\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{t40\_circcmb3 (TMMigiEngmUwBCJU3vZbdGFGovLWhtVanbv)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k4\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\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 $ m1\_circcmb3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_circcmb3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_circcmb3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k10\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_msafree2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_circcmb3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_relat\_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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(v1\_finset\_1~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~\\
X2~(k4\_finseq\_2~X0~X1)~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k4\_finseq\_2~X0~X1)~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v3\_card\_1~X3~X0){\unicdcdcdhd}(v1\_finseq\_1~X3)))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_circcmb3~\\
X4~X1){\unicdbdjdcd}((r1\_tarski~(k10\_xtuple\_0~X3)~(u1\_struct\_0~X4)){\unicdbdjdcd}((k3\_circcmb3~\\
(k4\_circcmb3~X0~X1~X2~X3) \in k2\_msafree2~X4){\unicdcdcdid}(k2\_msafree2~(k6\_circcmb3~\\
X1~X4~(k4\_circcmb3~X0~X1~X2~X3))=k2\_msafree2~X4)))))))\end{array}
\label{hyp:ehddfdpfdgjgchdgdgngcgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (r1\_tarski~(k2\_tarski~X0~X1)~\\
X2){\unicdbdjded}((X0 \in X2){\unicdcdcdhd}(X1 \in X2))\end{array}
\label{hyp:ehddcdpfkhggngjgdhdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k10\_xtuple\_0~(k10\_finseq\_1~X0~X1)=k2\_tarski~\\
X0~X1\end{array}
\label{hyp:ehbdcdhdpfggjgogdhfgbhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_2){\unicdcdcdhd}(m2\_subset\_1~np\_\_2~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_2~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_2~k1\_numbers))\end{array}
\label{hyp:dhahdgcdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k10\_finseq\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~\\
(k10\_finseq\_1~X0~X1))\end{array}
\label{hyp:ggdgidpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{v3\_card\_1}~{({{{k10\_finseq\_1}~{X0}}~{X1}})}}~{np\_\_2}}}}\label{hyp:ggdgcdfdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{v1\_finseq\_1}~{({{{k10\_finseq\_1}~{X0}}~{X1}})}}}}\label{hyp:ggdgbdadpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdgjgchdgdgngcgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(v1\_finset\_1~\\
X2)){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k4\_finseq\_2~\\
np\_\_2~X2)~X2){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k4\_finseq\_2~\\
np\_\_2~X2)~X2))))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_circcmb3~X4~X2){\unicdbdjdcd}(((X0 \in u1\_struct\_0~\\
X4){\unicdcdcdhd}(X1 \in u1\_struct\_0~X4)){\unicdbdjdcd}((k3\_circcmb3~(k4\_circcmb3~np\_\_2~X2~\\
X3~(k10\_finseq\_1~X0~X1)) \in k2\_msafree2~X4){\unicdcdcdid}(k2\_msafree2~(k6\_circcmb3~\\
X2~X4~(k4\_circcmb3~np\_\_2~X2~X3~(k10\_finseq\_1~X0~X1)))=k2\_msafree2~\\
X4)))))\end{array}$$
\end{theorem}
\end{document}
