\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{l138\_zmodul01 (TMXeuqcr3K21CxQKCtbyTMr24jJ2hfyNwSk)}
\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_zmodul01 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_zmodul01 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_zmodul01 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{{k3\_xboole\_0}~{X0}}~{X1}}={X0}})}}}}\label{hyp:ehcdidpfihcgpgpgmgfgpfbd}
\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 .  (m1\_zmodul01~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_zmodul01~\\
X2~X0){\unicdbdjdcd}(r1\_tarski~(u1\_struct\_0~X1)~(u1\_struct\_0~(k6\_zmodul01~\\
X0~X1~X2)))))\end{array}
\label{hyp:mgbdbdfdpfkhngpgegfhmgadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\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)))))))))){\unicdcdcdhd}((m1\_zmodul01~X1~X0){\unicdcdcdhd}(m1\_zmodul01~\\
X2~X0))){\unicdbdjdcd}((v1\_zmodul01~(k7\_zmodul01~X0~X1~X2)){\unicdcdcdhd}(m1\_zmodul01~(\\
k7\_zmodul01~X0~X1~X2)~X0))\end{array}
\label{hyp:egehpflghdpfkhngpgegfhmgadbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\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)))))))))){\unicdcdcdhd}((m1\_zmodul01~X1~X0){\unicdcdcdhd}(m1\_zmodul01~\\
X2~X0))){\unicdbdjdcd}((v1\_zmodul01~(k6\_zmodul01~X0~X1~X2)){\unicdcdcdhd}(m1\_zmodul01~(\\
k6\_zmodul01~X0~X1~X2)~X0))\end{array}
\label{hyp:egehpflggdpfkhngpgegfhmgadbd}
\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 .  (m1\_zmodul01~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_zmodul01~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_zmodul01~X3){\unicdcdcdhd}(m1\_zmodul01~X3~X0)){\unicdbdjdcd}((\\
X3=k7\_zmodul01~X0~X1~X2){\unicdbdjded}(u1\_struct\_0~X3=k3\_xboole\_0~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X2))))))\end{array}
\label{hyp:egbdfdpfkhngpgegfhmgadbd}
\end{equation}
\begin{theorem}\label{thm:mgbdddidpfkhngpgegfhmgadbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v2\_zmodul01~X0){\unicdcdcdhd}\\
((v3\_zmodul01~X0){\unicdcdcdhd}((v4\_zmodul01~X0){\unicdcdcdhd}((v5\_zmodul01~X0){\unicdcdcdhd}(l1\_zmodul01~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_zmodul01~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_zmodul01~\\
X2~X0){\unicdbdjdcd}(u1\_struct\_0~(k7\_zmodul01~X0~X1~(k6\_zmodul01~X0~X1~X2))=\\
u1\_struct\_0~X1)))\end{array}$$
\end{theorem}
\end{document}
