\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{l14\_pdiff\_1 (TMZbJcDC5JDfPaKDQzEnTsfM45VC9iaYLVE)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_funct\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_pdiff\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k1\_euclid : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}((v1\_funct\_1~(k2\_funct\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1))){\unicdcdcdhd}((v1\_funct\_2~\\
(k2\_funct\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1))~k1\_numbers~(k1\_euclid~np\_\_1)){\unicdcdcdhd}\\
(m1\_subset\_1~(k2\_funct\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1))~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~(k1\_euclid~np\_\_1)))))){\unicdcdcdhd}((v2\_funct\_1~\\
(k2\_funct\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1))){\unicdcdcdhd}((k9\_xtuple\_0~(k2\_funct\_1~\\
(k1\_pdiff\_1~np\_\_1~np\_\_1))=k1\_numbers){\unicdcdcdhd}((k10\_xtuple\_0~(k2\_funct\_1~\\
(k1\_pdiff\_1~np\_\_1~np\_\_1))=k1\_euclid~np\_\_1){\unicdcdcdhd}({\unicdcdaddd} X0 .  ((v1\_funct\_1~\\
X0){\unicdcdcdhd}((v1\_funct\_2~X0~k1\_numbers~(k1\_euclid~np\_\_1)){\unicdcdcdhd}(m1\_subset\_1~\\
X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~(k1\_euclid~np\_\_1)))))){\unicdcdcdhd}\\
((v3\_funct\_2~X0~k1\_numbers~(k1\_euclid~np\_\_1)){\unicdcdcdhd}(k2\_funct\_1~(k1\_pdiff\_1~\\
np\_\_1~np\_\_1)=X0))))))\end{array}
\label{hyp:ehcdpfahegjgggggpfbd}
\end{equation}
\begin{theorem}\label{thm:mgbdedpfahegjgggggpfbd}
$$\begin{array}{c}(v1\_funct\_1~(k2\_funct\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1))){\unicdcdcdhd}((v1\_funct\_2~\\
(k2\_funct\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1))~k1\_numbers~(k1\_euclid~np\_\_1)){\unicdcdcdhd}\\
(m1\_subset\_1~(k2\_funct\_1~(k1\_pdiff\_1~np\_\_1~np\_\_1))~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k1\_numbers~(k1\_euclid~np\_\_1)))))\end{array}$$
\end{theorem}
\end{document}
