\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{t26\_funcsdom (TMTRj5BhT9dLUCTSQkS5DkkrWszC2TmT86J)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k11\_funcsdom : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v13\_algstr\_0 : {{\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 $ 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 $ l6\_algstr\_0 : {{\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\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v36\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_algstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(k11\_funcsdom~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k11\_funcsdom~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k11\_funcsdom~X0))){\unicdbdjdcd}((k1\_algstr\_0~(k11\_funcsdom~X0)~X1~X2=k1\_algstr\_0~\\
(k11\_funcsdom~X0)~X2~X1){\unicdcdcdhd}((k1\_algstr\_0~(k11\_funcsdom~X0)~(k1\_algstr\_0~\\
(k11\_funcsdom~X0)~X1~X2)~X3=k1\_algstr\_0~(k11\_funcsdom~X0)~X1~(k1\_algstr\_0~\\
(k11\_funcsdom~X0)~X2~X3)){\unicdcdcdhd}((k1\_algstr\_0~(k11\_funcsdom~X0)~X1~(\\
k4\_struct\_0~(k11\_funcsdom~X0))=X1){\unicdcdcdhd}(({\unicdcdaddd} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k11\_funcsdom~X0))){\unicdcdcdhd}(k1\_algstr\_0~(k11\_funcsdom~\\
X0)~X1~X4=k4\_struct\_0~(k11\_funcsdom~X0))){\unicdcdcdhd}((k6\_algstr\_0~(k11\_funcsdom~\\
X0)~X1~X2=k6\_algstr\_0~(k11\_funcsdom~X0)~X2~X1){\unicdcdcdhd}((k6\_algstr\_0~(\\
k11\_funcsdom~X0)~(k6\_algstr\_0~(k11\_funcsdom~X0)~X1~X2)~X3=k6\_algstr\_0~\\
(k11\_funcsdom~X0)~X1~(k6\_algstr\_0~(k11\_funcsdom~X0)~X2~X3)){\unicdcdcdhd}((\\
k6\_algstr\_0~(k11\_funcsdom~X0)~X1~(k5\_struct\_0~(k11\_funcsdom~X0))=\\
X1){\unicdcdcdhd}((k6\_algstr\_0~(k11\_funcsdom~X0)~(k5\_struct\_0~(k11\_funcsdom~\\
X0))~X1=X1){\unicdcdcdhd}((k6\_algstr\_0~(k11\_funcsdom~X0)~X1~(k1\_algstr\_0~(\\
k11\_funcsdom~X0)~X2~X3)=k1\_algstr\_0~(k11\_funcsdom~X0)~(k6\_algstr\_0~\\
(k11\_funcsdom~X0)~X1~X2)~(k6\_algstr\_0~(k11\_funcsdom~X0)~X1~X3)){\unicdcdcdhd}\\
(k6\_algstr\_0~(k11\_funcsdom~X0)~(k1\_algstr\_0~(k11\_funcsdom~X0)~\\
X2~X3)~X1=k1\_algstr\_0~(k11\_funcsdom~X0)~(k6\_algstr\_0~(k11\_funcsdom~\\
X0)~X2~X1)~(k6\_algstr\_0~(k11\_funcsdom~X0)~X3~X1))))))))))))))\end{array}
\label{hyp:ehcdfdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k11\_funcsdom~X0)){\unicdcdcdhd}\\
(v36\_algstr\_0~(k11\_funcsdom~X0)))\end{array}
\label{hyp:ggdgbdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdaddd} X1 .  {{{m1\_subset\_1}~{X1}}~{X0}}}}\label{hyp:fgihjgdhehfgogdgfgpfngbdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l6\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l5\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmggdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l4\_algstr\_0}~{X0}})}{\unicdcdcdhd}{({{l4\_struct\_0}~{X0}})}})}}}\label{hyp:egehpfmgfdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l4\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l3\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l3\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgedpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l2\_algstr\_0}~{X0}})}{\unicdbdjdcd}{({{({{l2\_struct\_0}~{X0}})}{\unicdcdcdhd}{({{l1\_algstr\_0}~{X0}})}})}}}\label{hyp:egehpfmgcdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_struct\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k4\_struct\_0~X0)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgedpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v36\_algstr\_0~(k11\_funcsdom~X0)){\unicdcdcdhd}\\
(l6\_algstr\_0~(k11\_funcsdom~X0)))\end{array}
\label{hyp:egehpflgbdbdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l6\_algstr\_0~X0)){\unicdbdjdcd}((v5\_vectsp\_1~\\
X0){\unicdbdjded}({\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}((k6\_algstr\_0~X0~X1~(k1\_algstr\_0~X0~X2~X3)=k1\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~X1~X2)~(k6\_algstr\_0~X0~X1~X3)){\unicdcdcdhd}(k6\_algstr\_0~X0~\\
(k1\_algstr\_0~X0~X2~X3)~X1=k1\_algstr\_0~X0~(k6\_algstr\_0~X0~X2~X1)~(\\
k6\_algstr\_0~X0~X3~X1)))))))\end{array}
\label{hyp:eghdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l4\_algstr\_0~X0)){\unicdbdjdcd}((v4\_vectsp\_1~\\
X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}((k6\_algstr\_0~\\
X0~X1~(k5\_struct\_0~X0)=X1){\unicdcdcdhd}(k6\_algstr\_0~X0~(k5\_struct\_0~X0)~X1=\\
X1))))\end{array}
\label{hyp:eggdpfghfgdgehdhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}((v4\_rlvect\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_algstr\_0~X0~X1~(k4\_struct\_0~\\
X0)=X1)))\end{array}
\label{hyp:egedpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}((v3\_rlvect\_1~X0){\unicdbdjded}({\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}\\
(k1\_algstr\_0~X0~(k1\_algstr\_0~X0~X1~X2)~X3=k1\_algstr\_0~X0~X1~(k1\_algstr\_0~\\
X0~X2~X3))))))\end{array}
\label{hyp:egddpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}((v3\_group\_1~X0){\unicdbdjded}({\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}(k6\_algstr\_0~\\
X0~(k6\_algstr\_0~X0~X1~X2)~X3=k6\_algstr\_0~X0~X1~(k6\_algstr\_0~X0~X2~\\
X3))))))\end{array}
\label{hyp:egddpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_algstr\_0~X0){\unicdbdjdcd}((v2\_rlvect\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k1\_algstr\_0~X0~X1~X2=k1\_algstr\_0~X0~X2~X1))))\end{array}
\label{hyp:egcdpfchmgghfgdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}((v13\_algstr\_0~X0){\unicdbdjded}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}(v10\_algstr\_0~X1~X0)))\end{array}
\label{hyp:egbdgdpfbgmghgdhehchpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_algstr\_0~X0){\unicdbdjdcd}((v5\_group\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}(k6\_algstr\_0~X0~X1~X2=k6\_algstr\_0~X0~X2~X1))))\end{array}
\label{hyp:egbdcdpfhgchpgfhahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l2\_algstr\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdbdjdcd}((v10\_algstr\_0~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(k1\_algstr\_0~X0~X1~X2=k4\_struct\_0~X0))))\end{array}
\label{hyp:egbdbdpfbgmghgdhehchpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdgdpfggfhogdgdhegpgng}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k11\_funcsdom~X0)){\unicdcdcdhd}\\
((v13\_algstr\_0~(k11\_funcsdom~X0)){\unicdcdcdhd}((v3\_group\_1~(k11\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_group\_1~(k11\_funcsdom~X0)){\unicdcdcdhd}((v4\_vectsp\_1~(k11\_funcsdom~\\
X0)){\unicdcdcdhd}((v5\_vectsp\_1~(k11\_funcsdom~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k11\_funcsdom~\\
X0)){\unicdcdcdhd}((v3\_rlvect\_1~(k11\_funcsdom~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k11\_funcsdom~\\
X0)){\unicdcdcdhd}(l6\_algstr\_0~(k11\_funcsdom~X0)))))))))))\end{array}$$
\end{theorem}
\end{document}
