\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{t18\_heyting1 (TMMF2YumXwN5WK1bub699w2DU9wqT5pY4nW)}
\maketitle
Let $ m1\_subset\_1 : {{\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 $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k7\_heyting1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k8\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_normform : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_funcop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_heyting1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_funct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k8\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k8\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgidpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  m1\_subset\_1~(k7\_normform~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)))\end{array}
\label{hyp:egehpflghdpfogpgchngggpgchng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}(k7\_heyting1~X0~X1~X2=k8\_subset\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)~(ReplSep~(toset~({\uniddcgcg} X3 : \\
\iota .  m2\_funct\_2~X3~(k7\_normform~X0)~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))~(k9\_funct\_2~(k7\_normform~X0)~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)))))~({\uniddcgcg} X3 : \iota .  r1\_tarski~\\
(k8\_setwiseo~(k7\_normform~X0)~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(\\
k5\_finsub\_1~X0))~X3~X1)~X2)~({\uniddcgcg} X3 : \iota .  k6\_normform~(k7\_normform~\\
X0)~X0~X1~(k6\_funcop\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0))~(k7\_normform~X0)~(k5\_heyting1~X0)~X3~(k6\_funct\_3~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)))))))\end{array}
\label{hyp:eghdpfigfgjhehjgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (X2=k3\_xboole\_0~X0~X1){\unicdbdjded}({\unicdcdadad} X3 .  \\
(X3 \in X2){\unicdbdjded}((X3 \in X0){\unicdcdcdhd}(X3 \in X1)))\end{array}
\label{hyp:egedpfihcgpgpgmgfgpfad}
\end{equation}
\begin{theorem}\label{thm:ehbdidpfigfgjhehjgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)){\unicdbdjdcd}(\preoh (X3 \in k7\_heyting1~X0~\\
X1~X2){\unicdcdcdhd}({\unicdcdadad} X4 .  (m2\_funct\_2~X4~(k7\_normform~X0)~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k9\_funct\_2~(k7\_normform~X0)~\\
(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)))){\unicdbdjdcd}(\preoh (r1\_tarski~\\
(k8\_setwiseo~(k7\_normform~X0)~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(\\
k5\_finsub\_1~X0))~X4~X1)~X2){\unicdcdcdhd}(X3=k6\_normform~(k7\_normform~X0)~X0~\\
X1~(k6\_funcop\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~\\
(k7\_normform~X0)~(k5\_heyting1~X0)~X4~(k6\_funct\_3~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)))))))))\end{array}$$
\end{theorem}
\end{document}
