\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{l26\_aff\_1 (TMXw9xGcHYf4yiJeWR8Nu3mb8p5qiRxm79k)}
\maketitle
Let $ v7\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_diraf : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_analoaf : {{\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\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~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}(((X1 \in k2\_aff\_1~\\
X0~X2~X3){\unicdcdcdhd}(X4 \in k2\_aff\_1~X0~X2~X3)){\unicdbdjdcd}((X2=X3){\unicdcdcdid}(r1\_tarski~(k2\_aff\_1~\\
X0~X2~X3)~(k2\_aff\_1~X0~X1~X4))))))))\end{array}
\label{hyp:ehbdhdpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~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}(((X1 \in k2\_aff\_1~\\
X0~X2~X3){\unicdcdcdhd}(X4 \in k2\_aff\_1~X0~X2~X3)){\unicdbdjdcd}((X1=X4){\unicdcdcdid}(r1\_tarski~(k2\_aff\_1~\\
X0~X1~X4)~(k2\_aff\_1~X0~X2~X3))))))))\end{array}
\label{hyp:ehbdgdpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~\\
X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k2\_aff\_1~X0~X1~X2=k1\_aff\_1~X0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((v1\_aff\_1~X1~X0){\unicdbdjded}({\unicdcdaddd} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdcdcdhd}\\
({\unicdcdaddd} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~X0)){\unicdcdcdhd}((X2{\unicdcdgdad}X3){\unicdcdcdhd}(X1=\\
k2\_aff\_1~X0~X2~X3))))))\end{array}
\label{hyp:egddpfbgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0}={X1}})}{\unicdbdjded}{({{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdcdcdhd}{({{{r1\_tarski}~{X1}}~{X0}})}})}}}}\label{hyp:egbdadpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~\\
X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k2\_aff\_1~X0~X1~X2=k2\_aff\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfbgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:mgcdgdpfbgggggpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))){\unicdbdjdcd}(((v1\_aff\_1~X3~X0){\unicdcdcdhd}((X1 \in X3){\unicdcdcdhd}(X2 \in X3))){\unicdbdjdcd}(\\
(X1=X2){\unicdcdcdid}(X3=k2\_aff\_1~X0~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
