\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{l29\_topgen\_5 (TMLmm1RWjtcxdt652pffQPXr8W4JzegTeCx)}
\maketitle
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_topgen\_5 : {\iota}$ be given.
Let $ k2\_topgen\_5 : {\iota}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_topgen\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_euclid : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k1\_topreal9 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k3\_topgen\_5){\unicdcdcdhd}((v1\_pre\_topc~k3\_topgen\_5){\unicdcdcdhd}((v2\_pre\_topc~\\
k3\_topgen\_5){\unicdcdcdhd}(l1\_pre\_topc~k3\_topgen\_5)))\end{array}
\label{hyp:egehpflgddpfehpgahhgfgogpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v1\_pre\_topc~X0){\unicdcdcdhd}((v2\_pre\_topc~\\
X0){\unicdcdcdhd}(l1\_pre\_topc~X0)))){\unicdbdjdcd}((X0=k3\_topgen\_5){\unicdbdjded}((u1\_struct\_0~X0=\\
k2\_topgen\_5){\unicdcdcdhd}({\unicdcdaddd} X1 .  (m1\_topgen\_2~X1~X0){\unicdcdcdhd}(({\unicdcdadad} X2 .  (\\
m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(k1\_funct\_1~X1~(k19\_euclid~X2~k6\_numbers)=\\
ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m1\_subset\_1~X3~k1\_numbers))~({\uniddcgcg} X3 : \\
\iota .  \preoh r1\_xxreal\_0~X3~k6\_numbers)~({\uniddcgcg} X3 : \iota .  k4\_subset\_1~(u1\_struct\_0~\\
(k15\_euclid~np\_\_2))~(k1\_topreal9~np\_\_2~(k19\_euclid~X2~X3)~X3)~(\\
k6\_domain\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k19\_euclid~X2~k6\_numbers))))){\unicdcdcdhd}\\
({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~\\
X3~k1\_numbers){\unicdbdjdcd}((\preoh r1\_xxreal\_0~X3~k6\_numbers){\unicdbdjdcd}(k1\_funct\_1~X1~\\
(k19\_euclid~X2~X3)=ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~\\
k1\_numbers))~({\uniddcgcg} X4 : \iota .  \preoh r1\_xxreal\_0~X4~k6\_numbers)~({\uniddcgcg} X4 : \\
\iota .  k9\_subset\_1~(u1\_struct\_0~(k15\_euclid~np\_\_2))~(k1\_topreal9~\\
np\_\_2~(k19\_euclid~X2~X3)~X4)~k2\_topgen\_5)))))))))\end{array}
\label{hyp:egddpfehpgahhgfgogpffd}
\end{equation}
\begin{theorem}\label{thm:mgcdjdpfehpgahhgfgogpffd}
${{{u1\_struct\_0}~{k3\_topgen\_5}}={k2\_topgen\_5}}$.
\end{theorem}
\end{document}
