\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{t8\_algstr\_3 (TMF1nVUBRv3aMwMjwSHiZPqn1QwYtzNB7rM)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_algstr\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_algstr\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_algstr\_3~X0){\unicdcdcdhd}(l1\_algstr\_3~\\
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}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((k1\_algstr\_3~X0~X1~X2~X3=k1\_algstr\_3~X0~X1~X4~X3){\unicdbdjdcd}((X1=k4\_struct\_0~\\
X0){\unicdcdcdid}(X2=X4)))))))\end{array}
\label{hyp:ehgdpfbgmghgdhehchpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_algstr\_3~X0){\unicdcdcdhd}(l1\_algstr\_3~\\
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}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  (m1\_subset\_1~\\
X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(((k1\_algstr\_3~X0~X3~X1~X4=k1\_algstr\_3~X0~\\
X5~X1~X6){\unicdcdcdhd}(k1\_algstr\_3~X0~X3~X2~X4=k1\_algstr\_3~X0~X5~X2~X6)){\unicdbdjdcd}((X1=\\
X2){\unicdcdcdid}((X3=X5){\unicdcdcdhd}(X4=X6))))))))))\end{array}
\label{hyp:ehedpfbgmghgdhehchpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_algstr\_3~X0)){\unicdbdjdcd}((v2\_algstr\_3~\\
X0){\unicdbdjded}((k4\_struct\_0~X0{\unicdcdgdad}k5\_struct\_0~X0){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_algstr\_3~X0~X1~(k5\_struct\_0~X0)~(k4\_struct\_0~\\
X0)=X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_algstr\_3~\\
X0~(k5\_struct\_0~X0)~X1~(k4\_struct\_0~X0)=X1)){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k1\_algstr\_3~X0~X1~(k4\_struct\_0~X0)~X2=X2))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_algstr\_3~X0~(k4\_struct\_0~X0)~X1~X2=X2))){\unicdcdcdhd}\\
(({\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}({\unicdcdaddd} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
(k1\_algstr\_3~X0~X1~X2~X4=X3))))){\unicdcdcdhd}(({\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}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}((k1\_algstr\_3~X0~X1~X2~X3=k1\_algstr\_3~X0~X1~\\
X2~X4){\unicdbdjdcd}(X3=X4)))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}X2){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdcdcdhd}((k1\_algstr\_3~\\
X0~X5~X1~X6=X3){\unicdcdcdhd}(k1\_algstr\_3~X0~X5~X2~X6=X4))))))))){\unicdcdcdhd}(({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}((X1{\unicdcdgdad}X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdcdcdhd}(k1\_algstr\_3~X0~X1~X5~X3=k1\_algstr\_3~\\
X0~X2~X5~X4))))))){\unicdcdcdhd}({\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}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~X5~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X6 .  \\
(m1\_subset\_1~X6~(u1\_struct\_0~X0)){\unicdbdjdcd}(\preoh (k1\_algstr\_3~X0~X3~X1~X5=k1\_algstr\_3~\\
X0~X4~X1~X6){\unicdcdcdhd}((k1\_algstr\_3~X0~X3~X2~X5=k1\_algstr\_3~X0~X4~X2~X6){\unicdcdcdhd}((\\
X1{\unicdcdgdad}X2){\unicdcdcdhd}(X3{\unicdcdgdad}X4))))))))))))))))))))\end{array}
\label{hyp:egfdpfbgmghgdhehchpfdd}
\end{equation}
\begin{theorem}\label{thm:ehidpfbgmghgdhehchpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_algstr\_3~X0){\unicdcdcdhd}(l1\_algstr\_3~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
((k1\_algstr\_3~X0~X2~X1~X3=k1\_algstr\_3~X0~X4~X1~X3){\unicdbdjdcd}((X1=k4\_struct\_0~\\
X0){\unicdcdcdid}(X2=X4)))))))\end{array}$$
\end{theorem}
\end{document}
