\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{t30\_osalg\_1 (TMMVHkdFyHdzjemPwViT99gHYBmEfGYiJ3r)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ l1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v3\_relat\_2~X3){\unicdcdcdhd}\\
((v1\_partfun1~X3~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))))){\unicdbdjdcd}((X1 \in k6\_eqrel\_1~X0~X0~X3~X2){\unicdbdjded}(k4\_tarski~X1~X2 \in X3))\end{array}
\label{hyp:ehbdjdpffgbhchfgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~\\
X0){\unicdcdcdhd}(l1\_osalg\_1~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u4\_struct\_0~X0)))){\unicdbdjdcd}((r1\_osalg\_1~X0~X1~X2){\unicdbdjdcd}(r1\_osalg\_1~X0~X2~\\
X1))\end{array}
\label{hyp:dhjhngngfgehchjhpfchbdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_osalg\_1~X0){\unicdbdjdcd}((v3\_relat\_2~(u1\_osalg\_1~X0)){\unicdcdcdhd}((\\
v8\_relat\_2~(u1\_osalg\_1~X0)){\unicdcdcdhd}((v1\_partfun1~(u1\_osalg\_1~X0)~(u4\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~(u1\_osalg\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u4\_struct\_0~X0)~(u4\_struct\_0~X0)))))))\end{array}
\label{hyp:egehpffhbdpfpgdhbgmghgpfbd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}(l1\_osalg\_1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u4\_struct\_0~X0)){\unicdbdjdcd}((r1\_osalg\_1~X0~X1~X2){\unicdbdjded}(k4\_tarski~\\
X1~X2 \in u1\_osalg\_1~X0))))\end{array}
\label{hyp:egcdpfpgdhbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddadpfpgdhbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}((r1\_osalg\_1~X0~X1~X2){\unicdbdjded}(X2 \in k6\_eqrel\_1~(u4\_struct\_0~X0)~(\\
u4\_struct\_0~X0)~(u1\_osalg\_1~X0)~X1))))\end{array}$$
\end{theorem}
\end{document}
