\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{t40\_conlat\_1 (TMFxB87yjfFSL7LXnLyqLtT5d85XK7NDB7r)}
\maketitle
Let $ v1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v5\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v7\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ l2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k10\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k6\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k9\_setfam\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ u2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k5\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u3\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k9\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k4\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ l5\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v9\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g2\_conlat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k1\_conlat\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(u4\_struct\_0~X0))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(u4\_struct\_0~X0))){\unicdbdjdcd}((r1\_tarski~\\
X1~X2){\unicdbdjdcd}(r1\_tarski~(k3\_funct\_2~(k1\_zfmisc\_1~(u4\_struct\_0~X0))~\\
(k9\_setfam\_1~(u1\_struct\_0~X0))~(k2\_conlat\_1~X0)~X2)~(k3\_funct\_2~\\
(k1\_zfmisc\_1~(u4\_struct\_0~X0))~(k9\_setfam\_1~(u1\_struct\_0~X0))~\\
(k2\_conlat\_1~X0)~X1)))))\end{array}
\label{hyp:ehedpfdgpgogmgbgehpfbd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{{k3\_xboole\_0}~{X0}}~{X1}}={X0}})}}}}\label{hyp:ehcdidpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((u2\_conlat\_1~\\
X0~(k5\_conlat\_1~X0)=u1\_struct\_0~X0){\unicdcdcdhd}(u3\_conlat\_1~X0~(k6\_conlat\_1~\\
X0)=u4\_struct\_0~X0))\end{array}
\label{hyp:ehcdddpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r1\_tarski}~{X0}}~{X1}})}{\unicdbdjdcd}{({{{{k2\_xboole\_0}~{X0}}~{X1}}={X1}})}}}}\label{hyp:ehbdcdpfihcgpgpgmgfgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k3\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgjdpfdhfhcgdhfgehpfbd}
\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 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k2\_xboole\_0~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l5\_struct\_0~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(u3\_conlat\_1~X0~X1)~(k1\_zfmisc\_1~(u4\_struct\_0~X0)))\end{array}
\label{hyp:egehpffhddpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l5\_struct\_0~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0)){\unicdbdjdcd}\\
(m1\_subset\_1~(u2\_conlat\_1~X0~X1)~(k1\_zfmisc\_1~(u1\_struct\_0~X0)))\end{array}
\label{hyp:egehpffhcdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_conlat\_1}~{X0}})}{\unicdbdjdcd}{({{l5\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((v4\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((v7\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}((v9\_conlat\_1~(k6\_conlat\_1~X0)~X0){\unicdcdcdhd}(l2\_conlat\_1~\\
(k6\_conlat\_1~X0)~X0)))))\end{array}
\label{hyp:egehpflggdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}((v1\_funct\_1~\\
(k10\_conlat\_1~X0)){\unicdcdcdhd}((v1\_funct\_2~(k10\_conlat\_1~X0)~(k2\_zfmisc\_1~\\
(k8\_conlat\_1~X0)~(k8\_conlat\_1~X0))~(k8\_conlat\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k10\_conlat\_1~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k8\_conlat\_1~\\
X0)~(k8\_conlat\_1~X0))~(k8\_conlat\_1~X0))))))\end{array}
\label{hyp:egehpflgbdadpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~(k8\_conlat\_1~X0)~\\
(k8\_conlat\_1~X0))~(k8\_conlat\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k8\_conlat\_1~X0)~(k8\_conlat\_1~X0))~\\
(k8\_conlat\_1~X0)))))){\unicdbdjdcd}((X1=k10\_conlat\_1~X0){\unicdbdjded}({\unicdcdadad} X2 .  ((\\
v4\_conlat\_1~X2~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X2~X0){\unicdcdcdhd}((v7\_conlat\_1~X2~X0){\unicdcdcdhd}\\
(l2\_conlat\_1~X2~X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v4\_conlat\_1~X3~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~\\
X3~X0){\unicdcdcdhd}((v7\_conlat\_1~X3~X0){\unicdcdcdhd}(l2\_conlat\_1~X3~X0)))){\unicdbdjdcd}({\unicdcdaddd} X4 .  \\
(m1\_subset\_1~X4~(k1\_zfmisc\_1~(u1\_struct\_0~X0))){\unicdcdcdhd}({\unicdcdaddd} X5 .  \\
(m1\_subset\_1~X5~(k1\_zfmisc\_1~(u4\_struct\_0~X0))){\unicdcdcdhd}((k1\_binop\_1~\\
X1~X2~X3=g2\_conlat\_1~X0~X4~X5){\unicdcdcdhd}((X4=k3\_funct\_2~(k9\_setfam\_1~(u4\_struct\_0~\\
X0))~(k9\_setfam\_1~(u1\_struct\_0~X0))~(k2\_conlat\_1~X0)~(k3\_funct\_2~\\
(k1\_zfmisc\_1~(u1\_struct\_0~X0))~(k9\_setfam\_1~(u4\_struct\_0~X0))~\\
(k1\_conlat\_1~X0)~(k4\_subset\_1~(u1\_struct\_0~X0)~(u2\_conlat\_1~X0~\\
X2)~(u2\_conlat\_1~X0~X3)))){\unicdcdcdhd}(X5=k9\_subset\_1~(u4\_struct\_0~X0)~(\\
u3\_conlat\_1~X0~X2)~(u3\_conlat\_1~X0~X3))))))))))\end{array}
\label{hyp:egbdjdpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(l2\_conlat\_1~X1~X0){\unicdbdjdcd}((v7\_conlat\_1~X1~X0){\unicdbdjded}((k3\_funct\_2~(k1\_zfmisc\_1~\\
(u1\_struct\_0~X0))~(k9\_setfam\_1~(u4\_struct\_0~X0))~(k1\_conlat\_1~\\
X0)~(u2\_conlat\_1~X0~X1)=u3\_conlat\_1~X0~X1){\unicdcdcdhd}(k3\_funct\_2~(k1\_zfmisc\_1~\\
(u4\_struct\_0~X0))~(k9\_setfam\_1~(u1\_struct\_0~X0))~(k2\_conlat\_1~\\
X0)~(u3\_conlat\_1~X0~X1)=u2\_conlat\_1~X0~X1))))\end{array}
\label{hyp:egbdadpfdgpgogmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
X0)){\unicdbdjdcd}(k9\_subset\_1~X0~X1~X2=k9\_subset\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgjdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~X0))){\unicdbdjdcd}(k4\_subset\_1~X0~X1~X2=\\
k4\_subset\_1~X0~X2~X1)\end{array}
\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgedpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_xboole\_0}~{X0}}~{X1}}={{{k3\_xboole\_0}~{X1}}~{X0}}}}}\label{hyp:dgpgngngfhehbgehjgghjgehjhpflgddpfihcgpgpgmgfgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((l5\_struct\_0~X0){\unicdcdcdhd}(l2\_conlat\_1~X1~X0)){\unicdbdjdcd}\\
((v4\_conlat\_1~X1~X0){\unicdbdjdcd}(X1=g2\_conlat\_1~X0~(u2\_conlat\_1~X0~X1)~(u3\_conlat\_1~\\
X0~X1)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghedpfdgpgogmgbgehpfbd}
\end{equation}
\begin{theorem}\label{thm:ehedadpfdgpgogmgbgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v1\_conlat\_1~X0){\unicdcdcdhd}(l1\_conlat\_1~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
((v4\_conlat\_1~X1~X0){\unicdcdcdhd}((\preoh v5\_conlat\_1~X1~X0){\unicdcdcdhd}((v7\_conlat\_1~X1~X0){\unicdcdcdhd}\\
(l2\_conlat\_1~X1~X0)))){\unicdbdjdcd}(k1\_binop\_1~(k10\_conlat\_1~X0)~X1~(k6\_conlat\_1~\\
X0)=X1))\end{array}$$
\end{theorem}
\end{document}
