\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{t22\_euclid\_5 (TMMHuQ4F6sjPzkcBgXxT5vyCGXqAsggx2d4)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_euclid\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_euclid\_5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k15\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rlvect\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_euclid\_5 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
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~(k15\_euclid~np\_\_3))){\unicdbdjdcd}((k1\_euclid\_5~(k1\_rlvect\_1~\\
(k15\_euclid~np\_\_3)~X1~X0)=k8\_real\_1~X0~(k1\_euclid\_5~X1)){\unicdcdcdhd}((k2\_euclid\_5~\\
(k1\_rlvect\_1~(k15\_euclid~np\_\_3)~X1~X0)=k8\_real\_1~X0~(k2\_euclid\_5~\\
X1)){\unicdcdcdhd}(k3\_euclid\_5~(k1\_rlvect\_1~(k15\_euclid~np\_\_3)~X1~X0)=k8\_real\_1~\\
X0~(k3\_euclid\_5~X1)))))\end{array}
\label{hyp:ehjdpffgfhdgmgjgegpffd}
\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~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}(k1\_rlvect\_1~(k15\_euclid~np\_\_3)~\\
(k4\_euclid\_5~X1~X2~X3)~X0=k4\_euclid\_5~(k8\_real\_1~X0~X1)~(k8\_real\_1~\\
X0~X2)~(k8\_real\_1~X0~X3)))))\end{array}
\label{hyp:ehidpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k4\_struct\_0~(k15\_euclid~np\_\_3)=k4\_euclid\_5~k6\_numbers~k6\_numbers~\\
k6\_numbers\end{array}
\label{hyp:ehedpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k3\_xcmplx\_0}~{np\_\_1}}~{X0}}={X0}})}}}\label{hyp:ehddpfbgchjgehigng}
\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~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}((k1\_euclid\_5~\\
(k4\_euclid\_5~X0~X1~X2)=X0){\unicdcdcdhd}((k2\_euclid\_5~(k4\_euclid\_5~X0~X1~X2)=\\
X1){\unicdcdcdhd}(k3\_euclid\_5~(k4\_euclid\_5~X0~X1~X2)=X2)))))\end{array}
\label{hyp:ehcdpffgfhdgmgjgegpffd}
\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~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}(k5\_euclid\_5~\\
(k4\_euclid\_5~k6\_numbers~k6\_numbers~k6\_numbers)~(k4\_euclid\_5~\\
X0~X1~X2)=k4\_struct\_0~(k15\_euclid~np\_\_3))))\end{array}
\label{hyp:ehbdjdpffgfhdgmgjgegpffd}
\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~(k15\_euclid~np\_\_3))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}((k5\_euclid\_5~(k1\_rlvect\_1~\\
(k15\_euclid~np\_\_3)~X1~X0)~X2=k1\_rlvect\_1~(k15\_euclid~np\_\_3)~(k5\_euclid\_5~\\
X1~X2)~X0){\unicdcdcdhd}(k5\_euclid\_5~(k1\_rlvect\_1~(k15\_euclid~np\_\_3)~X1~X0)~\\
X2=k5\_euclid\_5~X1~(k1\_rlvect\_1~(k15\_euclid~np\_\_3)~X2~X0)))))\end{array}
\label{hyp:ehbdgdpffgfhdgmgjgegpffd}
\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~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  \\
(m1\_subset\_1~X3~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~X4~k1\_numbers){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  (m1\_subset\_1~X5~k1\_numbers){\unicdbdjdcd}(k5\_euclid\_5~(k4\_euclid\_5~\\
X0~X1~X2)~(k4\_euclid\_5~X3~X4~X5)=k4\_euclid\_5~(k9\_real\_1~(k8\_real\_1~\\
X1~X5)~(k8\_real\_1~X2~X4))~(k9\_real\_1~(k8\_real\_1~X2~X3)~(k8\_real\_1~\\
X0~X5))~(k9\_real\_1~(k8\_real\_1~X0~X4)~(k8\_real\_1~X1~X3))))))))\end{array}
\label{hyp:ehbdfdpffgfhdgmgjgegpffd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k8\_real\_1~X0~X1=k3\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xxreal\_0~\\
X0){\unicdcdcdhd}(v1\_xreal\_0~X0)))\end{array}
\label{hyp:chdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(m1\_subset\_1~(k8\_real\_1~X0~X1)~k1\_numbers)\end{array}
\label{hyp:egehpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}((v1\_xreal\_0~\\
X1){\unicdcdcdhd}(v1\_xreal\_0~X2))){\unicdbdjdcd}(m1\_subset\_1~(k4\_euclid\_5~X0~X1~X2)~(u1\_struct\_0~\\
(k15\_euclid~np\_\_3)))\end{array}
\label{hyp:egehpflgedpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k15\_euclid~np\_\_3))){\unicdbdjdcd}\\
(k5\_euclid\_5~X0~X1=k4\_euclid\_5~(k9\_real\_1~(k8\_real\_1~(k2\_euclid\_5~\\
X0)~(k3\_euclid\_5~X1))~(k8\_real\_1~(k3\_euclid\_5~X0)~(k2\_euclid\_5~\\
X1)))~(k9\_real\_1~(k8\_real\_1~(k3\_euclid\_5~X0)~(k1\_euclid\_5~X1))~\\
(k8\_real\_1~(k1\_euclid\_5~X0)~(k3\_euclid\_5~X1)))~(k9\_real\_1~(k8\_real\_1~\\
(k1\_euclid\_5~X0)~(k2\_euclid\_5~X1))~(k8\_real\_1~(k2\_euclid\_5~X0)~\\
(k1\_euclid\_5~X1)))))\end{array}
\label{hyp:egedpffgfhdgmgjgegpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k1\_numbers){\unicdcdcdhd}(v1\_xreal\_0~\\
X1)){\unicdbdjdcd}(k8\_real\_1~X0~X1=k8\_real\_1~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgidpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehcdcdpffgfhdgmgjgegpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k1\_numbers){\unicdbdjdcd}(k5\_euclid\_5~(k4\_euclid\_5~k6\_numbers~k6\_numbers~\\
X0)~(k4\_euclid\_5~k6\_numbers~k6\_numbers~X1)=k4\_struct\_0~(k15\_euclid~\\
np\_\_3)))\end{array}$$
\end{theorem}
\end{document}
