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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{l42\_sin\_cos9 (TMTmmHWTHS1xRzdkrVJkg4puj8oiAK6eVFp)}
\maketitle
Let $ v6\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k30\_sin\_cos : {\iota}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\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\_\_4 : {\iota}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\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 $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k31\_sin\_cos : {\iota}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xxreal\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v6\_xxreal\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_membered : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~k30\_sin\_cos~(\\
k2\_rcomp\_1~k6\_numbers~k32\_sin\_cos))\end{array}
\label{hyp:ehidpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))){\unicdbdjdcd}(((r1\_tarski~\\
X0~X1){\unicdcdcdhd}(v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~X1))){\unicdbdjdcd}\\
(v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~X2~X0)))\end{array}
\label{hyp:ehcdjdpfchggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k1\_xboole\_0}}~{k4\_ordinal1}}\label{hyp:ehbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\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}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
k2\_rcomp\_1~X0~X1=k4\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfchdgpgngahpfbd}
\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 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(k1\_rcomp\_1~\\
X0~X1=k1\_xxreal\_1~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos \in k2\_rcomp\_1~k6\_numbers~\\
k32\_sin\_cos\end{array}
\label{hyp:mgcdgdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
{{{{k10\_real\_1}~{k32\_sin\_cos}}~{np\_\_4}} \in {{{k2\_rcomp\_1}~{k6\_numbers}}~{k32\_sin\_cos}}}\label{hyp:mgcdfdpfdhjgogpfdgpgdhjd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v6\_valued\_0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k5\_relat\_1~X0~X1)){\unicdcdcdhd}(v6\_valued\_0~(k5\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgddpfchggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
v6\_xxreal\_2~(k4\_xxreal\_1~X0~X1))\end{array}
\label{hyp:ggdgbdgdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\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}(v1\_funct\_1~k30\_sin\_cos){\unicdcdcdhd}(m1\_subset\_1~k30\_sin\_cos~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~k1\_numbers)))\end{array}
\label{hyp:egehpflgddadpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgcdpfchdgpgngahpfbd}
\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 .  (v2\_membered~X0){\unicdbdjdcd}((v6\_xxreal\_2~X0){\unicdbdjded}({\unicdcdadad} X1 .  (\\
v1\_xxreal\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (v1\_xxreal\_0~X2){\unicdbdjdcd}(((X1 \in X0){\unicdcdcdhd}(X2 \in \\
X0)){\unicdbdjdcd}(r1\_tarski~(k1\_xxreal\_1~X1~X2)~X0)))))\end{array}
\label{hyp:egbdcdpfihihchfgbgmgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(v3\_membered~\\
X0)\end{array}
\label{hyp:dgdgidpfngfgngcgfgchfgeg}
\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 .  {{({{v3\_membered}~{X0}})}{\unicdbdjdcd}{({{v2\_membered}~{X0}})}}}\label{hyp:dgdgedpfngfgngcgfgchfgeg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_membered~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~X0){\unicdbdjdcd}\\
(v1\_xreal\_0~X1))\end{array}
\label{hyp:dgdgbdedpfngfgngcgfgchfgeg}
\end{equation}
\begin{theorem}\label{thm:mgedcdpfdhjgogpfdgpgdhjd}
$$\begin{array}{c}v6\_valued\_0~(k2\_partfun1~k1\_numbers~k1\_numbers~(k2\_partfun1~\\
k1\_numbers~k1\_numbers~k30\_sin\_cos~(k1\_rcomp\_1~(k10\_real\_1~k32\_sin\_cos~\\
np\_\_4)~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos)))~(k1\_rcomp\_1~\\
(k10\_real\_1~k32\_sin\_cos~np\_\_4)~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~\\
k32\_sin\_cos)))\end{array}$$
\end{theorem}
\end{document}
