\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{l39\_sppol\_1 (TMT4CsHEGYTdLRwDaLic8ue9b2yApHnTRDC)}
\maketitle
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 $ 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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(\preoh (k17\_euclid~X0{\unicdcdgdad}k17\_euclid~X1){\unicdcdcdhd}((k18\_euclid~X0{\unicdcdgdad}k18\_euclid~\\
X1){\unicdcdcdhd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(\preoh (X2 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~X0~X1){\unicdcdcdhd}((k17\_euclid~X2{\unicdcdgdad}\\
k17\_euclid~X0){\unicdcdcdhd}((k17\_euclid~X2{\unicdcdgdad}k17\_euclid~X1){\unicdcdcdhd}((k18\_euclid~\\
X2{\unicdcdgdad}k18\_euclid~X0){\unicdcdcdhd}(k18\_euclid~X2{\unicdcdgdad}k18\_euclid~X1)))))))))\end{array}
\label{hyp:ehbdedpfdhahahpgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((v3\_sppol\_1~X0){\unicdbdjded}({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}\\
(((r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~(k2\_nat\_1~X1~np\_\_2)~(k3\_finseq\_1~\\
X0))){\unicdbdjdcd}((k17\_euclid~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X0~X1){\unicdcdgdad}k17\_euclid~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X0~(k2\_nat\_1~X1~np\_\_2))){\unicdcdcdhd}(k18\_euclid~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~X1){\unicdcdgdad}k18\_euclid~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~(k2\_nat\_1~X1~np\_\_2)))))))\end{array}
\label{hyp:egedpfdhahahpgmgpfbd}
\end{equation}
\begin{theorem}\label{thm:mgddjdpfdhahahpgmgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (v3\_sppol\_1~\\
X0){\unicdcdcdhd}((r1\_xxreal\_0~np\_\_1~X1){\unicdcdcdhd}((r1\_xxreal\_0~(k2\_nat\_1~X1~np\_\_2)~\\
(k3\_finseq\_1~X0)){\unicdcdcdhd}((X2=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~X1){\unicdcdcdhd}((X3=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X0~(k2\_nat\_1~X1~np\_\_2)){\unicdcdcdhd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))){\unicdbdjdcd}(\preoh (X4 \in k1\_rltopsp1~(k15\_euclid~np\_\_2)~X2~\\
X3){\unicdcdcdhd}((k17\_euclid~X4{\unicdcdgdad}k17\_euclid~X2){\unicdcdcdhd}((k17\_euclid~X4{\unicdcdgdad}k17\_euclid~\\
X3){\unicdcdcdhd}((k18\_euclid~X4{\unicdcdgdad}k18\_euclid~X2){\unicdcdcdhd}(k18\_euclid~X4{\unicdcdgdad}k18\_euclid~\\
X3))))))))))))))\end{array}$$
\end{theorem}
\end{document}
