\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{t11\_modcat\_1 (TMMntb84RGP29LszgK5oXLGN6DDrgUYHarw)}
\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\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m4\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_funct\_1 : {{\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 $ k6\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_modcat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_mod\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\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))))))))){\unicdcdcdhd}\\
(m1\_modcat\_1~X1~X0)){\unicdbdjdcd}((v1\_funct\_1~(k10\_modcat\_1~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~\\
(k10\_modcat\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(\\
k4\_modcat\_1~X0~X1)~(k4\_modcat\_1~X0~X1))~(k4\_modcat\_1~X0~X1)))))\end{array}
\label{hyp:egehpflgbdadpfngpgegdgbgehpfbd}
\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\_modcat\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_modcat\_1~X2~X0~\\
(k4\_modcat\_1~X0~X1)){\unicdbdjdcd}(k6\_modcat\_1~X0~X1~X2=k3\_mod\_2~X0~X2)))\end{array}
\label{hyp:egjdpfngpgegdgbgehpfbd}
\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\_modcat\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_modcat\_1~X2~X0~\\
(k4\_modcat\_1~X0~X1)){\unicdbdjdcd}(k5\_modcat\_1~X0~X1~X2=k2\_mod\_2~X0~X2)))\end{array}
\label{hyp:egidpfngpgegdgbgehpfbd}
\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\_modcat\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_modcat\_1~\\
X0~X1)~(k4\_modcat\_1~X0~X1))~(k4\_modcat\_1~X0~X1))))){\unicdbdjdcd}((X2=k10\_modcat\_1~\\
X0~X1){\unicdbdjded}(({\unicdcdadad} X3 .  (m4\_modcat\_1~X3~X0~(k4\_modcat\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m4\_modcat\_1~X4~X0~(k4\_modcat\_1~X0~X1)){\unicdbdjdcd}((k4\_tarski~X3~X4 \in k1\_relset\_1~\\
(k2\_zfmisc\_1~(k4\_modcat\_1~X0~X1)~(k4\_modcat\_1~X0~X1))~X2){\unicdbdjded}(k5\_modcat\_1~\\
X0~X1~X3=k6\_modcat\_1~X0~X1~X4)))){\unicdcdcdhd}({\unicdcdadad} X3 .  (m4\_modcat\_1~X3~X0~\\
(k4\_modcat\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m4\_modcat\_1~X4~X0~(k4\_modcat\_1~\\
X0~X1)){\unicdbdjdcd}((k4\_tarski~X3~X4 \in k1\_relset\_1~(k2\_zfmisc\_1~(k4\_modcat\_1~\\
X0~X1)~(k4\_modcat\_1~X0~X1))~X2){\unicdbdjdcd}(k1\_binop\_1~X2~X3~X4=k8\_mod\_2~X0~\\
X3~X4))))))))\end{array}
\label{hyp:egbdedpfngpgegdgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfngpgegdgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}(\\
(v4\_vectsp\_1~X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0))))))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_modcat\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m4\_modcat\_1~X2~X0~\\
(k4\_modcat\_1~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m4\_modcat\_1~X3~X0~(k4\_modcat\_1~\\
X0~X1)){\unicdbdjdcd}((k4\_tarski~X2~X3 \in k1\_relset\_1~(k2\_zfmisc\_1~(k4\_modcat\_1~\\
X0~X1)~(k4\_modcat\_1~X0~X1))~(k10\_modcat\_1~X0~X1)){\unicdbdjded}(k2\_mod\_2~X0~X2=\\
k3\_mod\_2~X0~X3)))))\end{array}$$
\end{theorem}
\end{document}
