\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{l34\_heyting3 (TMQ4gKSbzzrWvRLLg8TSa2pY8iSKgEE3CeD)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k4\_heyting3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_heyting3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_heyting3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}(v1\_finset\_1~(k3\_heyting3~X0~X1))\end{array}
\label{hyp:ggdgfdpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}(v1\_finset\_1~(k2\_heyting3~X0~X1))\end{array}
\label{hyp:ggdgedpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}(m1\_subset\_1~(k4\_heyting3~X0~X1)~(k5\_finsub\_1~\\
(k4\_partfun1~k5\_numbers~(k6\_domain\_1~k5\_numbers~X1))))\end{array}
\label{hyp:egehpflgedpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~(k4\_partfun1~\\
k5\_numbers~(k6\_domain\_1~k5\_numbers~X1)))){\unicdbdjdcd}((X2=k4\_heyting3~\\
X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  (X3 \in X2){\unicdbdjded}(\preoh ({\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~X4){\unicdcdcdhd}\\
(m1\_subset\_1~X4~k5\_numbers)){\unicdbdjdcd}(\preoh (r1\_xxreal\_0~X4~X0){\unicdcdcdhd}(X3=k2\_heyting3~\\
X4~X1))){\unicdcdcdhd}(X3{\unicdcdgdad}k3\_heyting3~X0~X1))))))\end{array}
\label{hyp:egedpfigfgjhehjgoghgdd}
\end{equation}
\begin{theorem}\label{thm:mgddedpfigfgjhehjgoghgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (X2 \in k4\_heyting3~X0~X1){\unicdbdjdcd}(v1\_finset\_1~\\
X2)))\end{array}$$
\end{theorem}
\end{document}
