\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{t25\_lattice5 (TMGHookMgCMPK1mCwMfZWkiMcri8tMXp8CY)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_lattice3 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_yellow\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_orders\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_ordinal1 : {{\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 $ u1\_struct\_0 : {{\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 $ m1\_lattice5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k7\_lattice5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r2\_wellord2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r2\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v5\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_card\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_domain\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}}}}$ be given.
Let $ r3\_orders\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_lattice5 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k13\_lattice3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{r2\_wellord2}~{X0}}~{X1}})}{\unicdbdjded}{({{{r2\_tarski}~{X0}}~{X1}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfchcdpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k2\_relset\_1~X0~X1=k10\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v3\_orders\_2~\\
X1){\unicdcdcdhd}((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}\\
((v2\_lattice3~X1){\unicdcdcdhd}((v1\_yellow\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~(u1\_struct\_0~X1)))))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_lattice5~X3~X0~\\
X1~X2){\unicdbdjdcd}((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~(k4\_zfmisc\_1~X0~X0~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v5\_ordinal1~X3)))))\end{array}
\label{hyp:egehpfngbdpfmgbgehehjgdgfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (r2\_wellord2~X0~X1){\unicdbdjded}({\unicdcdaddd} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}(v1\_funct\_1~X2)){\unicdcdcdhd}((v2\_funct\_1~X2){\unicdcdcdhd}((k9\_xtuple\_0~X2=X0){\unicdcdcdhd}\\
(k10\_xtuple\_0~X2=X1))))\end{array}
\label{hyp:egedpfhhfgmgmgpgchegcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}((v1\_yellow\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((\\
v5\_relat\_1~X3~(k4\_zfmisc\_1~X0~X0~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1))){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v5\_ordinal1~X3)))){\unicdbdjdcd}((m1\_lattice5~X3~\\
X0~X1~X2){\unicdbdjded}((v1\_card\_1~(k9\_xtuple\_0~X3)){\unicdcdcdhd}((v2\_funct\_1~X3){\unicdcdcdhd}(k2\_relset\_1~\\
(k4\_zfmisc\_1~X0~X0~(u1\_struct\_0~X1)~(u1\_struct\_0~X1))~X3=ReplSep4~\\
(toset~({\uniddcgcg} X4 : \iota .  m1\_subset\_1~X4~X0))~({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \\
\iota .  m1\_subset\_1~X5~X0))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  toset~({\uniddcgcg} X6 : \\
\iota .  m1\_subset\_1~X6~(u1\_struct\_0~X1)))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  \\
{\uniddcgcg} X6 : \iota .  toset~({\uniddcgcg} X7 : \iota .  m1\_subset\_1~X7~(u1\_struct\_0~X1)))~\\
({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \iota .  {\uniddcgcg} X7 : \iota .  r3\_orders\_2~\\
X1~(k3\_lattice5~X0~X1~X2~X4~X5)~(k13\_lattice3~X1~X6~X7))~({\uniddcgcg} X4 : \iota .  \\
{\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \iota .  {\uniddcgcg} X7 : \iota .  k5\_domain\_1~X0~X0~(u1\_struct\_0~\\
X1)~(u1\_struct\_0~X1)~X4~X5~X6~X7))))))))\end{array}
\label{hyp:egbdddpfmgbgehehjgdgfgfd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}((v1\_yellow\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
(v1\_funct\_1~X2){\unicdcdcdhd}((v1\_funct\_2~X2~(k2\_zfmisc\_1~X0~X0)~(u1\_struct\_0~\\
X1)){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~\\
X0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X3 .  (v1\_card\_1~X3){\unicdbdjdcd}((X3=\\
k7\_lattice5~X0~X1~X2){\unicdbdjded}(r2\_tarski~X3~(ReplSep4~(toset~({\uniddcgcg} X4 : \iota .  \\
m1\_subset\_1~X4~X0))~({\uniddcgcg} X4 : \iota .  toset~({\uniddcgcg} X5 : \iota .  m1\_subset\_1~\\
X5~X0))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  toset~({\uniddcgcg} X6 : \iota .  m1\_subset\_1~\\
X6~(u1\_struct\_0~X1)))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \iota .  toset~\\
({\uniddcgcg} X7 : \iota .  m1\_subset\_1~X7~(u1\_struct\_0~X1)))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \\
\iota .  {\uniddcgcg} X6 : \iota .  {\uniddcgcg} X7 : \iota .  r3\_orders\_2~X1~(k3\_lattice5~X0~X1~\\
X2~X4~X5)~(k13\_lattice3~X1~X6~X7))~({\uniddcgcg} X4 : \iota .  {\uniddcgcg} X5 : \iota .  {\uniddcgcg} X6 : \\
\iota .  {\uniddcgcg} X7 : \iota .  k5\_domain\_1~X0~X0~(u1\_struct\_0~X1)~(u1\_struct\_0~\\
X1)~X4~X5~X6~X7)))))))\end{array}
\label{hyp:egbdbdpfmgbgehehjgdgfgfd}
\end{equation}
\begin{theorem}\label{thm:ehcdfdpfmgbgehehjgdgfgfd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v3\_orders\_2~X1){\unicdcdcdhd}\\
((v4\_orders\_2~X1){\unicdcdcdhd}((v5\_orders\_2~X1){\unicdcdcdhd}((v1\_lattice3~X1){\unicdcdcdhd}((v2\_lattice3~\\
X1){\unicdcdcdhd}((v1\_yellow\_0~X1){\unicdcdcdhd}(l1\_orders\_2~X1))))))){\unicdbdjdcd}({\unicdcdadad} X2 .  (\\
v3\_ordinal1~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~\\
(k2\_zfmisc\_1~X0~X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~(u1\_struct\_0~X1)))))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_lattice5~X4~X0~X1~X3){\unicdbdjdcd}((X2 \in k7\_lattice5~X0~X1~X3){\unicdbdjded}(X2 \in k9\_xtuple\_0~\\
X4))))))\end{array}$$
\end{theorem}
\end{document}
