\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{t42\_zmodul01 (TMcqv2X4Rb862EC8rTRaUsz9jPtxXvpw2Xf)}
\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 $ v2\_zmodul01 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_zmodul01 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_zmodul01 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_zmodul01 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_zmodul01 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_zmodul01 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_zmodul01 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_realset1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}\\
(r1\_tarski~X2~X3)){\unicdbdjdcd}(r1\_tarski~(k2\_zfmisc\_1~X0~X2)~(k2\_zfmisc\_1~\\
X1~X3))\end{array}
\label{hyp:ehjdgdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~X0~X1){\unicdbdjdcd}((r1\_tarski~\\
(k2\_zfmisc\_1~X0~X2)~(k2\_zfmisc\_1~X1~X2)){\unicdcdcdhd}(r1\_tarski~(k2\_zfmisc\_1~\\
X2~X0)~(k2\_zfmisc\_1~X2~X1)))\end{array}
\label{hyp:ehjdfdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((r1\_tarski~X0~X1){\unicdbdjdcd}((k5\_relat\_1~(k5\_relat\_1~X2~X0)~X1=k5\_relat\_1~\\
X2~X0){\unicdcdcdhd}(k5\_relat\_1~(k5\_relat\_1~X2~X1)~X0=k5\_relat\_1~X2~X0)))\end{array}
\label{hyp:ehfdbdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((r1\_tarski~X0~X1){\unicdcdcdhd}(r1\_tarski~\\
X1~X2)){\unicdbdjdcd}(r1\_tarski~X0~X2)\end{array}
\label{hyp:ehbdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_partfun1~\\
X0~X1~X2~X3=k5\_relat\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_relat\_1}~{({{{k2\_zfmisc\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdggdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_zmodul01~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_zmodul01~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_zmodul01~X0)~(k2\_zfmisc\_1~k4\_numbers~(u1\_struct\_0~\\
X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_zmodul01~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~k4\_numbers~(u1\_struct\_0~X0))~(u1\_struct\_0~\\
X0))))))\end{array}
\label{hyp:egehpffhbdpfkhngpgegfhmgadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(u1\_algstr\_0~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(u1\_algstr\_0~X0)~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_algstr\_0~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X0))~(u1\_struct\_0~X0))))))\end{array}
\label{hyp:egehpffhbdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_zmodul01}~{X0}})}{\unicdbdjdcd}{({{l2\_algstr\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfkhngpgegfhmgadbd}
\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}((v2\_zmodul01~X0){\unicdcdcdhd}\\
((v3\_zmodul01~X0){\unicdcdcdhd}((v4\_zmodul01~X0){\unicdcdcdhd}((v5\_zmodul01~X0){\unicdcdcdhd}(l1\_zmodul01~\\
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}\\
((v2\_zmodul01~X1){\unicdcdcdhd}((v3\_zmodul01~X1){\unicdcdcdhd}((v4\_zmodul01~X1){\unicdcdcdhd}((v5\_zmodul01~\\
X1){\unicdcdcdhd}(l1\_zmodul01~X1)))))))))){\unicdbdjdcd}((m1\_zmodul01~X1~X0){\unicdbdjded}((r1\_tarski~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X0)){\unicdcdcdhd}((k4\_struct\_0~X1=k4\_struct\_0~\\
X0){\unicdcdcdhd}((u1\_algstr\_0~X1=k1\_realset1~(u1\_algstr\_0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(u1\_zmodul01~X1=k2\_partfun1~(k2\_zfmisc\_1~k4\_numbers~(u1\_struct\_0~\\
X0))~(u1\_struct\_0~X0)~(u1\_zmodul01~X0)~(k2\_zfmisc\_1~k4\_numbers~\\
(u1\_struct\_0~X1))))))))\end{array}
\label{hyp:egjdpfkhngpgegfhmgadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  k1\_realset1~X0~X1=k5\_relat\_1~\\
X0~(k2\_zfmisc\_1~X1~X1))\end{array}
\label{hyp:egcdpfchfgbgmgdhfgehbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_relat\_1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_relat\_1~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedcdpfkhngpgegfhmgadbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v2\_zmodul01~X0){\unicdcdcdhd}\\
((v3\_zmodul01~X0){\unicdcdcdhd}((v4\_zmodul01~X0){\unicdcdcdhd}((v5\_zmodul01~X0){\unicdcdcdhd}(l1\_zmodul01~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~\\
X1){\unicdcdcdhd}((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}\\
((v2\_zmodul01~X1){\unicdcdcdhd}((v3\_zmodul01~X1){\unicdcdcdhd}((v4\_zmodul01~X1){\unicdcdcdhd}((v5\_zmodul01~\\
X1){\unicdcdcdhd}(l1\_zmodul01~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}\\
((v13\_algstr\_0~X2){\unicdcdcdhd}((v2\_rlvect\_1~X2){\unicdcdcdhd}((v3\_rlvect\_1~X2){\unicdcdcdhd}((v4\_rlvect\_1~\\
X2){\unicdcdcdhd}((v2\_zmodul01~X2){\unicdcdcdhd}((v3\_zmodul01~X2){\unicdcdcdhd}((v4\_zmodul01~X2){\unicdcdcdhd}\\
((v5\_zmodul01~X2){\unicdcdcdhd}(l1\_zmodul01~X2)))))))))){\unicdbdjdcd}(((m1\_zmodul01~\\
X0~X1){\unicdcdcdhd}(m1\_zmodul01~X1~X2)){\unicdbdjdcd}(m1\_zmodul01~X0~X2))))\end{array}$$
\end{theorem}
\end{document}
