\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{t2\_c0sp1 (TMd9YneV88eERYbs5HJTRXAgrceHHGJ5VHC)}
\maketitle
Let $ v2\_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 $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l6\_algstr\_0 : {{\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 $ v2\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ g6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k1\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_c0sp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_ideal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~\\
X4){\unicdcdcdhd}((v1\_funct\_2~X4~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v2\_struct\_0~\\
X5){\unicdcdcdhd}((v13\_algstr\_0~X5){\unicdcdcdhd}((v2\_rlvect\_1~X5){\unicdcdcdhd}((v3\_rlvect\_1~X5){\unicdcdcdhd}\\
((v4\_rlvect\_1~X5){\unicdcdcdhd}((v3\_group\_1~X5){\unicdcdcdhd}((v4\_vectsp\_1~X5){\unicdcdcdhd}((v5\_vectsp\_1~\\
X5){\unicdcdcdhd}(l6\_algstr\_0~X5))))))))){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~X6~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X5))){\unicdbdjdcd}(((X6=X0){\unicdcdcdhd}((X3=k1\_realset1~(u1\_algstr\_0~\\
X5)~X6){\unicdcdcdhd}((X4=k1\_realset1~(u2\_algstr\_0~X5)~X6){\unicdcdcdhd}((X1=k5\_struct\_0~\\
X5){\unicdcdcdhd}((X2=k4\_struct\_0~X5){\unicdcdcdhd}(v1\_c0sp1~X6~X5)))))){\unicdbdjdcd}(m1\_c0sp1~(g6\_algstr\_0~\\
X0~X3~X4~X1~X2)~X5))))))))\end{array}
\label{hyp:ehbdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_c0sp1~X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v3\_group\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}(l6\_algstr\_0~\\
X1))))))))))\end{array}
\label{hyp:egehpfngbdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k4\_c0sp1~X0~X1)~X1)\end{array}
\label{hyp:egehpflgedpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}\\
((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))){\unicdcdcdhd}(\\
m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}(m1\_subset\_1~\\
(k3\_c0sp1~X0~X1)~X1)\end{array}
\label{hyp:egehpflgddpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_c0sp1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k2\_c0sp1~X0~X1)~(k2\_zfmisc\_1~X1~\\
X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k2\_c0sp1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1)~X1)))))\end{array}
\label{hyp:egehpflgcdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k1\_c0sp1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k1\_c0sp1~X0~X1)~(k2\_zfmisc\_1~X1~\\
X1)~X1){\unicdcdcdhd}(m1\_subset\_1~(k1\_c0sp1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X1~X1)~X1)))))\end{array}
\label{hyp:egehpflgbdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v3\_c0sp1~X1~\\
X0){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}(k4\_c0sp1~X0~X1=k5\_struct\_0~X0))))\end{array}
\label{hyp:egidpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v3\_rlvect\_1~\\
X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_ideal\_1~X1~X0){\unicdcdcdhd}(v1\_c0sp1~\\
X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}(k3\_c0sp1~X0~X1=k4\_struct\_0~X0))))\end{array}
\label{hyp:eghdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l5\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v3\_c0sp1~X1~\\
X0){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}(k2\_c0sp1~X0~X1=k1\_realset1~(u2\_algstr\_0~\\
X0)~X1))))\end{array}
\label{hyp:eggdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l2\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v1\_ideal\_1~\\
X1~X0){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}(k1\_c0sp1~X0~X1=k1\_realset1~(u1\_algstr\_0~\\
X0)~X1))))\end{array}
\label{hyp:egfdpfdgaddhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}((v2\_c0sp1~X1~\\
X0){\unicdbdjdcd}((v1\_ideal\_1~X1~X0){\unicdcdcdhd}(v1\_c0sp1~X1~X0))))\end{array}
\label{hyp:dgdgbdpfdgaddhahbd}
\end{equation}
\begin{theorem}\label{thm:ehcdpfdgaddhahbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((v2\_c0sp1~X1~X0){\unicdcdcdhd}(v3\_c0sp1~X1~X0)){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}((\preoh v2\_struct\_0~\\
(g6\_algstr\_0~X1~(k1\_c0sp1~X0~X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~\\
(k3\_c0sp1~X0~X1))){\unicdcdcdhd}((v13\_algstr\_0~(g6\_algstr\_0~X1~(k1\_c0sp1~X0~\\
X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~X0~X1))){\unicdcdcdhd}((v2\_rlvect\_1~\\
(g6\_algstr\_0~X1~(k1\_c0sp1~X0~X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~\\
(k3\_c0sp1~X0~X1))){\unicdcdcdhd}((v3\_rlvect\_1~(g6\_algstr\_0~X1~(k1\_c0sp1~X0~\\
X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~X0~X1))){\unicdcdcdhd}((v4\_rlvect\_1~\\
(g6\_algstr\_0~X1~(k1\_c0sp1~X0~X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~\\
(k3\_c0sp1~X0~X1))){\unicdcdcdhd}((v3\_group\_1~(g6\_algstr\_0~X1~(k1\_c0sp1~X0~X1)~\\
(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~X0~X1))){\unicdcdcdhd}((v4\_vectsp\_1~\\
(g6\_algstr\_0~X1~(k1\_c0sp1~X0~X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~\\
(k3\_c0sp1~X0~X1))){\unicdcdcdhd}((v5\_vectsp\_1~(g6\_algstr\_0~X1~(k1\_c0sp1~X0~\\
X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~(k3\_c0sp1~X0~X1))){\unicdcdcdhd}(l6\_algstr\_0~\\
(g6\_algstr\_0~X1~(k1\_c0sp1~X0~X1)~(k2\_c0sp1~X0~X1)~(k4\_c0sp1~X0~X1)~\\
(k3\_c0sp1~X0~X1))))))))))))))\end{array}$$
\end{theorem}
\end{document}
