\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{t5\_heyting1 (TMJeoK23py87TjPLL2p8to2mUYV5RL3UrGq)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k12\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\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 $ k7\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_normform : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_heyting1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k10\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m2\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))~(k8\_normform~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (r1\_tarski~X2~X1){\unicdbdjdcd}(X2 \in k8\_normform~\\
X0))\end{array}
\label{hyp:ehedpfigfgjhehjgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{X0} \in {X1}})}{\unicdbdjdcd}{({{{m1\_subset\_1}~{X0}}~{X1}})}}}}\label{hyp:ehbdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k12\_normform~\\
X0))){\unicdbdjdcd}(m2\_subset\_1~(k3\_heyting1~X0~X1)~(k5\_finsub\_1~(k7\_normform~\\
X0))~(k8\_normform~X0))\end{array}
\label{hyp:egehpflgddpfigfgjhehjgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v3\_lattices~(k12\_normform~X0)){\unicdcdcdhd}(l3\_lattices~(k12\_normform~\\
X0))\end{array}
\label{hyp:egehpflgbdcdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k12\_normform~\\
X0))){\unicdbdjdcd}(k3\_heyting1~X0~X1=X1)\end{array}
\label{hyp:egddpfigfgjhehjgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v3\_lattices~X1){\unicdcdcdhd}(l3\_lattices~X1)){\unicdbdjdcd}(\\
(X1=k12\_normform~X0){\unicdbdjded}((u1\_struct\_0~X1=k8\_normform~X0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
(m2\_subset\_1~X2~(k5\_finsub\_1~(k7\_normform~X0))~(k8\_normform~X0)){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k5\_finsub\_1~(k7\_normform~X0))~(k8\_normform~\\
X0)){\unicdbdjdcd}((k1\_binop\_1~(u2\_lattices~X1)~X2~X3=k9\_normform~X0~(k5\_setwiseo~\\
(k7\_normform~X0)~X2~X3)){\unicdcdcdhd}(k1\_binop\_1~(u1\_lattices~X1)~X2~X3=k9\_normform~\\
X0~(k10\_normform~X0~X2~X3)))))))\end{array}
\label{hyp:egbdcdpfogpgchngggpgchng}
\end{equation}
\begin{theorem}\label{thm:ehfdpfigfgjhehjgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~(k12\_normform~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (r1\_tarski~X2~X1){\unicdbdjdcd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
(k12\_normform~X0))))\end{array}$$
\end{theorem}
\end{document}
