\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{t34\_ec\_pf\_2 (TMWocoP9iGUcC2gFsJGpxjDVoHoS9d7oqBx)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\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 $ k9\_int\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_ec\_pf\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_ec\_pf\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~(k9\_int\_3~X0))))){\unicdbdjdcd}((\preoh v1\_xboole\_0~(k6\_ec\_pf\_1~\\
X0~X1~X2)){\unicdcdcdhd}(m1\_subset\_1~(k6\_ec\_pf\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k3\_ec\_pf\_1~\\
(k9\_int\_3~X0)))))\end{array}
\label{hyp:egehpflggdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(u1\_struct\_0~(k9\_int\_3~X0))))){\unicdbdjdcd}((v1\_funct\_1~(k5\_ec\_pf\_1~X0~\\
X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k5\_ec\_pf\_1~X0~X1~X2)~(k3\_zfmisc\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0)))~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~(k5\_ec\_pf\_1~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_zfmisc\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0)))~(u1\_struct\_0~(k9\_int\_3~X0)))))))\end{array}
\label{hyp:egehpflgfdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}(k6\_ec\_pf\_1~X0~X1~X2=ReplSep~(toset~\\
({\uniddcgcg} X3 : \iota .  m2\_subset\_1~X3~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~\\
(k3\_ec\_pf\_1~(k9\_int\_3~X0))))~({\uniddcgcg} X3 : \iota .  k3\_funct\_2~(k3\_zfmisc\_1~\\
(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0)))~(u1\_struct\_0~(k9\_int\_3~X0))~(k5\_ec\_pf\_1~X0~X1~X2)~\\
X3=k4\_struct\_0~(k9\_int\_3~X0))~({\uniddcgcg} X3 : \iota .  X3))))\end{array}
\label{hyp:egjdpffgdgpfahggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k3\_zfmisc\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0)))~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k3\_zfmisc\_1~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0)))~(u1\_struct\_0~(k9\_int\_3~\\
X0))))))){\unicdbdjdcd}((r1\_ec\_pf\_2~X0~X1~X2){\unicdbdjded}(k3\_funct\_2~(k3\_zfmisc\_1~(u1\_struct\_0~\\
(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~\\
X0)))~(u1\_struct\_0~(k9\_int\_3~X0))~X2~X1=k4\_struct\_0~(k9\_int\_3~\\
X0)))))\end{array}
\label{hyp:eggdpffgdgpfahggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(v1\_xboole\_0~X1))\end{array}
\label{hyp:dgdgbdpfdhfhcgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddedpffgdgpfahggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(\\
u1\_struct\_0~(k9\_int\_3~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k3\_zfmisc\_1~\\
(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~(k9\_int\_3~X0))~(u1\_struct\_0~\\
(k9\_int\_3~X0)))~(k3\_ec\_pf\_1~(k9\_int\_3~X0))){\unicdbdjdcd}((r1\_ec\_pf\_2~X0~X3~\\
(k5\_ec\_pf\_1~X0~X1~X2)){\unicdbdjded}(m2\_subset\_1~X3~(k3\_ec\_pf\_1~(k9\_int\_3~X0))~\\
(k6\_ec\_pf\_1~X0~X1~X2))))))\end{array}$$
\end{theorem}
\end{document}
