\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{t11\_heyting1 (TMK1ZviBtS14KxMQ3hW5LyFw7Z8jCCwVpz7)}
\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 $ k6\_heyting1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_heyting1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k5\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k3\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_tarski : {{\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.
Let $ k2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\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}(k6\_heyting1~X0~X1=k8\_subset\_1~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)~(ReplSep~(toset~({\uniddcgcg} X2 : \\
\iota .  m2\_funct\_2~X2~(k7\_normform~X0)~(k1\_heyting1~X0)~(k9\_funct\_2~\\
(k7\_normform~X0)~(k1\_heyting1~X0))))~({\uniddcgcg} X2 : \iota .  {\unicdcdadad} X3 .  \\
(m2\_subset\_1~X3~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~\\
(k7\_normform~X0)){\unicdbdjdcd}((X3 \in X1){\unicdbdjdcd}(k3\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~\\
X0)~X2~X3 \in k5\_setwiseo~X0~(k2\_domain\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0)~X3)~(k3\_domain\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)~X3))))~(\\
{\uniddcgcg} X2 : \iota .  k4\_tarski~(ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m2\_subset\_1~\\
X3~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k7\_normform~\\
X0)))~({\uniddcgcg} X3 : \iota .  (k3\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~\\
X0)~X2~X3 \in k3\_domain\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)~X3){\unicdcdcdhd}(X3 \in \\
X1))~({\uniddcgcg} X3 : \iota .  k3\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~X0)~\\
X2~X3))~(ReplSep~(toset~({\uniddcgcg} X3 : \iota .  m2\_subset\_1~X3~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)))~({\uniddcgcg} X3 : \\
\iota .  (k3\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~X0)~X2~X3 \in k2\_domain\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)~X3){\unicdcdcdhd}(X3 \in X1))~({\uniddcgcg} X3 : \iota .  k3\_funct\_2~\\
(k7\_normform~X0)~(k1\_heyting1~X0)~X2~X3)))))\end{array}
\label{hyp:eggdpfigfgjhehjgoghgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k4\_tarski~X0~X1=k2\_tarski~(k2\_tarski~X0~\\
X1)~(k1\_tarski~X0)\end{array}
\label{hyp:egfdpfehbgchdhlgjg}
\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}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k2\_tarski}~{X0}}~{X1}}={{{k2\_tarski}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgcdpfehbgchdhlgjg}
\end{equation}
\begin{theorem}\label{thm:ehbdbdpfigfgjhehjgoghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k5\_finsub\_1~(k7\_normform~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~X2~(k2\_zfmisc\_1~(k5\_finsub\_1~\\
X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)){\unicdbdjdcd}(\preoh (X2 \in k6\_heyting1~X0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~(k7\_normform~X0)~(k1\_heyting1~\\
X0)~(k9\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~X0))){\unicdbdjdcd}(\preoh ({\unicdcdadad} X4 .  \\
(m2\_subset\_1~X4~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~\\
(k7\_normform~X0)){\unicdbdjdcd}((X4 \in X1){\unicdbdjdcd}(k3\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~\\
X0)~X3~X4 \in k5\_setwiseo~X0~(k2\_domain\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0)~X4)~(k3\_domain\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)~X4)))){\unicdcdcdhd}\\
(X2=k4\_tarski~(ReplSep~(toset~({\uniddcgcg} X4 : \iota .  m2\_subset\_1~X4~(k2\_zfmisc\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0))~(k7\_normform~X0)))~({\uniddcgcg} X4 : \\
\iota .  (k3\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~X0)~X3~X4 \in k3\_domain\_1~\\
(k5\_finsub\_1~X0)~(k5\_finsub\_1~X0)~X4){\unicdcdcdhd}(X4 \in X1))~({\uniddcgcg} X4 : \iota .  k3\_funct\_2~\\
(k7\_normform~X0)~(k1\_heyting1~X0)~X3~X4))~(ReplSep~(toset~({\uniddcgcg} X4 : \\
\iota .  m2\_subset\_1~X4~(k2\_zfmisc\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0))~(k7\_normform~X0)))~({\uniddcgcg} X4 : \iota .  (k3\_funct\_2~(k7\_normform~\\
X0)~(k1\_heyting1~X0)~X3~X4 \in k2\_domain\_1~(k5\_finsub\_1~X0)~(k5\_finsub\_1~\\
X0)~X4){\unicdcdcdhd}(X4 \in X1))~({\uniddcgcg} X4 : \iota .  k3\_funct\_2~(k7\_normform~X0)~(k1\_heyting1~\\
X0)~X3~X4)))))))\end{array}$$
\end{theorem}
\end{document}
