\documentclass{article}
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\newtheorem{theorem}{Theorem}
\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}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
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\begin{document}
\title{t8\_int\_7 (TMQ15gLNJR1APvLxiu8JX4pnFBLvy7eWv5Z)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_newton : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_poly : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_int\_7 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_nat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_polynom2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_newton : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~k10\_newton){\unicdcdcdhd}((v4\_valued\_0~X1){\unicdcdcdhd}(v2\_pre\_poly~X1)))))){\unicdbdjdcd}(((\\
v1\_int\_7~X1){\unicdcdcdhd}(r1\_int\_1~X0~(k8\_nat\_3~k10\_newton~X1))){\unicdbdjdcd}(X0 \in k1\_polynom2~\\
k10\_newton~X1)))\end{array}
\label{hyp:mgbdedpfjgogehpfhd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v1\_int\_2~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_partfun1~\\
X1~k10\_newton){\unicdcdcdhd}((v4\_valued\_0~X1){\unicdcdcdhd}(v2\_pre\_poly~X1)))))){\unicdbdjdcd}(((\\
v1\_int\_7~X1){\unicdcdcdhd}(X0 \in k1\_polynom2~k10\_newton~X1)){\unicdbdjdcd}((r1\_int\_1~X0~(\\
k8\_nat\_3~k10\_newton~X1)){\unicdcdcdhd}({\unicdcdaddd} X2 .  (v7\_ordinal1~X2){\unicdcdcdhd}(r1\_int\_1~\\
(k1\_newton~X0~X2)~(k8\_nat\_3~k10\_newton~X1))))))\end{array}
\label{hyp:mgbdadpfjgogehpfhd}
\end{equation}
\begin{theorem}\label{thm:ehidpfjgogehpfhd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_partfun1~X0~k10\_newton){\unicdcdcdhd}((v4\_valued\_0~X0){\unicdcdcdhd}(v2\_pre\_poly~\\
X0)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v7\_ordinal1~X1){\unicdcdcdhd}(v1\_int\_2~X1)){\unicdbdjdcd}((v1\_int\_7~\\
X0){\unicdbdjdcd}((r1\_int\_1~X1~(k8\_nat\_3~k10\_newton~X0)){\unicdbdjded}(X1 \in k1\_polynom2~\\
k10\_newton~X0))))\end{array}$$
\end{theorem}
\end{document}
