\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{t102\_sincos10 (TMXHkZAmTRmfsVAddf5jze186KYGjRPnLFc)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k7\_square\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_2 : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k10\_sincos10 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_real\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ np\_\_4 : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ k1\_seq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_fdiff\_9 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}(((r1\_xxreal\_0~(k1\_real\_1~\\
(k7\_square\_1~np\_\_2))~X0){\unicdcdcdhd}(r1\_xxreal\_0~X0~(k1\_real\_1~np\_\_1))){\unicdbdjdcd}\\
(k1\_seq\_1~k1\_fdiff\_9~(k10\_sincos10~X0)=X0))\end{array}
\label{hyp:ehjdadpfdhjgogdgpgdhbdad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(k1\_seq\_1~k1\_fdiff\_9~k6\_numbers=np\_\_1){\unicdcdcdhd}((k1\_seq\_1~k1\_fdiff\_9~\\
(k10\_real\_1~k32\_sin\_cos~np\_\_4)=k7\_square\_1~np\_\_2){\unicdcdcdhd}((k1\_seq\_1~\\
k1\_fdiff\_9~(k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos)=\\
k1\_real\_1~(k7\_square\_1~np\_\_2)){\unicdcdcdhd}(k1\_seq\_1~k1\_fdiff\_9~k32\_sin\_cos=\\
k1\_real\_1~np\_\_1)))\end{array}
\label{hyp:ehddbdpfdhjgogdgpgdhbdad}
\end{equation}
\begin{theorem}\label{thm:ehbdadcdpfdhjgogdgpgdhbdad}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k1\_numbers){\unicdbdjdcd}((((r1\_xxreal\_0~(k1\_real\_1~\\
(k7\_square\_1~np\_\_2))~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k1\_real\_1~np\_\_1)){\unicdcdcdhd}\\
(k10\_sincos10~X0=k8\_real\_1~(k10\_real\_1~np\_\_3~np\_\_4)~k32\_sin\_cos))){\unicdbdjdcd}\\
(X0=k1\_real\_1~(k7\_square\_1~np\_\_2))){\unicdcdcdhd}(((r1\_xxreal\_0~(k1\_real\_1~\\
(k7\_square\_1~np\_\_2))~X0){\unicdcdcdhd}((r1\_xxreal\_0~X0~(k1\_real\_1~np\_\_1)){\unicdcdcdhd}\\
(k10\_sincos10~X0=k32\_sin\_cos))){\unicdbdjdcd}(X0=k1\_real\_1~np\_\_1)))\end{array}$$
\end{theorem}
\end{document}
