\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}
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\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{l5\_sin\_cos3 (TMGnYLSqZRowZcJTE5Hy5wPphPoa837SPgC)}
\maketitle
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k10\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ k3\_sin\_cos3 : {\iota}$ be given.
Let $ k6\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_binop\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k15\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_binop\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\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 $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{\preoh{{({{X0} \in {X1}})}}}{\unicdcdcdhd}{({{v1\_xboole\_0}~{X1}})}}}}\label{hyp:ehhdpfcgpgpgmgfg}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))))){\unicdcdcdhd}(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k3\_funct\_2~X0~\\
X1~X2~X3=k1\_funct\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k2\_numbers}}}}\label{hyp:ggdgcdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~k3\_sin\_cos3){\unicdcdcdhd}((v1\_funct\_2~k3\_sin\_cos3~k2\_numbers~\\
k2\_numbers){\unicdcdcdhd}(m1\_subset\_1~k3\_sin\_cos3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k2\_numbers~k2\_numbers))))\end{array}
\label{hyp:egehpflgddpfdhjgogpfdgpgdhdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k2\_numbers~k2\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k2\_numbers~k2\_numbers))))){\unicdbdjdcd}\\
((X0=k3\_sin\_cos3){\unicdbdjded}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~k2\_numbers){\unicdbdjdcd}\\
(k3\_funct\_2~k2\_numbers~k2\_numbers~X0~X1=k6\_binop\_2~(k4\_binop\_2~\\
(k15\_sin\_cos~X1)~(k15\_sin\_cos~(k1\_binop\_2~X1)))~np\_\_2)))\end{array}
\label{hyp:egddpfdhjgogpfdgpgdhdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xcmplx\_0}~{X0}})}{\unicdbdjded}{({{X0} \in {k2\_numbers}})}}}\label{hyp:egcdpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3 \in X0){\unicdbdjdcd}\\
(k10\_funct\_2~X0~X1~X2~X3=k1\_funct\_1~X2~X3))))\end{array}
\label{hyp:egbdddpfggfhogdgehpfcd}
\end{equation}
\begin{theorem}\label{thm:mgfdpfdhjgogpfdgpgdhdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(k10\_funct\_2~k2\_numbers~k2\_numbers~\\
k3\_sin\_cos3~X0=k6\_binop\_2~(k4\_binop\_2~(k15\_sin\_cos~X0)~(k15\_sin\_cos~\\
(k1\_binop\_2~X0)))~np\_\_2)\end{array}$$
\end{theorem}
\end{document}
