\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=}
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\newcommand\unicdcdbdgd{\setminus}
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\newcommand\unicdcdadjd{\notin}
\newcommand\unicdbdjded{\Leftrightarrow}
\newcommand\unicdcdcdid{\lor}
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\newcommand\unicdcdaddd{\exists}
\newcommand\unicdcdidid{\not\subseteq}
\newcommand\preoh[1]{\lnot #1}
\newcommand\mname[1]{{\mathsf{#1}}}
\begin{document}
\title{t12\_heyting2 (TMd9eyqNWoKtQXgxCekySQuWYfLwG7eQMyu)}
\maketitle
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k2\_heyting2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~\\
(k4\_partfun1~X0~X1))){\unicdbdjdcd}((X2=k1\_xboole\_0){\unicdbdjdcd}(k3\_substlat~X0~X1~X2=\\
k1\_xboole\_0))\end{array}
\label{hyp:ehjdpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_finset\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~(k5\_finsub\_1~(k4\_partfun1~X0~X1))~(k1\_substlat~X0~X1)){\unicdbdjdcd}(k4\_substlat~\\
X0~X1~X2~(k2\_heyting2~X0~X1~X2)=k1\_xboole\_0))\end{array}
\label{hyp:ehjdpfigfgjhehjgoghgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{k5\_lattices}~{({{{k5\_substlat}~{X0}}~{X1}})}}={k1\_xboole\_0}}}}\label{hyp:ehcdgdpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdaddd} X1 .  (m1\_subset\_1~X1~(k5\_finsub\_1~X0)){\unicdcdcdhd}((v1\_xboole\_0~\\
X1){\unicdcdcdhd}(v1\_finset\_1~X1))\end{array}
\label{hyp:chdgbdpfdhfgehhhjgdhfgpg}
\end{equation}
\begin{theorem}\label{thm:ehbdcdpfigfgjhehjgoghgcd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_finset\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~(k5\_finsub\_1~(k4\_partfun1~X0~X1))~(k1\_substlat~X0~X1)){\unicdbdjdcd}(k3\_substlat~\\
X0~X1~(k4\_substlat~X0~X1~X2~(k2\_heyting2~X0~X1~X2))=k5\_lattices~(\\
k5\_substlat~X0~X1)))\end{array}$$
\end{theorem}
\end{document}
