\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{l5\_algstr\_2 (TMVvCJhcT3GbP7FCQcWdxiuAku6LeKrfQLk)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_vectsp\_1 : {\iota}$ be given.
Let $ k8\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v33\_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 $ v5\_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 $ k6\_numbers : {\iota}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k8\_group\_1~X0~(k4\_struct\_0~\\
X0)~X1=k4\_struct\_0~X0))\end{array}
\label{hyp:ehbdedpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v33\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}\\
((v4\_rlvect\_1~X0){\unicdcdcdhd}((v3\_group\_1~X0){\unicdcdcdhd}((v5\_group\_1~X0){\unicdcdcdhd}((v4\_vectsp\_1~\\
X0){\unicdcdcdhd}((v5\_vectsp\_1~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)))))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k8\_group\_1~X0~X1~(k4\_struct\_0~\\
X0)=k4\_struct\_0~X0))\end{array}
\label{hyp:ehbdddpfchfgbgmgdhfgehcd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={{k4\_struct\_0}~{k2\_vectsp\_1}}}\label{hyp:mgbdpfbgmghgdhehchpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v6\_struct\_0~k2\_vectsp\_1){\unicdcdcdhd}((v13\_algstr\_0~k2\_vectsp\_1){\unicdcdcdhd}((\\
v33\_algstr\_0~k2\_vectsp\_1){\unicdcdcdhd}((v36\_algstr\_0~k2\_vectsp\_1){\unicdcdcdhd}((v2\_rlvect\_1~\\
k2\_vectsp\_1){\unicdcdcdhd}((v3\_rlvect\_1~k2\_vectsp\_1){\unicdcdcdhd}((v4\_rlvect\_1~k2\_vectsp\_1){\unicdcdcdhd}\\
((v3\_group\_1~k2\_vectsp\_1){\unicdcdcdhd}((v5\_group\_1~k2\_vectsp\_1){\unicdcdcdhd}((v3\_vectsp\_1~\\
k2\_vectsp\_1){\unicdcdcdhd}((v5\_vectsp\_1~k2\_vectsp\_1){\unicdcdcdhd}(v6\_vectsp\_1~k2\_vectsp\_1)))))))))))\end{array}
\label{hyp:ggdgidpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k2\_vectsp\_1}})}{\unicdcdcdhd}{({{v4\_vectsp\_1}~{k2\_vectsp\_1}})}}\label{hyp:ggdggdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v2\_struct\_0}~{k2\_vectsp\_1}}}})}{\unicdcdcdhd}{({{v36\_algstr\_0}~{k2\_vectsp\_1}})}}\label{hyp:ggdgedpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({{v36\_algstr\_0}~{k2\_vectsp\_1}})}{\unicdcdcdhd}{({{l6\_algstr\_0}~{k2\_vectsp\_1}})}}\label{hyp:egehpflgcdpfghfgdgehdhahpfbd}
\end{equation}
\begin{theorem}\label{thm:mgfdpfbgmghgdhehchpfcd}
$$\begin{array}{c}({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k2\_vectsp\_1)){\unicdbdjdcd}(k8\_group\_1~\\
k2\_vectsp\_1~X0~(k4\_struct\_0~k2\_vectsp\_1)=k4\_struct\_0~k2\_vectsp\_1)){\unicdcdcdhd}\\
({\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~k2\_vectsp\_1)){\unicdbdjdcd}(k8\_group\_1~\\
k2\_vectsp\_1~(k4\_struct\_0~k2\_vectsp\_1)~X0=k4\_struct\_0~k2\_vectsp\_1))\end{array}$$
\end{theorem}
\end{document}
