\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{t34\_sppol\_1 (TMJuw6YoLgg18kiFK47MU9aYFz3YhdVp9Pd)}
\maketitle
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 $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_sppol\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(((v1\_topreal1~\\
X1){\unicdcdcdhd}((v3\_sppol\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k2\_nat\_1~X0~np\_\_2)~(k3\_finseq\_1~X1)){\unicdcdcdhd}(v1\_sppol\_1~(k2\_topreal1~\\
np\_\_2~X1~X0)))))){\unicdbdjdcd}(v2\_sppol\_1~(k2\_topreal1~np\_\_2~X1~(k2\_nat\_1~\\
X0~np\_\_1)))))\end{array}
\label{hyp:ehddddpfdhahahpgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(((v1\_topreal1~\\
X1){\unicdcdcdhd}((v3\_sppol\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k2\_nat\_1~X0~np\_\_2)~(k3\_finseq\_1~X1)){\unicdcdcdhd}(v2\_sppol\_1~(k2\_topreal1~\\
np\_\_2~X1~X0)))))){\unicdbdjdcd}(v1\_sppol\_1~(k2\_topreal1~np\_\_2~X1~(k2\_nat\_1~\\
X0~np\_\_1)))))\end{array}
\label{hyp:ehddcdpfdhahahpgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (v1\_topreal1~\\
X1){\unicdcdcdhd}((\preoh v2\_sppol\_1~(k2\_topreal1~np\_\_2~X1~X0)){\unicdcdcdhd}(\preoh v1\_sppol\_1~(k2\_topreal1~\\
np\_\_2~X1~X0)))))\end{array}
\label{hyp:ehbdjdpfdhahahpgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfdhahahpgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_finseq\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (v1\_topreal1~\\
X1){\unicdcdcdhd}((v3\_sppol\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}((r1\_xxreal\_0~\\
(k2\_nat\_1~X0~np\_\_2)~(k3\_finseq\_1~X1)){\unicdcdcdhd}((\preoh (v2\_sppol\_1~(k2\_topreal1~\\
np\_\_2~X1~X0)){\unicdcdcdhd}(v1\_sppol\_1~(k2\_topreal1~np\_\_2~X1~(k2\_nat\_1~X0~np\_\_1)))){\unicdcdcdhd}\\
(\preoh (v1\_sppol\_1~(k2\_topreal1~np\_\_2~X1~X0)){\unicdcdcdhd}(v2\_sppol\_1~(k2\_topreal1~\\
np\_\_2~X1~(k2\_nat\_1~X0~np\_\_1))))))))))\end{array}$$
\end{theorem}
\end{document}
