\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{t92\_zmodul01 (TMFWFQnKFwXgDcuyUPQEJsBcSeirSicxFQn)}
\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\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_zmodul01 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_zmodul01 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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}((\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)))))))))))\end{array}
\label{hyp:egehpfngbdpfkhngpgegfhmgadbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgcdpfdhehchfhdgehpfad}
\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 .  {\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 .  (l1\_struct\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (r1\_struct\_0~X0~X1){\unicdbdjded}\\
(X1 \in u1\_struct\_0~X0))\end{array}
\label{hyp:egfdpfdhehchfhdgehpfad}
\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=k6\_zmodul01~X0~X1~X2){\unicdbdjded}(u1\_struct\_0~X3=ReplSep2~(toset~({\uniddcgcg} X4 : \\
\iota .  m1\_subset\_1~X4~(u1\_struct\_0~X0)))~({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \\
\iota .  m1\_subset\_1~X5~(u1\_struct\_0~X0)))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \\
(r1\_struct\_0~X1~X4){\unicdcdcdhd}(r1\_struct\_0~X2~X5))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \\
\iota .  k3\_rlvect\_1~X0~X4~X5))))))\end{array}
\label{hyp:egbdedpfkhngpgegfhmgadbd}
\end{equation}
\begin{theorem}\label{thm:ehjdcdpfkhngpgegfhmgadbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v13\_algstr\_0~X1){\unicdcdcdhd}\\
((v2\_rlvect\_1~X1){\unicdcdcdhd}((v3\_rlvect\_1~X1){\unicdcdcdhd}((v4\_rlvect\_1~X1){\unicdcdcdhd}((v2\_zmodul01~\\
X1){\unicdcdcdhd}((v3\_zmodul01~X1){\unicdcdcdhd}((v4\_zmodul01~X1){\unicdcdcdhd}((v5\_zmodul01~X1){\unicdcdcdhd}\\
(l1\_zmodul01~X1)))))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_zmodul01~X2~X1){\unicdbdjdcd}(\\
{\unicdcdadad} X3 .  (m1\_zmodul01~X3~X1){\unicdbdjdcd}((r1\_struct\_0~(k6\_zmodul01~X1~\\
X2~X3)~X0){\unicdbdjded}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X1)){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X1)){\unicdcdcdhd}((r1\_struct\_0~X2~X4){\unicdcdcdhd}((r1\_struct\_0~\\
X3~X5){\unicdcdcdhd}(X0=k3\_rlvect\_1~X1~X4~X5))))))))\end{array}$$
\end{theorem}
\end{document}
