\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t35\_nat\_3 (TMShWenmzL8ZkjXvuqn1PDx8bybw3Gj2qnq)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_nat\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_int\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k11\_nat\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
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 $ r1\_int\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (X1 \in k9\_xtuple\_0~(k12\_nat\_3~\\
X0)){\unicdbdjdcd}((v7\_ordinal1~X1){\unicdcdcdhd}(v1\_int\_2~X1)))\end{array}
\label{hyp:ehddddpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(X0{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~X1~X0){\unicdcdcdhd}((X1{\unicdcdgdad}np\_\_1){\unicdcdcdhd}(k11\_nat\_3~\\
X0~X1{\unicdcdgdad}k6\_numbers)))))\end{array}
\label{hyp:ehcdddpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_1}}~{np\_\_1}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_relat\_1~(k12\_nat\_3~X0)){\unicdcdcdhd}((\\
v4\_relat\_1~(k12\_nat\_3~X0)~k10\_newton){\unicdcdcdhd}((v1\_funct\_1~(k12\_nat\_3~\\
X0)){\unicdcdcdhd}(v1\_partfun1~(k12\_nat\_3~X0)~k10\_newton))))\end{array}
\label{hyp:egehpflgbdcdpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~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)))){\unicdbdjdcd}\\
((X1=k12\_nat\_3~X0){\unicdbdjded}({\unicdcdadad} X2 .  ((v7\_ordinal1~X2){\unicdcdcdhd}(v1\_int\_2~\\
X2)){\unicdbdjdcd}(k1\_funct\_1~X1~X2=k11\_nat\_3~X0~X2))))\end{array}
\label{hyp:egidpfogbgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_int\_2~X0){\unicdbdjded}((\preoh r1\_xxreal\_0~X0~\\
np\_\_1){\unicdcdcdhd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh (r1\_int\_1~X1~X0){\unicdcdcdhd}((X1{\unicdcdgdad}\\
np\_\_1){\unicdcdcdhd}(X1{\unicdcdgdad}X0))))))\end{array}
\label{hyp:egedpfjgogehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
((X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((X2=k1\_funct\_1~X0~X1){\unicdbdjded}(k4\_tarski~X1~X2 \in \\
X0))){\unicdcdcdhd}((\preoh X1 \in k9\_xtuple\_0~X0){\unicdbdjdcd}((X2=k1\_funct\_1~X0~X1){\unicdbdjded}(X2=k1\_xboole\_0))))\end{array}
\label{hyp:egcdpfggfhogdgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddfdpfogbgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(\preoh r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((X1{\unicdcdgdad}k6\_numbers){\unicdcdcdhd}(k1\_funct\_1~(k12\_nat\_3~\\
X1)~X0{\unicdcdgdad}k6\_numbers))))\end{array}$$
\end{theorem}
\end{document}
