\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}
\newcommand\unicdcdadad{\forall}
\newcommand\unicdbdjdcd{\Rightarrow}
\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
\newcommand\unicdcdcdhd{\land}
\newcommand\uniddcgcg{\lambda}
\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t19\_sin\_cos (TMcGGARQESqyhT79je4hNDjM687aHEHVxF2)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_numbers : {\iota}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k18\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_series\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_sin\_cos : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k17\_complex1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k9\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ 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 $ k6\_numbers : {\iota}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_funct\_2~X0~k5\_numbers~k1\_numbers){\unicdcdcdhd}\\
(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers))))){\unicdbdjdcd}\\
(({\unicdcdadad} X1 .  (m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(r1\_xxreal\_0~\\
k6\_numbers~(k8\_nat\_1~k1\_numbers~X0~X1))){\unicdbdjdcd}(({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((r1\_xxreal\_0~X1~X2){\unicdbdjdcd}(k18\_complex1~(k9\_real\_1~(\\
k8\_nat\_1~k1\_numbers~(k3\_series\_1~X0)~X2)~(k8\_nat\_1~k1\_numbers~\\
(k3\_series\_1~X0)~X1))=k9\_real\_1~(k8\_nat\_1~k1\_numbers~(k3\_series\_1~\\
X0)~X2)~(k8\_nat\_1~k1\_numbers~(k3\_series\_1~X0)~X1))))){\unicdcdcdhd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(k18\_complex1~(k8\_nat\_1~\\
k1\_numbers~(k3\_series\_1~X0)~X1)=k8\_nat\_1~k1\_numbers~(k3\_series\_1~\\
X0)~X1))))\end{array}
\label{hyp:ehjdpfdgpgngdhfgbhpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}(r1\_xxreal\_0~k6\_numbers~(k8\_nat\_1~\\
k1\_numbers~(k4\_sin\_cos~(k17\_complex1~X0))~X1)))\end{array}
\label{hyp:ehbdidpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k4\_sin\_cos~X0)){\unicdcdcdhd}((\\
v1\_funct\_2~(k4\_sin\_cos~X0)~k5\_numbers~k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
(k4\_sin\_cos~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k5\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgedpfdhjgogpfdgpgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xcmplx\_0~X0){\unicdbdjdcd}(m1\_subset\_1~(k17\_complex1~X0)~k1\_numbers)\end{array}
\label{hyp:egehpflgbdhdpfdgpgngahmgfgihbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k2\_numbers}})}{\unicdbdjdcd}{({{v1\_xcmplx\_0}~{X0}})}}}\label{hyp:dgdgddpfihdgngahmgihpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdjdpfdhjgogpfdgpgdh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k2\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_subset\_1~\\
X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~k1\_numbers~\\
k5\_numbers){\unicdbdjdcd}((k18\_complex1~(k8\_nat\_1~k1\_numbers~(k3\_series\_1~\\
(k4\_sin\_cos~(k17\_complex1~X0)))~X1)=k8\_nat\_1~k1\_numbers~(k3\_series\_1~\\
(k4\_sin\_cos~(k17\_complex1~X0)))~X1){\unicdcdcdhd}((r1\_xxreal\_0~X1~X2){\unicdbdjdcd}(k18\_complex1~\\
(k9\_real\_1~(k8\_nat\_1~k1\_numbers~(k3\_series\_1~(k4\_sin\_cos~(k17\_complex1~\\
X0)))~X2)~(k8\_nat\_1~k1\_numbers~(k3\_series\_1~(k4\_sin\_cos~(k17\_complex1~\\
X0)))~X1))=k9\_real\_1~(k8\_nat\_1~k1\_numbers~(k3\_series\_1~(k4\_sin\_cos~\\
(k17\_complex1~X0)))~X2)~(k8\_nat\_1~k1\_numbers~(k3\_series\_1~(k4\_sin\_cos~\\
(k17\_complex1~X0)))~X1))))))\end{array}$$
\end{theorem}
\end{document}
