\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{t11\_afproj (TMUjRNzfNHvAZodWsmamUuASfYgv5xZ9Svk)}
\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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_afproj : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r5\_aff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ r1\_aff\_4 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v3\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_eqrel\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_afproj : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_afproj : {{\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~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
((v1\_aff\_1~X1~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2 \in k5\_afproj~X0~X1){\unicdbdjded}({\unicdcdaddd} X3 .  \\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}((X2=X3){\unicdcdcdhd}((\\
v1\_aff\_1~X3~X0){\unicdcdcdhd}(r1\_aff\_4~X0~X1~X3)))))))\end{array}
\label{hyp:ehjdpfbgggahchpgkg}
\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}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((v1\_aff\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_1~X2~X0)){\unicdbdjdcd}((r5\_aff\_1~X0~X1~X2){\unicdbdjded}(r1\_aff\_4~\\
X0~X1~X2)))))\end{array}
\label{hyp:ehedadpfbgggggpfed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v3\_relat\_2~X2){\unicdcdcdhd}((v8\_relat\_2~\\
X2){\unicdcdcdhd}((v1\_partfun1~X2~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}((X1 \in k6\_eqrel\_1~X0~X0~X2~X3){\unicdbdjded}\\
(k6\_eqrel\_1~X0~X0~X2~X3=k6\_eqrel\_1~X0~X0~X2~X1)))\end{array}
\label{hyp:ehcdddpffgbhchfgmgpfbd}
\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~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))))){\unicdbdjdcd}((r5\_aff\_1~\\
X0~X1~X2){\unicdbdjdcd}(r5\_aff\_1~X0~X2~X1))\end{array}
\label{hyp:dhjhngngfgehchjhpfchfdpfbgggggpfbd}
\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}\\
((v3\_relat\_2~(k3\_afproj~X0)){\unicdcdcdhd}((v8\_relat\_2~(k3\_afproj~X0)){\unicdcdcdhd}(\\
(v1\_partfun1~(k3\_afproj~X0)~(k1\_afproj~X0)){\unicdcdcdhd}(m1\_subset\_1~(k3\_afproj~\\
X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_afproj~X0)~(k1\_afproj~X0)))))))\end{array}
\label{hyp:egehpflgddpfbgggahchpgkg}
\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}\\
(k5\_afproj~X0~X1=k6\_eqrel\_1~(k1\_afproj~X0)~(k1\_afproj~X0)~(k3\_afproj~\\
X0)~X1))\end{array}
\label{hyp:egfdpfbgggahchpgkg}
\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}\\
(k1\_afproj~X0=ReplSep~(toset~({\uniddcgcg} X1 : \iota .  m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))))~({\uniddcgcg} X1 : \iota .  v1\_aff\_1~X1~X0)~({\uniddcgcg} X1 : \iota .  \\
X1))\end{array}
\label{hyp:egbdpfbgggahchpgkg}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfbgggahchpgkg}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v7\_struct\_0~X0){\unicdcdcdhd}((v1\_diraf~X0){\unicdcdcdhd}(l1\_analoaf~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdbdjdcd}\\
(((v1\_aff\_1~X1~X0){\unicdcdcdhd}(v1\_aff\_1~X2~X0)){\unicdbdjdcd}((k5\_afproj~X0~X1=k5\_afproj~\\
X0~X2){\unicdbdjded}(r5\_aff\_1~X0~X1~X2)))))\end{array}$$
\end{theorem}
\end{document}
