\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{t38\_heyting3 (TMYjUDcinPNUJj2yYxS9Wfjskvqgxg6RC9W)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_heyting3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{r1\_tarski}~{X0}}~{k1\_xboole\_0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehddpfihcgpgpgmgfgpfbd}
\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~(u1\_struct\_0~(k1\_heyting3~k5\_numbers~(k6\_domain\_1~k5\_numbers~\\
X0)))){\unicdbdjdcd}((k1\_xboole\_0 \in X1){\unicdbdjdcd}(X1=k1\_tarski~k1\_xboole\_0)))\end{array}
\label{hyp:ehddcdpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~\\
(k1\_heyting3~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~\\
(k1\_heyting3~X0~X1))){\unicdbdjdcd}((r3\_orders\_2~(k1\_heyting3~X0~X1)~X2~X3){\unicdbdjded}\\
({\unicdcdadad} X4 .  \preoh (X4 \in X2){\unicdcdcdhd}({\unicdcdadad} X5 .  \preoh (X5 \in X3){\unicdcdcdhd}(r1\_tarski~X5~X4)))))\end{array}
\label{hyp:ehbdcdpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
{{k1\_xboole\_0} \in {{k1\_tarski}~{k1\_xboole\_0}}}\label{hyp:mgedpfbgihjgpgngdh}
\end{equation}
\begin{theorem}\label{thm:ehddidpfigfgjhehjgoghgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~\\
X1~(u1\_struct\_0~(k1\_heyting3~k5\_numbers~(k6\_domain\_1~k5\_numbers~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(k1\_heyting3~\\
k5\_numbers~(k6\_domain\_1~k5\_numbers~X0)))){\unicdbdjdcd}(((r3\_orders\_2~(k1\_heyting3~\\
k5\_numbers~(k6\_domain\_1~k5\_numbers~X0))~X1~X2){\unicdcdcdhd}(X1=k1\_tarski~\\
k1\_xboole\_0)){\unicdbdjdcd}(X2=k1\_tarski~k1\_xboole\_0))))\end{array}$$
\end{theorem}
\end{document}
