\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{t7\_modcat\_1 (TMdmjYNz6rN5dde6D3ASmQYiuC8f8HNUpSt)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_classes2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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 $ k2\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v8\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v9\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v10\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_grcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k17\_grcat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ g2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdcdcdhd}\\
((\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)))))))))){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k2\_modcat\_1~X0~X1))\end{array}
\label{hyp:ggdgbdpfngpgegdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\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))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(X2=k2\_modcat\_1~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjded}({\unicdcdaddd} X4 .  (X4 \in \\
ReplSep2~(toset~({\uniddcgcg} X5 : \iota .  m2\_grcat\_1~X5~(k17\_grcat\_1~X0)))~\\
({\uniddcgcg} X5 : \iota .  toset~({\uniddcgcg} X6 : \iota .  m2\_funct\_2~X6~(k2\_zfmisc\_1~(u1\_struct\_0~\\
X1)~np\_\_1)~np\_\_1~(k9\_funct\_2~(k2\_zfmisc\_1~(u1\_struct\_0~X1)~np\_\_1)~\\
np\_\_1)))~({\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \iota .  True)~({\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \\
\iota .  k4\_tarski~X5~X6)){\unicdcdcdhd}(r1\_modcat\_1~X4~X3~X1)))))\end{array}
\label{hyp:eggdpfngpgegdgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}\\
((v3\_group\_1~X2){\unicdcdcdhd}((v4\_vectsp\_1~X2){\unicdcdcdhd}((v5\_vectsp\_1~X2){\unicdcdcdhd}(l6\_algstr\_0~\\
X2))))))))){\unicdbdjdcd}((r1\_modcat\_1~X0~X1~X2){\unicdbdjded}({\unicdcdaddd} X3 .  {\unicdcdaddd} X4 .  (\\
X0=k4\_tarski~X3~X4){\unicdcdcdhd}({\unicdcdaddd} 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}\\
((v7\_vectsp\_1~X5~X2){\unicdcdcdhd}((v8\_vectsp\_1~X5~X2){\unicdcdcdhd}((v9\_vectsp\_1~X5~X2){\unicdcdcdhd}\\
((v10\_vectsp\_1~X5~X2){\unicdcdcdhd}((v11\_vectsp\_1~X5~X2){\unicdcdcdhd}(l1\_vectsp\_1~X5~X2))))))))))){\unicdcdcdhd}\\
((X1=X5){\unicdcdcdhd}((X3=g2\_algstr\_0~(u1\_struct\_0~X5)~(u1\_algstr\_0~X5)~\\
(u2\_struct\_0~X5)){\unicdcdcdhd}(X4=u1\_vectsp\_1~X2~X5))))))\end{array}
\label{hyp:egfdpfngpgegdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehhdpfngpgegdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_classes2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((\\
v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v3\_group\_1~X1){\unicdcdcdhd}((v4\_vectsp\_1~\\
X1){\unicdcdcdhd}((v5\_vectsp\_1~X1){\unicdcdcdhd}(l6\_algstr\_0~X1))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k2\_modcat\_1~X0~X1)){\unicdbdjdcd}((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v13\_algstr\_0~\\
X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~X2){\unicdcdcdhd}\\
((v7\_vectsp\_1~X2~X1){\unicdcdcdhd}((v8\_vectsp\_1~X2~X1){\unicdcdcdhd}((v9\_vectsp\_1~X2~X1){\unicdcdcdhd}\\
((v10\_vectsp\_1~X2~X1){\unicdcdcdhd}((v11\_vectsp\_1~X2~X1){\unicdcdcdhd}(l1\_vectsp\_1~X2~X1)))))))))))))\end{array}$$
\end{theorem}
\end{document}
