\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{l35\_real\_lat (TMJv7hrLJ9gkgUwvfrfvDeuquX1DUom6hnC)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ g3\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k4\_real\_lat : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_real\_lat : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_lattices : {{\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 $ r2\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funcsdom : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ 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 $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k1\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l3\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_lattices : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ u1\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ u2\_lattices : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_funct\_2~X1~X0~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_funct\_2~X2~X0~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~k1\_numbers~\\
(k9\_funct\_2~X0~k1\_numbers)){\unicdbdjdcd}(r2\_funct\_2~X0~k1\_numbers~(k1\_funcsdom~\\
X0~k1\_numbers~(k5\_real\_lat~X0)~(k1\_funcsdom~X0~k1\_numbers~(k5\_real\_lat~\\
X0)~X1~X2)~X3)~(k1\_funcsdom~X0~k1\_numbers~(k5\_real\_lat~X0)~X1~(k1\_funcsdom~\\
X0~k1\_numbers~(k5\_real\_lat~X0)~X2~X3))))))\end{array}
\label{hyp:ehbdbdpfchfgbgmgpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X2){\unicdcdcdhd}\\
((v1\_funct\_2~X2~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))){\unicdbdjdcd}((r2\_funct\_2~X0~X1~X2~\\
X3){\unicdbdjded}(X2=X3))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjded}(m1\_subset\_1~X3~\\
X2))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  (((v1\_funct\_1~X1){\unicdcdcdhd}\\
((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((m1\_subset\_1~X2~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X3~X0))){\unicdbdjdcd}(k5\_binop\_1~X0~X1~X2~X3=k1\_binop\_1~X1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfcgjgogpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  ((\preoh v1\_xboole\_0~\\
X1){\unicdcdcdhd}(((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~(k9\_funct\_2~\\
X0~X1)~(k9\_funct\_2~X0~X1))~(k9\_funct\_2~X0~X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(\\
k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_funct\_2~X0~X1)~(k9\_funct\_2~\\
X0~X1))~(k9\_funct\_2~X0~X1)))))){\unicdcdcdhd}((m1\_subset\_1~X3~(k9\_funct\_2~X0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X4~(k9\_funct\_2~X0~X1))))){\unicdbdjdcd}(k1\_funcsdom~X0~X1~\\
X2~X3~X4=k1\_binop\_1~X2~X3~X4)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfggfhogdgdhegpgng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  {\unicdcdadad} X4 .  {\unicdcdadad} X5 .  \\
(g3\_lattices~X0~X1~X2=g3\_lattices~X3~X4~X5){\unicdbdjdcd}((X0=X3){\unicdcdcdhd}((X1=X4){\unicdcdcdhd}\\
(X2=X5))))\end{array}
\label{hyp:ggchfgfgpfhgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((\\
v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(g3\_lattices~\\
X0~X1~X2)){\unicdcdcdhd}(v3\_lattices~(g3\_lattices~X0~X1~X2)))\end{array}
\label{hyp:ggdgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}(m1\_funct\_2~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_funct\_2~X3~X0~X1~X2){\unicdbdjdcd}((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X1))))))\end{array}
\label{hyp:egehpfngcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_funct\_2~X2~X0~X1){\unicdbdjdcd}(\preoh v1\_xboole\_0~\\
X2)\end{array}
\label{hyp:egehpfngbdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l3\_lattices}~{X0}})}{\unicdbdjdcd}{({{({{l1\_lattices}~{X0}})}{\unicdcdcdhd}{({{l2\_lattices}~{X0}})}})}}}\label{hyp:egehpfmgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}(m1\_funct\_2~(k9\_funct\_2~\\
X0~X1)~X0~X1)\end{array}
\label{hyp:egehpflgjdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k5\_real\_lat~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k5\_real\_lat~X0)~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k1\_numbers)~\\
(k9\_funct\_2~X0~k1\_numbers))~(k9\_funct\_2~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
(k5\_real\_lat~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_funct\_2~\\
X0~k1\_numbers)~(k9\_funct\_2~X0~k1\_numbers))~(k9\_funct\_2~X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgfdpfchfgbgmgpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k4\_real\_lat~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k4\_real\_lat~X0)~(k2\_zfmisc\_1~(k9\_funct\_2~X0~k1\_numbers)~\\
(k9\_funct\_2~X0~k1\_numbers))~(k9\_funct\_2~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
(k4\_real\_lat~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_funct\_2~\\
X0~k1\_numbers)~(k9\_funct\_2~X0~k1\_numbers))~(k9\_funct\_2~X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgedpfchfgbgmgpfmgbgeh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lattices~\\
X0)){\unicdcdcdhd}((m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdcdcdhd}(m1\_subset\_1~X2~(u1\_struct\_0~\\
X0)))){\unicdbdjdcd}(m1\_subset\_1~(k2\_lattices~X0~X1~X2)~(u1\_struct\_0~X0))\end{array}
\label{hyp:egehpflgcdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~\\
X1~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~\\
(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X0)~X0)))))){\unicdbdjdcd}((v3\_lattices~(g3\_lattices~X0~X1~\\
X2)){\unicdcdcdhd}(l3\_lattices~(g3\_lattices~X0~X1~X2)))\end{array}
\label{hyp:egehpfhgddpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}(l1\_lattices~X0)){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m1\_subset\_1~X1~(u1\_struct\_0~X0)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~\\
(u1\_struct\_0~X0)){\unicdbdjdcd}(k2\_lattices~X0~X1~X2=k5\_binop\_1~(u1\_struct\_0~\\
X0)~(u1\_lattices~X0)~X1~X2)))\end{array}
\label{hyp:egcdpfmgbgehehjgdgfgdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (l3\_lattices~X0){\unicdbdjdcd}((v3\_lattices~X0){\unicdbdjdcd}(X0=g3\_lattices~\\
(u1\_struct\_0~X0)~(u2\_lattices~X0)~(u1\_lattices~X0)))\end{array}
\label{hyp:bgcgdhehchbgdgehogfgdhdhpfghddpfmgbgehehjgdgfgdh}
\end{equation}
\begin{theorem}\label{thm:mgddfdpfchfgbgmgpfmgbgeh}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m1\_subset\_1~X1~(u1\_struct\_0~\\
(g3\_lattices~(k9\_funct\_2~X0~k1\_numbers)~(k4\_real\_lat~X0)~(k5\_real\_lat~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(u1\_struct\_0~(g3\_lattices~\\
(k9\_funct\_2~X0~k1\_numbers)~(k4\_real\_lat~X0)~(k5\_real\_lat~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(u1\_struct\_0~(g3\_lattices~(k9\_funct\_2~\\
X0~k1\_numbers)~(k4\_real\_lat~X0)~(k5\_real\_lat~X0)))){\unicdbdjdcd}(k2\_lattices~\\
(g3\_lattices~(k9\_funct\_2~X0~k1\_numbers)~(k4\_real\_lat~X0)~(k5\_real\_lat~\\
X0))~X1~(k2\_lattices~(g3\_lattices~(k9\_funct\_2~X0~k1\_numbers)~(\\
k4\_real\_lat~X0)~(k5\_real\_lat~X0))~X2~X3)=k2\_lattices~(g3\_lattices~\\
(k9\_funct\_2~X0~k1\_numbers)~(k4\_real\_lat~X0)~(k5\_real\_lat~X0))~\\
(k2\_lattices~(g3\_lattices~(k9\_funct\_2~X0~k1\_numbers)~(k4\_real\_lat~\\
X0)~(k5\_real\_lat~X0))~X1~X2)~X3))))\end{array}$$
\end{theorem}
\end{document}
