\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{t23\_osalg\_1 (TMY5A9sZUpNj2CNWfUP5xLgu1sSnwnux2aw)}
\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 $ r6\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ l2\_osalg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v4\_orders\_2~X0){\unicdcdcdhd}(l1\_orders\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
(((r1\_orders\_2~X0~X1~X2){\unicdcdcdhd}(r1\_orders\_2~X0~X2~X3)){\unicdbdjdcd}(r1\_orders\_2~\\
X0~X1~X3)))))\end{array}
\label{hyp:ehddpfpgchegfgchdhpfcd}
\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}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u4\_struct\_0~X0)){\unicdbdjdcd}(((r1\_osalg\_1~X0~X1~X2){\unicdcdcdhd}(r1\_osalg\_1~X0~X2~X3)){\unicdbdjdcd}\\
(r1\_osalg\_1~X0~X1~X3)))))\end{array}
\label{hyp:ehcdpfpgdhbgmghgpfbd}
\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 .  (m2\_finseq\_2~\\
X1~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_2~X2~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_finseq\_2~X3~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}(((r2\_osalg\_1~X0~X1~X2){\unicdcdcdhd}(r2\_osalg\_1~X0~X2~X3)){\unicdbdjdcd}(r2\_osalg\_1~\\
X0~X1~X3)))))\end{array}
\label{hyp:ehcdbdpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v3\_orders\_2~\\
X0){\unicdcdcdhd}(l1\_orders\_2~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(\\
m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}((r3\_orders\_2~X0~X1~X2){\unicdbdjded}(r1\_orders\_2~\\
X0~X1~X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchddpfpgchegfgchdhpfcd}
\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 .  {{({{l2\_osalg\_1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_msualg\_1}~{X0}})}{\unicdcdcdhd}{({{l1\_orders\_2}~{X0}})}})}}}\label{hyp:egehpfmgcdpfpgdhbgmghgpfbd}
\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}(m1\_subset\_1~X1~(u4\_struct\_0~X0))){\unicdbdjdcd}(m1\_subset\_1~\\
(k2\_msualg\_1~X0~X1)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgcdpfngdhfhbgmghgpfbd}
\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}(m1\_subset\_1~X1~(u4\_struct\_0~X0))){\unicdbdjdcd}(m2\_finseq\_2~\\
(k1\_msualg\_1~X0~X1)~(u1\_struct\_0~X0)~(k3\_finseq\_2~(u1\_struct\_0~\\
X0)))\end{array}
\label{hyp:egehpflgbdpfngdhfhbgmghgpfbd}
\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 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}((r6\_osalg\_1~X0~X1~X2){\unicdbdjded}((r1\_osalg\_1~X0~X1~X2){\unicdcdcdhd}((r2\_osalg\_1~\\
X0~(k1\_msualg\_1~X0~X1)~(k1\_msualg\_1~X0~X2)){\unicdcdcdhd}(r3\_orders\_2~X0~(k2\_msualg\_1~\\
X0~X1)~(k2\_msualg\_1~X0~X2)))))))\end{array}
\label{hyp:egcdadpfpgdhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_osalg\_1~X0){\unicdbdjdcd}((v4\_osalg\_1~X0){\unicdbdjdcd}((v3\_orders\_2~X0){\unicdcdcdhd}\\
((v4\_orders\_2~X0){\unicdcdcdhd}(v5\_orders\_2~X0))))\end{array}
\label{hyp:dgdgbdpfpgdhbgmghgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdddpfpgdhbgmghgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((\preoh v11\_struct\_0~X0){\unicdcdcdhd}((v4\_osalg\_1~\\
X0){\unicdcdcdhd}((v5\_osalg\_1~X0){\unicdcdcdhd}(l3\_osalg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u4\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u4\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u4\_struct\_0~X0)){\unicdbdjdcd}(((r6\_osalg\_1~\\
X0~X1~X2){\unicdcdcdhd}(r6\_osalg\_1~X0~X2~X3)){\unicdbdjdcd}(r6\_osalg\_1~X0~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
