\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{t42\_sin\_cos9 (TMdvFbevJTEM3DR3S9VWCSRFXuxeiUFVorq)}
\maketitle
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k30\_sin\_cos : {\iota}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k2\_sin\_cos4 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k18\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k19\_sin\_cos : {\iota}$ be given.
Let $ k16\_sin\_cos : {\iota}$ be given.
Let $ k3\_sin\_cos6 : {{\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 $ k7\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_0 : {\iota}$ be given.
Let $ k2\_sin\_cos6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k20\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_sin\_cos6 : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}(k21\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=k6\_numbers){\unicdcdcdhd}((\\
k18\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=np\_\_1){\unicdcdcdhd}((k21\_sin\_cos~\\
k32\_sin\_cos=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k18\_sin\_cos~k32\_sin\_cos=k6\_numbers){\unicdcdcdhd}\\
((k21\_sin\_cos~(k7\_real\_1~k32\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~\\
np\_\_2))=k6\_numbers){\unicdcdcdhd}((k18\_sin\_cos~(k7\_real\_1~k32\_sin\_cos~(\\
k10\_real\_1~k32\_sin\_cos~np\_\_2))=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k21\_sin\_cos~\\
(k8\_real\_1~np\_\_2~k32\_sin\_cos)=np\_\_1){\unicdcdcdhd}(k18\_sin\_cos~(k8\_real\_1~\\
np\_\_2~k32\_sin\_cos)=k6\_numbers)))))))\end{array}
\label{hyp:ehhdhdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_seq\_1~k19\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=k6\_numbers){\unicdcdcdhd}\\
((k1\_seq\_1~k16\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=np\_\_1){\unicdcdcdhd}\\
((k1\_seq\_1~k19\_sin\_cos~k32\_sin\_cos=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k1\_seq\_1~\\
k16\_sin\_cos~k32\_sin\_cos=k6\_numbers){\unicdcdcdhd}((k1\_seq\_1~k19\_sin\_cos~\\
(k7\_real\_1~k32\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2))=k6\_numbers){\unicdcdcdhd}\\
((k1\_seq\_1~k16\_sin\_cos~(k7\_real\_1~k32\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~\\
np\_\_2))=k1\_real\_1~np\_\_1){\unicdcdcdhd}((k1\_seq\_1~k19\_sin\_cos~(k8\_real\_1~\\
np\_\_2~k32\_sin\_cos)=np\_\_1){\unicdcdcdhd}(k1\_seq\_1~k16\_sin\_cos~(k8\_real\_1~\\
np\_\_2~k32\_sin\_cos)=k6\_numbers)))))))\end{array}
\label{hyp:ehhdgdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{{k3\_sin\_cos6}~{np\_\_1}}={{{k10\_real\_1}~{k32\_sin\_cos}}~{np\_\_2}}}\label{hyp:ehhdcdpfdhjgogpfdgpgdhgd}
\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}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{{k7\_xcmplx\_0}~{X0}}~{np\_\_1}}={X0}})}}}\label{hyp:ehgdpfbgchjgehigng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((k1\_seq\_1~k16\_sin\_cos~\\
X0{\unicdcdgdad}k6\_numbers){\unicdbdjdcd}(k1\_seq\_1~k30\_sin\_cos~X0=k2\_sin\_cos4~X0))\end{array}
\label{hyp:ehbdgdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}={np\_\_0}}\label{hyp:chbhcffgbgmgbeegegpfpflgcdpfihdgngahmgihpfadpfpfchbdpfchngbdpfchad}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k3\_sin\_cos6}~{X0}}={{k2\_sin\_cos6}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k21\_sin\_cos~X0=k20\_sin\_cos~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdbdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(k18\_sin\_cos~X0=k17\_sin\_cos~\\
X0)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdidpfdhjgogpfdgpgdh}
\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}
{{{{k2\_xcmplx\_0}~{np\_\_1}}~{({{k4\_xcmplx\_0}~{np\_\_1}})}}={k6\_numbers}}\label{hyp:mgbdddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k3\_sin\_cos6}~{X0}})}}~{k1\_numbers}}}\label{hyp:egehpflgddpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k2\_sin\_cos6}~{X0}}={{{k1\_seq\_1}~{k1\_sin\_cos6}}~{X0}}}}\label{hyp:egcdpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k2\_sin\_cos4~X0=k7\_xcmplx\_0~(k20\_sin\_cos~\\
X0)~(k17\_sin\_cos~X0))\end{array}
\label{hyp:egcdpfdhjgogpfdgpgdhed}
\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:ehedcdpfdhjgogpfdgpgdhjd}
$$\begin{array}{c}(k1\_seq\_1~k30\_sin\_cos~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=k6\_numbers){\unicdcdcdhd}\\
(k2\_sin\_cos4~(k10\_real\_1~k32\_sin\_cos~np\_\_2)=k6\_numbers)\end{array}$$
\end{theorem}
\end{document}
