\documentclass{article}
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\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
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\begin{document}
\title{t98\_sin\_cos6 (TMa9ygMp9SSmRLeyLkrN652nXX7m7SFihGH)}
\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 $ k6\_sin\_cos6 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k21\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k18\_sin\_cos : {{\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.
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}(k21\_sin\_cos~(k6\_sin\_cos6~X0)=X0))\end{array}
\label{hyp:ehjdbdpfdhjgogpfdgpgdhgd}
\end{equation}
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}
\begin{theorem}\label{thm:ehjdidpfdhjgogpfdgpgdhgd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~np\_\_1)~\\
X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~np\_\_1){\unicdcdcdhd}(k6\_sin\_cos6~X0=k32\_sin\_cos))){\unicdbdjdcd}\\
(X0=k1\_real\_1~np\_\_1))\end{array}$$
\end{theorem}
\end{document}
