\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{t62\_prob\_3 (TMN38y7ZXTdJbmKzNSpgyP35aM2qrzD3VbK)}
\maketitle
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_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 $ k1\_afinsq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdaddd} X1 .  ((v5\_ordinal1~\\
X1){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~X1~k1\_numbers){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}(v1\_finset\_1~X1))))){\unicdcdcdhd}((k1\_afinsq\_1~X1=k2\_nat\_1~(k3\_finseq\_1~\\
X0)~np\_\_1){\unicdcdcdhd}((k1\_seq\_1~X1~k6\_numbers=k6\_numbers){\unicdcdcdhd}(({\unicdcdadad} X2 .  \\
(v7\_ordinal1~X2){\unicdbdjdcd}((\preoh r1\_xxreal\_0~(k3\_finseq\_1~X0)~X2){\unicdbdjdcd}(k1\_seq\_1~\\
X1~(k1\_nat\_1~X2~np\_\_1)=k7\_real\_1~(k1\_seq\_1~X1~X2)~(k1\_seq\_1~X0~(\\
k1\_nat\_1~X2~np\_\_1))))){\unicdcdcdhd}(k18\_rvsum\_1~X0=k1\_seq\_1~X1~(k3\_finseq\_1~\\
X0))))))\end{array}
\label{hyp:ehedpfahchhgdgpgchpfcd}
\end{equation}
\begin{theorem}\label{thm:ehgdcdpfahchpgcgpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~k1\_numbers){\unicdbdjdcd}((k3\_finseq\_1~X0=k6\_numbers){\unicdbdjdcd}\\
(k18\_rvsum\_1~X0=k6\_numbers))\end{array}$$
\end{theorem}
\end{document}
