\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{t21\_topreal1 (TMVRipmVNVN6RXgnNL5xj8x4LaCqkgJj67W)}
\maketitle
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_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 $ k2\_topreal1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v13\_algstr\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v6\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_rltopsp1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~X0){\unicdcdcdhd}((v2\_rlvect\_1~\\
X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}((v5\_rlvect\_1~X0){\unicdcdcdhd}\\
((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~X0){\unicdcdcdhd}(l1\_rlvect\_1~\\
X0)))))))))){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~X0)){\unicdbdjdcd}(X1 \in k1\_rltopsp1~\\
X0~X1~X2)))\end{array}
\label{hyp:ehgdidpfchmgehpgahdhahbd}
\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 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v2\_pre\_topc~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v13\_algstr\_0~(k15\_euclid~X0)){\unicdcdcdhd}((v2\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v3\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}((v4\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v5\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}((v6\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
((v7\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}((v8\_rlvect\_1~(k15\_euclid~X0)){\unicdcdcdhd}\\
(v5\_rltopsp1~(k15\_euclid~X0)))))))))))\end{array}
\label{hyp:ggdggdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((\preoh v2\_struct\_0~(k15\_euclid~X0)){\unicdcdcdhd}\\
(v5\_rltopsp1~(k15\_euclid~X0)))\end{array}
\label{hyp:ggdgfdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_finseq\_1~X1~X0){\unicdbdjdcd}((v1\_relat\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))\end{array}
\label{hyp:egehpfngbdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_rltopsp1}~{X0}})}{\unicdbdjdcd}{({{({{l1\_rlvect\_1}~{X0}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{X0}})}})}}}\label{hyp:egehpfmgbdpfchmgehpgahdhahbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v5\_relat\_1~\\
X1~X0){\unicdcdcdhd}(v1\_funct\_1~X1))){\unicdbdjdcd}(m1\_subset\_1~(k7\_partfun1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflghdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v5\_rltopsp1~(k15\_euclid~X0)){\unicdcdcdhd}\\
(l1\_rltopsp1~(k15\_euclid~X0)))\end{array}
\label{hyp:egehpflgbdfdpffgfhdgmgjgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(u1\_struct\_0~\\
(k15\_euclid~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (v7\_ordinal1~X2){\unicdbdjdcd}((((r1\_xxreal\_0~\\
np\_\_1~X2){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_nat\_1~X2~np\_\_1)~(k3\_finseq\_1~X1))){\unicdbdjdcd}\\
(k2\_topreal1~X0~X1~X2=k1\_rltopsp1~(k15\_euclid~X0)~(k7\_partfun1~\\
(u1\_struct\_0~(k15\_euclid~X0))~X1~X2)~(k7\_partfun1~(u1\_struct\_0~\\
(k15\_euclid~X0))~X1~(k1\_nat\_1~X2~np\_\_1)))){\unicdcdcdhd}((\preoh (r1\_xxreal\_0~np\_\_1~\\
X2){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_nat\_1~X2~np\_\_1)~(k3\_finseq\_1~X1))){\unicdbdjdcd}(k2\_topreal1~\\
X0~X1~X2=k1\_xboole\_0)))))\end{array}
\label{hyp:egddpfehpgahchfgbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v13\_algstr\_0~\\
X0){\unicdcdcdhd}((v2\_rlvect\_1~X0){\unicdcdcdhd}((v3\_rlvect\_1~X0){\unicdcdcdhd}((v4\_rlvect\_1~X0){\unicdcdcdhd}\\
((v5\_rlvect\_1~X0){\unicdcdcdhd}((v6\_rlvect\_1~X0){\unicdcdcdhd}((v7\_rlvect\_1~X0){\unicdcdcdhd}((v8\_rlvect\_1~\\
X0){\unicdcdcdhd}(l1\_rlvect\_1~X0)))))))))){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~X0)))){\unicdbdjdcd}(k1\_rltopsp1~X0~X1~X2=\\
k1\_rltopsp1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgbdpfchmgehpgahdhahbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m1\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjdcd}{({{{v5\_relat\_1}~{X1}}~{X0}})}}}}\label{hyp:dgdgddpfggjgogdhfgbhpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfehpgahchfgbgmgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m2\_finseq\_1~X2~(u1\_struct\_0~(k15\_euclid~X0))){\unicdbdjdcd}(((r1\_xxreal\_0~\\
np\_\_1~X1){\unicdcdcdhd}(r1\_xxreal\_0~(k1\_nat\_1~X1~np\_\_1)~(k3\_finseq\_1~X2))){\unicdbdjdcd}\\
((k7\_partfun1~(u1\_struct\_0~(k15\_euclid~X0))~X2~X1 \in k2\_topreal1~\\
X0~X2~X1){\unicdcdcdhd}(k7\_partfun1~(u1\_struct\_0~(k15\_euclid~X0))~X2~(k1\_nat\_1~\\
X1~np\_\_1) \in k2\_topreal1~X0~X2~X1)))))\end{array}$$
\end{theorem}
\end{document}
