\documentclass{article}
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\newtheorem{lemma}{Lemma}
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\newtheorem{definition}{Definition}
\newtheorem{example}{Example}
\newtheorem{conjecture}{Conjecture}
\newcommand\unicdcdgdad{\not=}
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\newcommand\unicdbdjded{\Leftrightarrow}
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\begin{document}
\title{t38\_sin\_cos4 (TMbuFhgTgfEtKRQ1WkBmTknSevbDEtvk5DA)}
\maketitle
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k17\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k3\_xcmplx\_0~(k20\_sin\_cos~X0)~(k20\_sin\_cos~\\
X0)=k6\_xcmplx\_0~np\_\_1~(k3\_xcmplx\_0~(k17\_sin\_cos~X0)~(k17\_sin\_cos~\\
X0)))\end{array}
\label{hyp:ehfdpfdhjgogpfdgpgdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}(k3\_xcmplx\_0~(k17\_sin\_cos~X0)~(k17\_sin\_cos~\\
X0)=k6\_xcmplx\_0~np\_\_1~(k3\_xcmplx\_0~(k20\_sin\_cos~X0)~(k20\_sin\_cos~\\
X0)))\end{array}
\label{hyp:ehedpfdhjgogpfdgpgdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k3\_xcmplx\_0~\\
(k17\_sin\_cos~(k2\_xcmplx\_0~X0~X1))~(k17\_sin\_cos~(k6\_xcmplx\_0~X0~\\
X1))=k6\_xcmplx\_0~(k3\_xcmplx\_0~(k17\_sin\_cos~X0)~(k17\_sin\_cos~\\
X0))~(k3\_xcmplx\_0~(k17\_sin\_cos~X1)~(k17\_sin\_cos~X1))))\end{array}
\label{hyp:ehddhdpfdhjgogpfdgpgdhed}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((k2\_xcmplx\_0~(k3\_square\_1~(k20\_sin\_cos~\\
X0))~(k3\_square\_1~(k17\_sin\_cos~X0))=np\_\_1){\unicdcdcdhd}(k2\_xcmplx\_0~(k3\_xcmplx\_0~\\
(k20\_sin\_cos~X0)~(k20\_sin\_cos~X0))~(k3\_xcmplx\_0~(k17\_sin\_cos~\\
X0)~(k17\_sin\_cos~X0))=np\_\_1))\end{array}
\label{hyp:ehcdjdpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xcmplx\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(v1\_xcmplx\_0~X2){\unicdbdjdcd}(k6\_xcmplx\_0~(k6\_xcmplx\_0~(k2\_xcmplx\_0~X0~X1)~\\
X2)~X1=k6\_xcmplx\_0~X0~X2)))\end{array}
\label{hyp:ehcdcdgdpfihdgngahmgihpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}(v1\_xreal\_0~\\
(k3\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdggdpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k20\_sin\_cos}~{X0}})}})}}}\label{hyp:ggdgedpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{({{k17\_sin\_cos}~{X0}})}})}}}\label{hyp:ggdgddpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjdcd}{({{{k3\_square\_1}~{X0}}={{{k3\_xcmplx\_0}~{X0}}~{X0}}})}}}\label{hyp:egbdpfdhbhfhbgchfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehddidpfdhjgogpfdgpgdhed}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v1\_xreal\_0~X1){\unicdbdjdcd}(k3\_xcmplx\_0~\\
(k17\_sin\_cos~(k2\_xcmplx\_0~X0~X1))~(k17\_sin\_cos~(k6\_xcmplx\_0~X0~\\
X1))=k6\_xcmplx\_0~(k3\_xcmplx\_0~(k20\_sin\_cos~X1)~(k20\_sin\_cos~\\
X1))~(k3\_xcmplx\_0~(k20\_sin\_cos~X0)~(k20\_sin\_cos~X0))))\end{array}$$
\end{theorem}
\end{document}
