\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{t34\_heyting3 (TMZ5FkNdKyihjqRVuzNkp9wmW1475WUXy77)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ 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 $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ k1\_heyting2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k3\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_finset\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k5\_finsub\_1~(k4\_partfun1~X0~X1))){\unicdbdjdcd}(r1\_tarski~(k1\_heyting2~\\
X0~X1~X2)~X0))\end{array}
\label{hyp:ehgdpfigfgjhehjgoghgcd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~(k1\_heyting3~k5\_numbers~(k6\_domain\_1~\\
k5\_numbers~X0))))){\unicdbdjdcd}(\preoh (X1{\unicdcdgdad}k1\_tarski~k1\_xboole\_0){\unicdcdcdhd}({\unicdcdadad} X2 .  \\
((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finset\_1~X2))){\unicdbdjdcd}(\preoh (X2 \in \\
X1){\unicdcdcdhd}(X2{\unicdcdgdad}k1\_xboole\_0)))))\end{array}
\label{hyp:ehddddpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~X1~X0)){\unicdbdjdcd}\\
(k6\_domain\_1~X0~X1=k1\_tarski~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfegpgngbgjgogpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(v1\_relat\_1~X0)){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
(k9\_xtuple\_0~X0))\end{array}
\label{hyp:ggdgidpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_finset\_1~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k5\_finsub\_1~(k4\_partfun1~X0~X1)))){\unicdbdjdcd}(v1\_finset\_1~(k1\_heyting2~\\
X0~X1~X2))\end{array}
\label{hyp:ggdgbdpfigfgjhehjgoghgcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v1\_finset\_1}~{({{k1\_tarski}~{X0}})}}}\label{hyp:ggdgbdpfggjgogdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjded}{({{\unicdcdadad} X1 .  {\preoh{{{X1} \in {X0}}}}})}}}\label{hyp:egbdpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  k1\_heyting3~X0~X1=k3\_lattice3~(k5\_substlat~\\
X0~X1)\end{array}
\label{hyp:egbdpfigfgjhehjgoghgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_finset\_1~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~(k5\_finsub\_1~(k4\_partfun1~X0~X1))){\unicdbdjdcd}({\unicdcdadad} X3 .  (X3=k1\_heyting2~\\
X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  (X4 \in X3){\unicdbdjded}({\unicdcdaddd} X5 .  ((v1\_relat\_1~X5){\unicdcdcdhd}(\\
(v1\_funct\_1~X5){\unicdcdcdhd}(v1\_finset\_1~X5))){\unicdcdcdhd}((X5 \in X2){\unicdcdcdhd}(X4 \in k9\_xtuple\_0~\\
X5))))))\end{array}
\label{hyp:egbdpfigfgjhehjgoghgcd}
\end{equation}
\begin{theorem}\label{thm:ehddedpfigfgjhehjgoghgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~(k1\_heyting3~k5\_numbers~(k6\_domain\_1~\\
k5\_numbers~X0))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k5\_finsub\_1~\\
(k4\_partfun1~k5\_numbers~(k6\_domain\_1~k5\_numbers~X0)))){\unicdbdjdcd}((X1=\\
X2){\unicdbdjdcd}((X1=k1\_tarski~k1\_xboole\_0){\unicdcdcdid}((\preoh v1\_xboole\_0~(k1\_heyting2~\\
k5\_numbers~(k6\_domain\_1~k5\_numbers~X0)~X2)){\unicdcdcdhd}((v1\_finset\_1~(k1\_heyting2~\\
k5\_numbers~(k6\_domain\_1~k5\_numbers~X0)~X2)){\unicdcdcdhd}(m1\_subset\_1~(k1\_heyting2~\\
k5\_numbers~(k6\_domain\_1~k5\_numbers~X0)~X2)~(k1\_zfmisc\_1~k5\_numbers))))))))\end{array}$$
\end{theorem}
\end{document}
