\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{t87\_complex2 (TMa6MrCo3qPt39Avfms4yJdQwMEospXm1qn)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k4\_complex2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_5 : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k31\_sin\_cos : {\iota}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_numbers){\unicdbdjdcd}((k4\_complex2~\\
X0~X1~X2=k32\_sin\_cos){\unicdbdjdcd}((X0=X1){\unicdcdcdid}((X1=X2){\unicdcdcdid}((k4\_complex2~X1~X2~\\
X0=k6\_numbers){\unicdcdcdhd}(k4\_complex2~X2~X0~X1=k6\_numbers)))))))\end{array}
\label{hyp:ehidgdpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k4\_complex2~X0~X1~X2)~k32\_sin\_cos){\unicdcdcdhd}\\
(\preoh (k2\_xcmplx\_0~(k2\_xcmplx\_0~(k4\_complex2~X0~X1~X2)~(k4\_complex2~\\
X1~X2~X0))~(k4\_complex2~X2~X0~X1)=k8\_real\_1~np\_\_5~k32\_sin\_cos){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~(k4\_complex2~X1~X2~X0)~k32\_sin\_cos){\unicdcdcdhd}(\preoh r1\_xxreal\_0~\\
(k4\_complex2~X2~X0~X1)~k32\_sin\_cos))))))))\end{array}
\label{hyp:ehidfdpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k4\_complex2~X0~X1~X2)~k6\_numbers){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~k32\_sin\_cos~(k4\_complex2~X0~X1~X2)){\unicdcdcdhd}(\preoh (k2\_xcmplx\_0~\\
(k2\_xcmplx\_0~(k4\_complex2~X0~X1~X2)~(k4\_complex2~X1~X2~X0))~(k4\_complex2~\\
X2~X0~X1)=k32\_sin\_cos){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k4\_complex2~X1~X2~X0)~k6\_numbers){\unicdcdcdhd}\\
(\preoh r1\_xxreal\_0~(k4\_complex2~X2~X0~X1)~k6\_numbers)))))))))\end{array}
\label{hyp:ehidedpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}((X0{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((k4\_complex2~X0~X1~X2=k6\_numbers){\unicdcdcdhd}(\\
(k4\_complex2~X1~X2~X0=k6\_numbers){\unicdcdcdhd}(k4\_complex2~X2~X0~X1=k6\_numbers))))))))\end{array}
\label{hyp:ehidddpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(\preoh (\preoh \\
r1\_xxreal\_0~X0~X1){\unicdcdcdhd}((\preoh v2\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X1))))\end{array}
\label{hyp:ehhdpfchfgbgmg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~\\
k6\_numbers~(k4\_complex2~X0~X1~X2)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k8\_real\_1~np\_\_2~\\
k32\_sin\_cos)~(k4\_complex2~X0~X1~X2)))))\end{array}
\label{hyp:ehhdadpfdgpgngahmgfgihcd}
\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}(\preoh r1\_xxreal\_0~(k10\_real\_1~k32\_sin\_cos~np\_\_2)~k6\_numbers){\unicdcdcdhd}((\\
\preoh r1\_xxreal\_0~k32\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)){\unicdcdcdhd}((\\
\preoh r1\_xxreal\_0~k32\_sin\_cos~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2)~(k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_2))){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~(k8\_real\_1~np\_\_2~k32\_sin\_cos)~k32\_sin\_cos){\unicdcdcdhd}(\\
(\preoh r1\_xxreal\_0~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_2)~k32\_sin\_cos)~\\
(k10\_real\_1~k32\_sin\_cos~np\_\_2)){\unicdcdcdhd}((\preoh r1\_xxreal\_0~k6\_numbers~(\\
k1\_real\_1~(k10\_real\_1~k32\_sin\_cos~np\_\_2))){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(\\
k8\_real\_1~np\_\_2~k32\_sin\_cos)~k6\_numbers){\unicdcdcdhd}((\preoh r1\_xxreal\_0~(k8\_real\_1~\\
(k10\_real\_1~np\_\_3~np\_\_2)~k32\_sin\_cos)~k32\_sin\_cos){\unicdcdcdhd}((\preoh r1\_xxreal\_0~\\
(k8\_real\_1~np\_\_2~k32\_sin\_cos)~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_2)~\\
k32\_sin\_cos)){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_2)~\\
k32\_sin\_cos)~k6\_numbers))))))))))\end{array}
\label{hyp:ehfdpfdgpgngahehchjghg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xxreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xxreal\_0~X1){\unicdbdjdcd}((\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdhd}(r1\_xxreal\_0~X1~X0)){\unicdbdjdcd}(X0=X1)))\end{array}
\label{hyp:ehbdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xboole\_0}~{np\_\_0}}\label{hyp:dhahdgadpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{{r1\_xxreal\_0}~{np\_\_0}}~{np\_\_0}}\label{hyp:chbhmefgdhdhpechfebhfhbgmgpfpfchbdpfihihchfgbgmgpfadpfpfchadpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k32\_sin\_cos}={k31\_sin\_cos}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddcdpfdhjgogpfdgpgdh}
\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 .  {\unicdcdadad} X2 .  ((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~\\
X1){\unicdcdcdhd}(v1\_xcmplx\_0~X2))){\unicdbdjdcd}(v1\_xreal\_0~(k4\_complex2~X0~X1~X2))\end{array}
\label{hyp:egehpflgedpfdgpgngahmgfgihcd}
\end{equation}
Assume the following.
\begin{equation}
{{v1\_xreal\_0}~{k31\_sin\_cos}}\label{hyp:egehpflgddbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v3\_xxreal\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v2\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdgfdpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v2\_xxreal\_0~X0)){\unicdbdjdcd}((\preoh v1\_xboole\_0~\\
X0){\unicdcdcdhd}((v1\_xxreal\_0~X0){\unicdcdcdhd}(\preoh v3\_xxreal\_0~X0)))\end{array}
\label{hyp:dgdgddpfihihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
\begin{theorem}\label{thm:ehidhdpfdgpgngahmgfgihcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~k2\_numbers){\unicdbdjdcd}(\preoh (X0{\unicdcdgdad}\\
X1){\unicdcdcdhd}((X0{\unicdcdgdad}X2){\unicdcdcdhd}((X1{\unicdcdgdad}X2){\unicdcdcdhd}((k4\_complex2~X0~X1~X2=k6\_numbers){\unicdcdcdhd}(\\
(\preoh (k4\_complex2~X1~X2~X0=k6\_numbers){\unicdcdcdhd}(k4\_complex2~X2~X0~X1=k32\_sin\_cos)){\unicdcdcdhd}\\
(\preoh (k4\_complex2~X1~X2~X0=k32\_sin\_cos){\unicdcdcdhd}(k4\_complex2~X2~X0~X1=k6\_numbers)))))))))\end{array}$$
\end{theorem}
\end{document}
