\documentclass{article}
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\newtheorem{lemma}{Lemma}
\newtheorem{proposition}{Proposition}
\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
\newcommand\unicdcdcdbg{\cup}
\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t61\_sincos10 (TMSg1f1Tw5zknNz1fhXnabAjvWDo61evKNe)}
\maketitle
Let $ k3\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_fdiff\_9 : {\iota}$ be given.
Let $ k3\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\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\_sincos10 : {\iota}$ be given.
Let $ k1\_partfun2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_relat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v2\_funct\_1~X0){\unicdbdjdcd}\\
((k3\_relat\_1~X0~(k2\_funct\_1~X0)=k4\_relat\_1~(k9\_xtuple\_0~X0)){\unicdcdcdhd}\\
(k3\_relat\_1~(k2\_funct\_1~X0)~X0=k4\_relat\_1~(k10\_xtuple\_0~X0))))\end{array}
\label{hyp:ehddjdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_relset\_1~k1\_numbers~k1\_sincos10=k3\_rcomp\_1~k6\_numbers~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2)\end{array}
\label{hyp:ehcdfdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k2\_relset\_1~X0~X1=k10\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v2\_funct\_1~\\
X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}(k2\_partfun2~\\
X0~X1~X2=k2\_funct\_1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_partfun1~\\
X0~X1~X2~X3=k5\_relat\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0))){\unicdbdjdcd}(k1\_partfun2~X0~X1=k4\_relat\_1~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfahbgchehggfhogcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k2\_funct\_1~k1\_sincos10=k2\_partfun1~k1\_numbers~k1\_numbers~k1\_fdiff\_9~\\
(k3\_rcomp\_1~k6\_numbers~(k10\_real\_1~k32\_sin\_cos~np\_\_2))\end{array}
\label{hyp:mggdbdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
{{({{v1\_funct\_1}~{k1\_sincos10}})}{\unicdcdcdhd}{({{v2\_funct\_1}~{k1\_sincos10}})}}\label{hyp:ggdgfdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_relat\_1~(k5\_relat\_1~k1\_fdiff\_9~(k3\_rcomp\_1~k6\_numbers~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2)))){\unicdcdcdhd}(v2\_funct\_1~(k5\_relat\_1~k1\_fdiff\_9~(k3\_rcomp\_1~\\
k6\_numbers~(k10\_real\_1~k32\_sin\_cos~np\_\_2))))\end{array}
\label{hyp:ggdgbdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_relset\_1~X0~X1)~(k1\_zfmisc\_1~X0))\end{array}
\label{hyp:egehpflgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}((v1\_funct\_1~\\
(k2\_partfun1~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k2\_partfun1~X0~X1~X2~X3)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))\end{array}
\label{hyp:egehpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~(\\
k2\_funct\_1~X0)){\unicdcdcdhd}(v1\_funct\_1~(k2\_funct\_1~X0)))\end{array}
\label{hyp:egehpflgcdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_sincos10){\unicdcdcdhd}(m1\_subset\_1~k1\_sincos10~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgbdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k1\_fdiff\_9){\unicdcdcdhd}(m1\_subset\_1~k1\_fdiff\_9~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgbdpfggegjgggggpfjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_sincos10=k2\_partfun2~k1\_numbers~k1\_numbers~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~k1\_fdiff\_9~(k3\_rcomp\_1~k6\_numbers~(k10\_real\_1~\\
k32\_sin\_cos~np\_\_2)))\end{array}
\label{hyp:egbdpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehgdbdpfdhjgogdgpgdhbdad}
$$\begin{array}{c}k3\_relat\_1~(k2\_partfun1~k1\_numbers~k1\_numbers~k1\_fdiff\_9~(k3\_rcomp\_1~\\
k6\_numbers~(k10\_real\_1~k32\_sin\_cos~np\_\_2)))~k1\_sincos10=k1\_partfun2~\\
k1\_numbers~(k3\_rcomp\_1~k6\_numbers~(k10\_real\_1~k32\_sin\_cos~np\_\_2))\end{array}$$
\end{theorem}
\end{document}
