\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{t6\_yellow15 (TMN8kgWbWqKfVAg8NY4QLzJzpbHXzg7JfoW)}
\maketitle
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_margrel1 : {\iota}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_margrel1 : {\iota}$ be given.
Let $ k1\_yellow15 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_margrel1 : {\iota}$ be given.
Let $ k2\_xboolean : {\iota}$ be given.
Let $ k1\_xboolean : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_card\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k14\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k8\_margrel1}={k2\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k7\_margrel1}={k1\_xboolean}}\label{hyp:chfgegfgggjgogjgehjgpgogpflghdpfngbgchhgchfgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdaddd} X1 .  (v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~k5\_numbers){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_finset\_1~X1){\unicdcdcdhd}((v3\_card\_1~\\
X1~X0){\unicdcdcdhd}((v1\_finseq\_1~X1){\unicdcdcdhd}(v2\_finseq\_1~X1)))))))\end{array}
\label{hyp:chdghdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_finseq\_1~X1~(k9\_setfam\_1~\\
X0)){\unicdcdcdhd}(m1\_finseq\_1~X2~k6\_margrel1)){\unicdbdjdcd}(m2\_finseq\_1~(k1\_yellow15~\\
X0~X1~X2)~(k9\_setfam\_1~X0))\end{array}
\label{hyp:egehpflgbdpfjhfgmgmgpghhbdfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X0=X1){\unicdbdjdcd}(k14\_funcop\_1~\\
X0~X1~X2~X3=X2)){\unicdcdcdhd}((X0{\unicdcdgdad}X1){\unicdbdjdcd}(k14\_funcop\_1~X0~X1~X2~X3=X3))\end{array}
\label{hyp:egidpfggfhogdgpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_xboolean}={np\_\_1}}\label{hyp:egcdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k9\_setfam\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_1~X2~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_finseq\_1~X3~(k9\_setfam\_1~\\
X0)){\unicdbdjdcd}((X3=k1\_yellow15~X0~X1~X2){\unicdbdjded}((k3\_finseq\_1~X3=k3\_finseq\_1~\\
X1){\unicdcdcdhd}({\unicdcdadad} X4 .  (v7\_ordinal1~X4){\unicdbdjdcd}((X4 \in k4\_finseq\_1~X1){\unicdbdjdcd}(k1\_funct\_1~\\
X3~X4=k14\_funcop\_1~(k1\_funct\_1~X2~X4)~k8\_margrel1~(k1\_funct\_1~\\
X1~X4)~(k6\_subset\_1~X0~(k1\_funct\_1~X1~X4)))))))))\end{array}
\label{hyp:egbdpfjhfgmgmgpghhbdfd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboolean}={k6\_numbers}}\label{hyp:egbdpfihcgpgpgmgfgbgog}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{v3\_card\_1}~{X0}}~{np\_\_1}})}{\unicdbdjdcd}{({{({\preoh{{{v1\_xboole\_0}~{X0}}}})}{\unicdcdcdhd}{({{v1\_zfmisc\_1}~{X0}})}})}}}\label{hyp:dgdgjdpfdgbgchegpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{v3\_card\_1}~{X0}}~{k1\_xboole\_0}})}{\unicdbdjdcd}{({{v1\_xboole\_0}~{X0}})}}}\label{hyp:dgdghdpfdgbgchegpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdpfjhfgmgmgpghhbdfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k9\_setfam\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_1~X2~k6\_margrel1){\unicdbdjdcd}({\unicdcdadad} X3 .  (v7\_ordinal1~X3){\unicdbdjdcd}(\\
((X3 \in k4\_finseq\_1~X1){\unicdcdcdhd}(k1\_funct\_1~X2~X3=k7\_margrel1)){\unicdbdjdcd}(k1\_funct\_1~\\
(k1\_yellow15~X0~X1~X2)~X3=k6\_subset\_1~X0~(k1\_funct\_1~X1~X3)))))\end{array}$$
\end{theorem}
\end{document}
