\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{t16\_endalg (TMb6rNUrd9KrdFnDJLtW5G25PgZYctGeHwA)}
\maketitle
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_endalg : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_endalg : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_endalg : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_msualg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v6\_group\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_group\_6 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ k1\_endalg : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k16\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v11\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v22\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_group\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_vectsp\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_msualg\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_struct\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_msualg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l4\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~(k3\_endalg~X0))~(u1\_struct\_0~\\
(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0)))){\unicdcdcdhd}((v6\_group\_1~\\
X1~(k3\_endalg~X0)~(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0))){\unicdcdcdhd}\\
((v1\_group\_6~X1~(k3\_endalg~X0)~(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~\\
(k3\_endalg~X0))~(u1\_struct\_0~(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~\\
X0)))))))))){\unicdbdjdcd}(({\unicdcdadad} X2 .  (X2 \in k1\_endalg~X0){\unicdbdjdcd}(k1\_funct\_1~X1~\\
X2=k16\_funcop\_1~k6\_numbers~X2)){\unicdbdjdcd}(v3\_funct\_2~X1~(u1\_struct\_0~\\
(k3\_endalg~X0))~(u1\_struct\_0~(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~\\
X0))))))\end{array}
\label{hyp:ehbdfdpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}(((k9\_xtuple\_0~X1=k1\_endalg~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(X2 \in k1\_endalg~X0){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k16\_funcop\_1~k6\_numbers~\\
X2))){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(u1\_struct\_0~(k3\_endalg~\\
X0))~(u1\_struct\_0~(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0)))){\unicdcdcdhd}\\
((v6\_group\_1~X1~(k3\_endalg~X0)~(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~\\
X0))){\unicdcdcdhd}((v1\_group\_6~X1~(k3\_endalg~X0)~(k6\_endalg~(k6\_msualg\_1~\\
X0)~(k9\_msualg\_1~X0))){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k3\_endalg~X0))~(u1\_struct\_0~(k6\_endalg~(k6\_msualg\_1~\\
X0)~(k9\_msualg\_1~X0))))))))))))\end{array}
\label{hyp:ehbdedpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 : \iota{\unicdbdjdcd}\iota .  {\unicdcdadad} X1 .  {\unicdcdaddd} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(\\
v1\_funct\_1~X2)){\unicdcdcdhd}((k9\_xtuple\_0~X2=X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (X3 \in X1){\unicdbdjdcd}(\\
k1\_funct\_1~X2~X3=X0~X3)))\end{array}
\label{hyp:dhddpfggfhogdgehpfbd}
\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}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}\\
((v22\_algstr\_0~(k6\_endalg~X0~X1)){\unicdcdcdhd}((v3\_group\_1~(k6\_endalg~X0~\\
X1)){\unicdcdcdhd}(v4\_vectsp\_1~(k6\_endalg~X0~X1))))\end{array}
\label{hyp:ggdgedpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v3\_msualg\_1~(\\
k9\_msualg\_1~X0)~(k6\_msualg\_1~X0)){\unicdcdcdhd}(v4\_msualg\_1~(k9\_msualg\_1~\\
X0)~(k6\_msualg\_1~X0)))\end{array}
\label{hyp:ggdgddpfngdhfhbgmghgpfbd}
\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}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}\\
((\preoh v2\_struct\_0~(k6\_endalg~X0~X1)){\unicdcdcdhd}(v22\_algstr\_0~(k6\_endalg~X0~\\
X1)))\end{array}
\label{hyp:ggdgddpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v7\_struct\_0~(\\
k6\_msualg\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k6\_msualg\_1~X0)){\unicdcdcdhd}((v13\_struct\_0~\\
(k6\_msualg\_1~X0)~np\_\_1){\unicdcdcdhd}((v1\_msualg\_1~(k6\_msualg\_1~X0)){\unicdcdcdhd}(v5\_msualg\_1~\\
(k6\_msualg\_1~X0))))))\end{array}
\label{hyp:ggdgcdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v22\_algstr\_0~\\
(k3\_endalg~X0)){\unicdcdcdhd}((v3\_group\_1~(k3\_endalg~X0)){\unicdcdcdhd}(v4\_vectsp\_1~(\\
k3\_endalg~X0))))\end{array}
\label{hyp:ggdgcdpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
(k3\_endalg~X0)){\unicdcdcdhd}(v22\_algstr\_0~(k3\_endalg~X0)))\end{array}
\label{hyp:ggdgbdpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l5\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgfdpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_msualg\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v3\_msualg\_1~(\\
k9\_msualg\_1~X0)~(k6\_msualg\_1~X0)){\unicdcdcdhd}(l3\_msualg\_1~(k9\_msualg\_1~\\
X0)~(k6\_msualg\_1~X0)))\end{array}
\label{hyp:egehpflgjdpfngdhfhbgmghgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v7\_struct\_0~(\\
k6\_msualg\_1~X0)){\unicdcdcdhd}((\preoh v11\_struct\_0~(k6\_msualg\_1~X0)){\unicdcdcdhd}((v1\_msualg\_1~\\
(k6\_msualg\_1~X0)){\unicdcdcdhd}((v5\_msualg\_1~(k6\_msualg\_1~X0)){\unicdcdcdhd}(l1\_msualg\_1~\\
(k6\_msualg\_1~X0))))))\end{array}
\label{hyp:egehpflggdpfngdhfhbgmghgpfbd}
\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}((v4\_msualg\_1~X1~X0){\unicdcdcdhd}(l3\_msualg\_1~X1~X0))){\unicdbdjdcd}\\
((v22\_algstr\_0~(k6\_endalg~X0~X1)){\unicdcdcdhd}(l4\_algstr\_0~(k6\_endalg~X0~\\
X1)))\end{array}
\label{hyp:egehpflggdpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}((v22\_algstr\_0~\\
(k3\_endalg~X0)){\unicdcdcdhd}(l4\_algstr\_0~(k3\_endalg~X0)))\end{array}
\label{hyp:egehpflgddpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k16\_funcop\_1~X0~X1=k7\_funcop\_1~(k1\_tarski~\\
X0)~X1\end{array}
\label{hyp:egjdpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v4\_vectsp\_1~X0){\unicdcdcdhd}(l4\_algstr\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v4\_vectsp\_1~X1){\unicdcdcdhd}(l4\_algstr\_0~\\
X1))){\unicdbdjdcd}((r1\_endalg~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(u1\_struct\_0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v6\_group\_1~X2~X0~X1){\unicdcdcdhd}(\\
(v1\_group\_6~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~X0)~(u1\_struct\_0~X1)))))))){\unicdcdcdhd}(v3\_funct\_2~X2~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)))))\end{array}
\label{hyp:eghdpffgogegbgmghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l1\_struct\_0~X0){\unicdbdjdcd}((v13\_struct\_0~X0~np\_\_1){\unicdbdjdcd}((\preoh v2\_struct\_0~\\
X0){\unicdcdcdhd}(v7\_struct\_0~X0)))\end{array}
\label{hyp:dgdgbdbdpfdhehchfhdgehpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpffgogegbgmghg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}(l1\_unialg\_1~X0))))){\unicdbdjdcd}(r1\_endalg~(k3\_endalg~\\
X0)~(k6\_endalg~(k6\_msualg\_1~X0)~(k9\_msualg\_1~X0)))\end{array}$$
\end{theorem}
\end{document}
