~X5~X6)))))))))))\end{array}$$
\end{theorem}
\end{document}
