\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{l19\_series\_5 (TMSoSL9ihqKvcrFap9WeUqYFEatXYwnJxQq)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k13\_complex1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}(X0=\\
k2\_xcmplx\_0~(k6\_xcmplx\_0~X0~X1)~X1))\end{array}
\label{hyp:ehcdhdpfihdgngahmgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~\\
X1){\unicdcdcdhd}(v1\_xcmplx\_0~X2))){\unicdbdjdcd}(k2\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~X2=k2\_xcmplx\_0~\\
X0~(k2\_xcmplx\_0~X1~X2))\end{array}
\label{hyp:dhahdggdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
{{{k4\_xcmplx\_0}~{({{k4\_xcmplx\_0}~{np\_\_2}})}}={np\_\_2}}\label{hyp:chbhcffgbgmgoefghgpfpflgedpfihdgngahmgihpfadpfpfchngcdpfchcd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k6\_xcmplx\_0}~{np\_\_2}}~{np\_\_1}}={np\_\_1}}\label{hyp:chbhcffgbgmgeejgggggpfpflggdpfihdgngahmgihpfadpfpfchcdpfchbdpfchbd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}={{k4\_xcmplx\_0}~{np\_\_2}}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchngbdpfchngbdpfchngcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k13\_complex1~X0~X1=k7\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdddpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
(v1\_xreal\_0~X1){\unicdcdcdhd}(v2\_xxreal\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_xreal\_0~\\
X2){\unicdcdcdhd}(v2\_xxreal\_0~X2)){\unicdbdjdcd}((k2\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~X2=np\_\_1){\unicdbdjdcd}\\
(k6\_xcmplx\_0~(k13\_complex1~np\_\_1~X0)~np\_\_1=k13\_complex1~(k2\_xcmplx\_0~\\
X1~X2)~X0))))\end{array}
\label{hyp:mgbdhdpfdhfgchjgfgdhpffd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgfdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
v1\_xcmplx\_0~(k7\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgfdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
v1\_xcmplx\_0~(k6\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgedpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_xcmplx\_0~(k4\_xcmplx\_0~X0)){\unicdcdcdhd}\\
(v1\_xreal\_0~(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ggdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
v1\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{({{k4\_xcmplx\_0}~{X0}})}})}}}\label{hyp:egehpflgedpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}(v1\_xcmplx\_0~X1)){\unicdbdjdcd}(\\
k2\_xcmplx\_0~X0~X1=k2\_xcmplx\_0~X1~X0)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdjdpfdhfgchjgfgdhpffd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  (\\
(v1\_xreal\_0~X1){\unicdcdcdhd}(v2\_xxreal\_0~X1)){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_xreal\_0~\\
X2){\unicdcdcdhd}(v2\_xxreal\_0~X2)){\unicdbdjdcd}((k2\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~X2=np\_\_1){\unicdbdjdcd}\\
(k2\_xcmplx\_0~np\_\_1~(k13\_complex1~np\_\_1~X0)=k2\_xcmplx\_0~np\_\_2~\\
(k13\_complex1~(k2\_xcmplx\_0~X1~X2)~X0)))))\end{array}$$
\end{theorem}
\end{document}
