\documentclass{article}
\newtheorem{axiom}{Axiom}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l34\_fomodel2 (TMWiCCBQqx7P3G1275q9fMebjuHbxnRrmmK)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v11\_fomodel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_fomodel1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k23\_fomodel2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k16\_fomodel2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k6\_margrel1 : {\iota}$ 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 $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_mcart\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k37\_fomodel1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k22\_fomodel2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
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}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((\preoh v6\_struct\_0~X1){\unicdcdcdhd}((v11\_fomodel1~X1){\unicdcdcdhd}(l1\_fomodel1~X1))){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}((v1\_funct\_1~(k1\_funct\_5~(k8\_nat\_1~\\
(k3\_rfunct\_3~(k8\_mcart\_1~(k9\_funct\_2~(k37\_fomodel1~X1)~(k3\_rfunct\_3~\\
(k3\_finseq\_2~X2)~(k2\_xboole\_0~X2~k6\_margrel1)))~(k3\_finseq\_2~\\
(k1\_fomodel1~X1))~(k16\_fomodel2~X1~X2)~(k6\_subset\_1~(k3\_finseq\_2~\\
(k1\_fomodel1~X1))~(k1\_tarski~k1\_xboole\_0)))~k6\_margrel1)~(k22\_fomodel2~\\
X1~X2)~X0))){\unicdcdcdhd}((v1\_funct\_2~(k1\_funct\_5~(k8\_nat\_1~(k3\_rfunct\_3~\\
(k8\_mcart\_1~(k9\_funct\_2~(k37\_fomodel1~X1)~(k3\_rfunct\_3~(k3\_finseq\_2~\\
X2)~(k2\_xboole\_0~X2~k6\_margrel1)))~(k3\_finseq\_2~(k1\_fomodel1~\\
X1))~(k16\_fomodel2~X1~X2)~(k6\_subset\_1~(k3\_finseq\_2~(k1\_fomodel1~\\
X1))~(k1\_tarski~k1\_xboole\_0)))~k6\_margrel1)~(k22\_fomodel2~X1~\\
X2)~X0))~(k16\_fomodel2~X1~X2)~(k3\_rfunct\_3~(k6\_subset\_1~(k3\_finseq\_2~\\
(k1\_fomodel1~X1))~(k1\_tarski~k1\_xboole\_0))~k6\_margrel1)){\unicdcdcdhd}(m1\_subset\_1~\\
(k1\_funct\_5~(k8\_nat\_1~(k3\_rfunct\_3~(k8\_mcart\_1~(k9\_funct\_2~(\\
k37\_fomodel1~X1)~(k3\_rfunct\_3~(k3\_finseq\_2~X2)~(k2\_xboole\_0~X2~\\
k6\_margrel1)))~(k3\_finseq\_2~(k1\_fomodel1~X1))~(k16\_fomodel2~\\
X1~X2)~(k6\_subset\_1~(k3\_finseq\_2~(k1\_fomodel1~X1))~(k1\_tarski~\\
k1\_xboole\_0)))~k6\_margrel1)~(k22\_fomodel2~X1~X2)~X0))~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k16\_fomodel2~X1~X2)~(k3\_rfunct\_3~(k6\_subset\_1~(\\
k3\_finseq\_2~(k1\_fomodel1~X1))~(k1\_tarski~k1\_xboole\_0))~k6\_margrel1))))))))\end{array}
\label{hyp:mgddddpfggpgngpgegfgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v11\_fomodel1~\\
X0){\unicdcdcdhd}(l1\_fomodel1~X0))){\unicdcdcdhd}((v7\_ordinal1~X1){\unicdcdcdhd}(\preoh v1\_xboole\_0~X2))){\unicdbdjdcd}\\
(m2\_rfunct\_3~(k23\_fomodel2~X0~X1~X2)~(k8\_mcart\_1~(k9\_funct\_2~(\\
k37\_fomodel1~X0)~(k3\_rfunct\_3~(k3\_finseq\_2~X2)~(k2\_xboole\_0~X2~\\
k6\_margrel1)))~(k3\_finseq\_2~(k1\_fomodel1~X0))~(k16\_fomodel2~\\
X0~X2)~(k6\_subset\_1~(k3\_finseq\_2~(k1\_fomodel1~X0))~(k1\_tarski~\\
k1\_xboole\_0)))~k6\_margrel1~(k3\_rfunct\_3~(k8\_mcart\_1~(k9\_funct\_2~\\
(k37\_fomodel1~X0)~(k3\_rfunct\_3~(k3\_finseq\_2~X2)~(k2\_xboole\_0~\\
X2~k6\_margrel1)))~(k3\_finseq\_2~(k1\_fomodel1~X0))~(k16\_fomodel2~\\
X0~X2)~(k6\_subset\_1~(k3\_finseq\_2~(k1\_fomodel1~X0))~(k1\_tarski~\\
k1\_xboole\_0)))~k6\_margrel1))\end{array}
\label{hyp:egehpflgcdddpfggpgngpgegfgmgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v6\_struct\_0~X0){\unicdcdcdhd}((v11\_fomodel1~X0){\unicdcdcdhd}(l1\_fomodel1~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~\\
X2){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_rfunct\_3~X3~(k8\_mcart\_1~(k9\_funct\_2~(k37\_fomodel1~\\
X0)~(k3\_rfunct\_3~(k3\_finseq\_2~X2)~(k2\_xboole\_0~X2~k6\_margrel1)))~\\
(k3\_finseq\_2~(k1\_fomodel1~X0))~(k16\_fomodel2~X0~X2)~(k6\_subset\_1~\\
(k3\_finseq\_2~(k1\_fomodel1~X0))~(k1\_tarski~k1\_xboole\_0)))~k6\_margrel1~\\
(k3\_rfunct\_3~(k8\_mcart\_1~(k9\_funct\_2~(k37\_fomodel1~X0)~(k3\_rfunct\_3~\\
(k3\_finseq\_2~X2)~(k2\_xboole\_0~X2~k6\_margrel1)))~(k3\_finseq\_2~\\
(k1\_fomodel1~X0))~(k16\_fomodel2~X0~X2)~(k6\_subset\_1~(k3\_finseq\_2~\\
(k1\_fomodel1~X0))~(k1\_tarski~k1\_xboole\_0)))~k6\_margrel1)){\unicdbdjdcd}(\\
(X3=k23\_fomodel2~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((X1=X4){\unicdbdjdcd}(X3=k8\_nat\_1~(k3\_rfunct\_3~(k8\_mcart\_1~\\
(k9\_funct\_2~(k37\_fomodel1~X0)~(k3\_rfunct\_3~(k3\_finseq\_2~X2)~(\\
k2\_xboole\_0~X2~k6\_margrel1)))~(k3\_finseq\_2~(k1\_fomodel1~X0))~\\
(k16\_fomodel2~X0~X2)~(k6\_subset\_1~(k3\_finseq\_2~(k1\_fomodel1~X0))~\\
(k1\_tarski~k1\_xboole\_0)))~k6\_margrel1)~(k22\_fomodel2~X0~X2)~X4)))))))\end{array}
\label{hyp:egcdbdpfggpgngpgegfgmgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v7\_ordinal1}~{X0}})}{\unicdbdjded}{({{X0} \in {k4\_ordinal1}})}}}\label{hyp:egbdcdpfpgchegjgogbgmgbd}
\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:mgddedpfggpgngpgegfgmgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v6\_struct\_0~X1){\unicdcdcdhd}\\
((v11\_fomodel1~X1){\unicdcdcdhd}(l1\_fomodel1~X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~\\
X2){\unicdbdjdcd}((v1\_funct\_1~(k1\_funct\_5~(k23\_fomodel2~X1~X0~X2))){\unicdcdcdhd}((v1\_funct\_2~\\
(k1\_funct\_5~(k23\_fomodel2~X1~X0~X2))~(k16\_fomodel2~X1~X2)~(k3\_rfunct\_3~\\
(k6\_subset\_1~(k3\_finseq\_2~(k1\_fomodel1~X1))~(k1\_tarski~k1\_xboole\_0))~\\
k6\_margrel1)){\unicdcdcdhd}(m1\_subset\_1~(k1\_funct\_5~(k23\_fomodel2~X1~X0~X2))~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k16\_fomodel2~X1~X2)~(k3\_rfunct\_3~(\\
k6\_subset\_1~(k3\_finseq\_2~(k1\_fomodel1~X1))~(k1\_tarski~k1\_xboole\_0))~\\
k6\_margrel1))))))))\end{array}$$
\end{theorem}
\end{document}
