\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{l25\_cfdiff\_2 (TMNL9tkdsfLkxVpH4eTKoxeLA5nazuBend9)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_real\_ns1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_normsp\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\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 $ k2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rvsum\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k7\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ m2\_finseq\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}({\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}((X0 \in k2\_finseq\_1~X1){\unicdbdjdcd}\\
((k1\_relset\_1~(k1\_euclid~X1)~(k1\_pdiff\_1~X0~X1)=k1\_euclid~X1){\unicdcdcdhd}\\
(k1\_rvsum\_1~(k1\_pdiff\_1~X0~X1)=k1\_numbers))))){\unicdcdcdhd}({\unicdcdadad} X0 .  \\
(m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((k1\_seq\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1)~\\
(k12\_finseq\_1~k1\_numbers~X0)=X0){\unicdcdcdhd}(k1\_funct\_1~(k2\_funct\_1~(k1\_pdiff\_1~\\
np\_\_1~np\_\_1))~X0=k12\_finseq\_1~k1\_numbers~X0)))\end{array}
\label{hyp:ehbdpfahegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))){\unicdbdjdcd}((X1=k12\_finseq\_1~k1\_numbers~\\
X0){\unicdbdjdcd}(k1\_normsp\_0~(k4\_real\_ns1~np\_\_1)~X1=k18\_complex1~X0)))\end{array}
\label{hyp:mgcdedpfdgggegjgggggpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}\\
((m1\_subset\_1~X1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~(k4\_real\_ns1~\\
X0))))){\unicdbdjdcd}((v1\_funct\_1~(k7\_pdiff\_1~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k7\_pdiff\_1~\\
X0~X1~X2)~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~(k4\_real\_ns1~\\
X0))){\unicdcdcdhd}(m1\_subset\_1~(k7\_pdiff\_1~X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~(k4\_real\_ns1~\\
X0)))))))\end{array}
\label{hyp:egehpflghdpfahegjgggggpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m2\_subset\_1~X0~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k4\_real\_ns1~X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~\\
X3){\unicdcdcdhd}((v1\_funct\_2~X3~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~\\
(k4\_real\_ns1~X0))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~(k4\_real\_ns1~\\
X0))))))){\unicdbdjdcd}((X3=k7\_pdiff\_1~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))){\unicdbdjdcd}({\unicdcdaddd} X5 .  (m1\_subset\_1~\\
X5~k1\_numbers){\unicdcdcdhd}({\unicdcdaddd} X6 .  (m2\_finseq\_2~X6~k1\_numbers~(k1\_euclid~\\
X0)){\unicdcdcdhd}((X4=k12\_finseq\_1~k1\_numbers~X5){\unicdcdcdhd}((X6=X2){\unicdcdcdhd}(k3\_funct\_2~\\
(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))~(u1\_struct\_0~(k4\_real\_ns1~\\
X0))~X3~X4=k3\_funct\_2~k1\_numbers~(k1\_euclid~X0)~(k6\_pdiff\_1~X0~\\
X1~X6)~X5))))))))))\end{array}
\label{hyp:eggdpfahegjgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:mgcdfdpfdgggegjgggggpfcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k4\_real\_ns1~np\_\_1))){\unicdbdjdcd}\\
(k18\_complex1~(k1\_seq\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1)~X0)=k1\_normsp\_0~\\
(k4\_real\_ns1~np\_\_1)~X0)\end{array}$$
\end{theorem}
\end{document}
