\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{t77\_sin\_cos6 (TMS2GXGZF1PvsdcYZPaG711VHgSZsX4iXCK)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_sin\_cos6 : {{\iota}{\unicdbdjdcd}{\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 $ k1\_comptrig : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_complex1 : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~\\
X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~np\_\_1)){\unicdbdjdcd}((r1\_xxreal\_0~(k1\_real\_1~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2))~(k3\_sin\_cos6~X0)){\unicdcdcdhd}(r1\_xxreal\_0~(k3\_sin\_cos6~\\
X0)~(k10\_real\_1~k32\_sin\_cos~np\_\_2))))\end{array}
\label{hyp:ehhdgdpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~\\
X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(k3\_sin\_cos6~X0=k10\_real\_1~k32\_sin\_cos~\\
np\_\_2))){\unicdbdjdcd}(X0=np\_\_1))\end{array}
\label{hyp:ehhdfdpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~\\
X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(k3\_sin\_cos6~X0=k1\_real\_1~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2)))){\unicdbdjdcd}(X0=k1\_real\_1~np\_\_1))\end{array}
\label{hyp:ehhdddpfdhjgogpfdgpgdhgd}
\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}
{{{k1\_comptrig}~{k7\_complex1}}={{{k10\_real\_1}~{k32\_sin\_cos}}~{np\_\_2}}}\label{hyp:ehedadpfdgpgngahehchjghg}
\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}
\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}
{{\unicdcdadad} X0 .  {{{m1\_subset\_1}~{({{k3\_sin\_cos6}~{X0}})}}~{k1\_numbers}}}\label{hyp:egehpflgddpfdhjgogpfdgpgdhgd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(m1\_subset\_1~(k1\_real\_1~\\
X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
(r1\_xxreal\_0~X0~X1){\unicdcdcdid}(r1\_xxreal\_0~X1~X0))\end{array}
\label{hyp:dgpgogogfgdgehfgegogfgdhdhpfchbdpfihihchfgbgmgpfad}
\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}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehhdhdpfdhjgogpfdgpgdhgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(\preoh (\preoh r1\_xxreal\_0~X0~(k1\_real\_1~np\_\_1)){\unicdcdcdhd}\\
((\preoh r1\_xxreal\_0~np\_\_1~X0){\unicdcdcdhd}(\preoh (\preoh r1\_xxreal\_0~(k3\_sin\_cos6~X0)~(k1\_real\_1~\\
(k10\_real\_1~k32\_sin\_cos~np\_\_2))){\unicdcdcdhd}(\preoh r1\_xxreal\_0~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2)~(k3\_sin\_cos6~X0)))))\end{array}$$
\end{theorem}
\end{document}
