\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\_unialg\_2 (TMRM7mJ8VRktykMKG6wd9nXd2iV35NhFUQT)}
\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 $ v2\_unialg\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\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 $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u1\_unialg\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_unialg\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ 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\_unialg\_1~\\
X1){\unicdcdcdhd}(m1\_unialg\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X2=u1\_struct\_0~X1){\unicdbdjdcd}(k7\_unialg\_2~\\
X0~X2=X1))))\end{array}
\label{hyp:ehbdjdpffhogjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{({{{k3\_xboole\_0}~{X0}}~{X1}})}}~{X0}}}}\label{hyp:ehbdhdpfihcgpgpgmgfgpfbd}
\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}((v2\_unialg\_2~X0){\unicdcdcdhd}(l1\_unialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_unialg\_2~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_unialg\_2~X2~X0){\unicdbdjdcd}\\
(\preoh r2\_subset\_1~(u1\_struct\_0~X1)~(u1\_struct\_0~X2))))\end{array}
\label{hyp:ehbdhdpffhogjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{{k2\_xboole\_0}~{X0}}~{X1}}={X1}})}}}}\label{hyp:ehbdcdpfihcgpgpgmgfgpfbd}
\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 .  (m1\_unialg\_2~\\
X1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}\\
((v4\_unialg\_1~X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))))\end{array}
\label{hyp:egehpfngbdpffhogjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\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))))){\unicdcdcdhd}\\
((m1\_unialg\_2~X1~X0){\unicdcdcdhd}(m1\_unialg\_2~X2~X0))){\unicdbdjdcd}((v1\_unialg\_1~(k5\_unialg\_2~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_unialg\_2~(k5\_unialg\_2~X0~X1~X2)~X0))\end{array}
\label{hyp:egehpflgfdpffhogjgbgmghgpfcd}
\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 .  (m1\_unialg\_2~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_unialg\_2~X2~X0){\unicdbdjdcd}((\preoh r2\_subset\_1~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_unialg\_1~X3){\unicdcdcdhd}(m1\_unialg\_2~\\
X3~X0)){\unicdbdjdcd}((X3=k5\_unialg\_2~X0~X1~X2){\unicdbdjded}((u1\_struct\_0~X3=k3\_xboole\_0~\\
(u1\_struct\_0~X1)~(u1\_struct\_0~X2)){\unicdcdcdhd}({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))){\unicdbdjdcd}((X4=u1\_struct\_0~\\
X3){\unicdbdjdcd}((u1\_unialg\_1~X3=k3\_unialg\_2~X0~X4){\unicdcdcdhd}(v1\_unialg\_2~X4~X0))))))))))\end{array}
\label{hyp:egjdpffhogjgbgmghgpfcd}
\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 .  ((\preoh \\
v2\_struct\_0~X1){\unicdcdcdhd}((v2\_unialg\_1~X1){\unicdcdcdhd}((v3\_unialg\_1~X1){\unicdcdcdhd}((v4\_unialg\_1~\\
X1){\unicdcdcdhd}(l1\_unialg\_1~X1))))){\unicdbdjdcd}((m1\_unialg\_2~X1~X0){\unicdbdjded}((m1\_subset\_1~\\
(u1\_struct\_0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((X2=u1\_struct\_0~X1){\unicdbdjdcd}((u1\_unialg\_1~X1=k3\_unialg\_2~X0~\\
X2){\unicdcdcdhd}(v1\_unialg\_2~X2~X0)))))))\end{array}
\label{hyp:eghdpffhogjgbgmghgpfcd}
\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 .  (m1\_unialg\_2~\\
X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_unialg\_2~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_unialg\_1~\\
X3){\unicdcdcdhd}(m1\_unialg\_2~X3~X0)){\unicdbdjdcd}((X3=k8\_unialg\_2~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  \\
((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}((X4=k2\_xboole\_0~(u1\_struct\_0~X1)~(u1\_struct\_0~X2)){\unicdbdjdcd}\\
(X3=k7\_unialg\_2~X0~X4)))))))\end{array}
\label{hyp:egbdddpffhogjgbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_xboole\_0}~{X0}}~{X1}}={{{k2\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdddpffhogjgbgmghgpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_unialg\_1~X0){\unicdcdcdhd}((v3\_unialg\_1~\\
X0){\unicdcdcdhd}((v4\_unialg\_1~X0){\unicdcdcdhd}((v2\_unialg\_2~X0){\unicdcdcdhd}(l1\_unialg\_1~X0)))))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_unialg\_1~X1){\unicdcdcdhd}(m1\_unialg\_2~X1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((v1\_unialg\_1~X2){\unicdcdcdhd}(m1\_unialg\_2~X2~X0)){\unicdbdjdcd}(k8\_unialg\_2~X0~(k5\_unialg\_2~\\
X0~X1~X2)~X2=X2)))\end{array}$$
\end{theorem}
\end{document}
