\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{t16\_sprect\_3 (TMckx2N2mTq3dVAWZG7kaerEAov91y8BN7R)}
\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 $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v4\_topreal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_matrix\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((v4\_topreal1~X0){\unicdcdcdhd}(k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k1\_rltopsp1~(k15\_euclid~np\_\_2)~X1~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~np\_\_1))~(k3\_topreal1~np\_\_2~X0)=k1\_tarski~\\
(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~np\_\_1))){\unicdbdjdcd}((\\
X1=k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~np\_\_1){\unicdcdcdid}((\\
(k17\_euclid~X1{\unicdcdgdad}k17\_euclid~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~\\
np\_\_2))~X0~np\_\_1)){\unicdcdcdhd}(k18\_euclid~X1{\unicdcdgdad}k18\_euclid~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~np\_\_1))){\unicdcdcdid}((v4\_topreal1~(k8\_finseq\_1~(\\
u1\_struct\_0~(k15\_euclid~np\_\_2))~(k12\_finseq\_1~(u1\_struct\_0~(\\
k15\_euclid~np\_\_2))~X1)~X0)){\unicdcdcdhd}(m2\_finseq\_1~(k8\_finseq\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k12\_finseq\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
X1)~X0)~(u1\_struct\_0~(k15\_euclid~np\_\_2))))))))\end{array}
\label{hyp:ehgdadpfdhahchfgdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k4\_matrix\_2~X0~X1=k5\_finseq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfngbgehchjgihpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k12\_finseq\_1~X0~X1=k5\_finseq\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_finseq\_1~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~\\
X0)))))\end{array}
\label{hyp:egehpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~X0))){\unicdbdjdcd}(v1\_xboole\_0~X2))\end{array}
\label{hyp:dgdgedpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
((v4\_topreal1~X0){\unicdbdjdcd}(\preoh v1\_xboole\_0~X0))\end{array}
\label{hyp:dgdgddpfdhahahpgmgpfcd}
\end{equation}
\begin{theorem}\label{thm:ehbdgdpfdhahchfgdgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m2\_finseq\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_2))){\unicdbdjdcd}\\
(((v4\_topreal1~X0){\unicdcdcdhd}(k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~\\
(k1\_rltopsp1~(k15\_euclid~np\_\_2)~X1~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~np\_\_1))~(k3\_topreal1~np\_\_2~X0)=k1\_tarski~\\
(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~np\_\_1))){\unicdbdjdcd}((\\
k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~np\_\_1=X1){\unicdcdcdid}((\\
(k17\_euclid~(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~X0~\\
np\_\_1){\unicdcdgdad}k17\_euclid~X1){\unicdcdcdhd}(k18\_euclid~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X0~np\_\_1){\unicdcdgdad}k18\_euclid~X1)){\unicdcdcdid}(v4\_topreal1~(\\
k8\_finseq\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k4\_matrix\_2~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~X1)~X0))))))\end{array}$$
\end{theorem}
\end{document}
