\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{t29\_heyting3 (TMSTNNDFRcCxkRbu28FVCVNFpXbfLHFJmyw)}
\maketitle
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ 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 $ v1\_finset\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_tarski : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k2\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ g1\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v10\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_finsub\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v4\_finsub\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v8\_relat\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k3\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_substlat : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k3\_lattice3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_orders\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((X0 \in X1){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X2))){\unicdbdjdcd}(m1\_subset\_1~X0~X2)\end{array}
\label{hyp:ehedpfdhfhcgdhfgeh}
\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 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~X1){\unicdbdjdcd}((v1\_xboole\_0~X1){\unicdcdcdid}\\
(X0 \in X1))\end{array}
\label{hyp:ehcdpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((X3 \in k1\_substlat~\\
X0~X1){\unicdcdcdhd}(X2 \in X3)){\unicdbdjdcd}((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finset\_1~\\
X2)))\end{array}
\label{hyp:ehbdpfigfgjhehjgoghgcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  r1\_tarski~(k4\_partfun1~X0~X1)~(k9\_setfam\_1~\\
(k2\_zfmisc\_1~X0~X1))\end{array}
\label{hyp:ehbdgdpfahchfgpfahpgmgjh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{{k9\_setfam\_1}~{X0}}={{k1\_zfmisc\_1}~{X0}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfgehggbgngpfbd}
\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 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_substlat~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_substlat~X0~X1))){\unicdbdjdcd}(k2\_substlat~\\
X0~X1~X2~X2=X2)\end{array}
\label{hyp:jgegfgngahpgehfgogdgfgpflgcdpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (g1\_orders\_2~X0~X1=g1\_orders\_2~\\
X2~X3){\unicdbdjdcd}((X0=X2){\unicdcdcdhd}(X1=X3)))\end{array}
\label{hyp:ggchfgfgpfhgbdpfpgchegfgchdhpfcd}
\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 .  (v3\_lattices~(k5\_substlat~X0~X1)){\unicdcdcdhd}(v10\_lattices~\\
(k5\_substlat~X0~X1))\end{array}
\label{hyp:ggdgddpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v2\_struct\_0~(k5\_substlat~X0~X1)){\unicdcdcdhd}(v3\_lattices~\\
(k5\_substlat~X0~X1))\end{array}
\label{hyp:ggdgcdpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~(k5\_finsub\_1~X0)){\unicdcdcdhd}(v4\_finsub\_1~(k5\_finsub\_1~\\
X0))\end{array}
\label{hyp:ggdgcdpfggjgogdhfhcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k1\_substlat}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgbdpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k4\_partfun1}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v3\_lattices~(k5\_substlat~X0~X1)){\unicdcdcdhd}(l3\_lattices~\\
(k5\_substlat~X0~X1))\end{array}
\label{hyp:egehpflgfdpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{v4\_finsub\_1}~{({{k5\_finsub\_1}~{X0}})}}}\label{hyp:egehpflgfdpfggjgogdhfhcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_substlat~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_substlat~X0~X1))){\unicdbdjdcd}(m1\_subset\_1~\\
(k2\_substlat~X0~X1~X2~X3)~(k5\_finsub\_1~(k4\_partfun1~X0~X1)))\end{array}
\label{hyp:egehpflgcdpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}((v1\_partfun1~(k2\_lattice3~X0)~(u1\_struct\_0~X0)){\unicdcdcdhd}((v1\_relat\_2~\\
(k2\_lattice3~X0)){\unicdcdcdhd}((v4\_relat\_2~(k2\_lattice3~X0)){\unicdcdcdhd}((v8\_relat\_2~\\
(k2\_lattice3~X0)){\unicdcdcdhd}(m1\_subset\_1~(k2\_lattice3~X0)~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X0))))))))\end{array}
\label{hyp:egehpflgcdpfmgbgehehjgdgfgdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0))){\unicdbdjdcd}((v1\_orders\_2~(g1\_orders\_2~X0~X1)){\unicdcdcdhd}(l1\_orders\_2~(g1\_orders\_2~\\
X0~X1)))\end{array}
\label{hyp:egehpfhgbdpfpgchegfgchdhpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v4\_finsub\_1~X1){\unicdbdjdcd}((X1=k5\_finsub\_1~X0){\unicdbdjded}\\
({\unicdcdadad} X2 .  (X2 \in X1){\unicdbdjded}((r1\_tarski~X2~X0){\unicdcdcdhd}(v1\_finset\_1~X2))))\end{array}
\label{hyp:egfdpfggjgogdhfhcgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v3\_lattices~X2){\unicdcdcdhd}(l3\_lattices~\\
X2)){\unicdbdjdcd}((X2=k5\_substlat~X0~X1){\unicdbdjded}((u1\_struct\_0~X2=k1\_substlat~X0~\\
X1){\unicdcdcdhd}({\unicdcdadad} X3 .  (m2\_subset\_1~X3~(k5\_finsub\_1~(k4\_partfun1~X0~\\
X1))~(k1\_substlat~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_subset\_1~X4~(k5\_finsub\_1~\\
(k4\_partfun1~X0~X1))~(k1\_substlat~X0~X1)){\unicdbdjdcd}((k1\_binop\_1~(u2\_lattices~\\
X2)~X3~X4=k3\_substlat~X0~X1~(k2\_substlat~X0~X1~X3~X4)){\unicdcdcdhd}(k1\_binop\_1~\\
(u1\_lattices~X2)~X3~X4=k3\_substlat~X0~X1~(k4\_substlat~X0~X1~X3~X4)))))))\end{array}
\label{hyp:egedpfdhfhcgdhehmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_lattices~X0){\unicdcdcdhd}(l3\_lattices~\\
X0))){\unicdbdjdcd}(k3\_lattice3~X0=g1\_orders\_2~(u1\_struct\_0~X0)~(k2\_lattice3~\\
X0))\end{array}
\label{hyp:egcdpfmgbgehehjgdgfgdd}
\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 .  (l1\_orders\_2~X0){\unicdbdjdcd}((v1\_orders\_2~X0){\unicdbdjdcd}(X0=g1\_orders\_2~\\
(u1\_struct\_0~X0)~(u1\_orders\_2~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghbdpfpgchegfgchdhpfcd}
\end{equation}
\begin{theorem}\label{thm:ehcdjdpfigfgjhehjgoghgdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  \\
{\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(k1\_heyting3~X1~(k6\_domain\_1~\\
k5\_numbers~X0)))){\unicdbdjdcd}((X2 \in X3){\unicdbdjdcd}((v1\_finset\_1~X2){\unicdcdcdhd}(m1\_subset\_1~\\
X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X1~(k6\_domain\_1~k5\_numbers~X0)))))))\end{array}$$
\end{theorem}
\end{document}
