\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{l25\_waybel30 (TMZpiJS8uNQqkgr3gTbx6UddpA9PS9BEMtS)}
\maketitle
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k13\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X2 \in X0){\unicdcdcdhd}(X3 \in X1)){\unicdbdjdcd}\\
(k1\_binop\_1~(k13\_funct\_3~(k10\_funct\_3~X0~X1)~(k9\_funct\_3~X0~X1))~\\
X2~X3=k4\_tarski~X3~X2)\end{array}
\label{hyp:mgbdpfjhfgmgmgpghhbdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~(k13\_funct\_3~(k10\_funct\_3~\\
X0~X1)~(k9\_funct\_3~X0~X1))){\unicdcdcdhd}((v1\_funct\_1~(k13\_funct\_3~(k10\_funct\_3~\\
X0~X1)~(k9\_funct\_3~X0~X1))){\unicdcdcdhd}(v2\_funct\_1~(k13\_funct\_3~(k10\_funct\_3~\\
X0~X1)~(k9\_funct\_3~X0~X1))))\end{array}
\label{hyp:ggdgcdpfjhfgmgmgpghhbdcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
k1\_binop\_1~X0~X1~X2=k1\_funct\_1~X0~(k4\_tarski~X1~X2))\end{array}
\label{hyp:egbdpfcgjgogpgahpfbd}
\end{equation}
\begin{theorem}\label{thm:mgcdfdpfhhbgjhcgfgmgddad}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X2 \in X0){\unicdcdcdhd}(X3 \in X1)){\unicdbdjdcd}\\
(k1\_funct\_1~(k13\_funct\_3~(k10\_funct\_3~X0~X1)~(k9\_funct\_3~X0~X1))~\\
(k4\_tarski~X2~X3)=k4\_tarski~X3~X2)\end{array}$$
\end{theorem}
\end{document}
