\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{t20\_osalg\_2 (TMFXGEMHyxXGvVKmYxkeuT4mdqkVDbyjpt8)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v12\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_osalg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_msualg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_msualg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v11\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_msualg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (l3\_msualg\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pboole~\\
X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}((X2 \in k6\_msualg\_2~X0~X1){\unicdbdjded}\\
(v3\_msualg\_2~X2~X0~X1))))\end{array}
\label{hyp:ehbdedpfngdhfhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
(l1\_msualg\_1~X0))){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~(k6\_msualg\_2~\\
X0~X1))\end{array}
\label{hyp:ggdgidpfngdhfhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}\\
((v4\_osalg\_1~X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdcdcdhd}((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_osalg\_2~X2~X0~X1){\unicdbdjdcd}\\
(m3\_pboole~X2~(u1\_struct\_0~X0)~(u3\_msualg\_1~X0~X1)))\end{array}
\label{hyp:egehpfngcdpfpgdhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_osalg\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_osalg\_1}~{X0}})}{\unicdcdcdhd}{({{l2\_osalg\_1}~{X0}})}})}}}\label{hyp:egehpfmgddpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_osalg\_1}~{X0}})}{\unicdbdjdcd}{({{l1\_msualg\_1}~{X0}})}}}\label{hyp:egehpfmgbdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}(k6\_osalg\_2~X0~X1=ReplSep~(toset~(\\
{\uniddcgcg} X2 : \iota .  m1\_subset\_1~X2~(k6\_msualg\_2~X0~X1)))~({\uniddcgcg} X2 : \iota .  \\
(v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}((v1\_partfun1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(v11\_osalg\_1~X2~X0)))))~\\
({\uniddcgcg} X2 : \iota .  X2)))\end{array}
\label{hyp:egidpfpgdhbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m3\_pboole~X2~(u1\_struct\_0~\\
X0)~(u3\_msualg\_1~X0~X1)){\unicdbdjdcd}((m2\_osalg\_2~X2~X0~X1){\unicdbdjded}((v1\_relat\_1~X2){\unicdcdcdhd}\\
((v4\_relat\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_partfun1~\\
X2~(u1\_struct\_0~X0)){\unicdcdcdhd}(v11\_osalg\_1~X2~X0))))))))\end{array}
\label{hyp:egcdpfpgdhbgmghgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfpgdhbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v12\_osalg\_1~\\
X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_osalg\_2~X2~X0~X1){\unicdbdjdcd}\\
((X2 \in k6\_osalg\_2~X0~X1){\unicdbdjded}(v3\_msualg\_2~X2~X0~X1))))\end{array}$$
\end{theorem}
\end{document}
