\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{t20\_modelc\_1 (TMTvm9GggXDu1MvbkSBv2uGeEdigr5VhtoA)}
\maketitle
Let $ v1\_modelc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ k30\_modelc\_1 : {{\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 $ k18\_modelc\_1 : {\iota}$ be given.
Let $ u3\_modelc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k48\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ r4\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}}$ be given.
Let $ k8\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v10\_modelc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l2\_modelc\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k24\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k2\_lattices : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ r3\_modelc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  ((\preoh v2\_struct\_0~X2){\unicdcdcdhd}((v10\_modelc\_1~X2){\unicdcdcdhd}(l2\_modelc\_1~\\
X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k18\_modelc\_1~\\
(u3\_modelc\_1~X2)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k18\_modelc\_1~(u3\_modelc\_1~X2)))))){\unicdbdjdcd}(k24\_modelc\_1~X2~X3~(k8\_modelc\_1~\\
X0~X1)=k2\_lattices~X2~(k24\_modelc\_1~X2~X3~X0)~(k24\_modelc\_1~X2~X3~\\
X1)))))\end{array}
\label{hyp:ehgdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
(m1\_subset\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(k1\_zfmisc\_1~(k30\_modelc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X4 .  (m1\_subset\_1~\\
X4~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X3))){\unicdbdjdcd}({\unicdcdadad} X5 .  (m1\_subset\_1~\\
X5~(u1\_struct\_0~(k48\_modelc\_1~X0~X1~X3))){\unicdbdjdcd}((r3\_modelc\_1~X0~X1~X3~\\
X2~(k2\_lattices~(k48\_modelc\_1~X0~X1~X3)~X4~X5)){\unicdbdjded}((r3\_modelc\_1~X0~\\
X1~X3~X2~X4){\unicdcdcdhd}(r3\_modelc\_1~X0~X1~X3~X2~X5))))))))\end{array}
\label{hyp:ehbdddpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{({{{m2\_finseq\_1}~{X1}}~{X0}})}{\unicdbdjded}{({{{m1\_finseq\_1}~{X1}}~{X0}})}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_modelc\_1~X0){\unicdcdcdhd}(m1\_finseq\_1~X0~k5\_numbers)){\unicdcdcdhd}\\
((v1\_modelc\_1~X1){\unicdcdcdhd}(m1\_finseq\_1~X1~k5\_numbers))){\unicdbdjdcd}(v1\_modelc\_1~\\
(k8\_modelc\_1~X0~X1))\end{array}
\label{hyp:ggdgfdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdcdcdhd}((\\
\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))))){\unicdbdjdcd}((\preoh v2\_struct\_0~(k48\_modelc\_1~X0~X1~X2)){\unicdcdcdhd}(v10\_modelc\_1~\\
(k48\_modelc\_1~X0~X1~X2)))\end{array}
\label{hyp:ggdgbdcdpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_finseq\_1~X0~k5\_numbers){\unicdcdcdhd}(m1\_finseq\_1~\\
X1~k5\_numbers)){\unicdbdjdcd}(m2\_finseq\_1~(k8\_modelc\_1~X0~X1)~k5\_numbers)\end{array}
\label{hyp:egehpflgidpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_partfun1~\\
X1~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdcdcdhd}((\\
\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))))){\unicdbdjdcd}(l2\_modelc\_1~(k48\_modelc\_1~X0~X1~X2))\end{array}
\label{hyp:egehpflgedidpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v10\_modelc\_1~\\
X0){\unicdcdcdhd}(l2\_modelc\_1~X0))){\unicdcdcdhd}(((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~k18\_modelc\_1~\\
(u3\_modelc\_1~X0)){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k18\_modelc\_1~(u3\_modelc\_1~X0)))))){\unicdcdcdhd}((v1\_modelc\_1~X2){\unicdcdcdhd}(m1\_finseq\_1~\\
X2~k5\_numbers)))){\unicdbdjdcd}(m1\_subset\_1~(k24\_modelc\_1~X0~X1~X2)~(u1\_struct\_0~\\
X0))\end{array}
\label{hyp:egehpflgcdedpfngpgegfgmgdgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_partfun1~X1~X0){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  \\
((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k30\_modelc\_1~\\
X0)))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~k18\_modelc\_1~\\
(u3\_modelc\_1~(k48\_modelc\_1~X0~X1~X2))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~k18\_modelc\_1~(u3\_modelc\_1~(k48\_modelc\_1~X0~X1~X2))))))){\unicdbdjdcd}\\
({\unicdcdadad} X4 .  (m1\_subset\_1~X4~X0){\unicdbdjdcd}({\unicdcdadad} X5 .  ((v1\_modelc\_1~X5){\unicdcdcdhd}\\
(m2\_finseq\_1~X5~k5\_numbers)){\unicdbdjdcd}((r4\_modelc\_1~X0~X1~X2~X3~X4~X5){\unicdbdjded}(\\
r3\_modelc\_1~X0~X1~X2~X4~(k24\_modelc\_1~(k48\_modelc\_1~X0~X1~X2)~X3~X5))))))))\end{array}
\label{hyp:eggdadpfngpgegfgmgdgpfbd}
\end{equation}
\begin{theorem}\label{thm:ehcdadpfngpgegfgmgdgpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_modelc\_1~X0){\unicdcdcdhd}(m2\_finseq\_1~X0~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X1 .  ((v1\_modelc\_1~X1){\unicdcdcdhd}(m2\_finseq\_1~X1~k5\_numbers)){\unicdbdjdcd}(\\
{\unicdcdadad} X2 .  (\preoh v1\_xboole\_0~X2){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_partfun1~X3~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X2~X2)))){\unicdbdjdcd}({\unicdcdadad} X4 .  \\
(m1\_subset\_1~X4~X2){\unicdbdjdcd}({\unicdcdadad} X5 .  ((\preoh v1\_xboole\_0~X5){\unicdcdcdhd}(m1\_subset\_1~\\
X5~(k1\_zfmisc\_1~(k30\_modelc\_1~X2)))){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_funct\_1~\\
X6){\unicdcdcdhd}((v1\_funct\_2~X6~k18\_modelc\_1~(u3\_modelc\_1~(k48\_modelc\_1~\\
X2~X3~X5))){\unicdcdcdhd}(m1\_subset\_1~X6~(k1\_zfmisc\_1~(k2\_zfmisc\_1~k18\_modelc\_1~\\
(u3\_modelc\_1~(k48\_modelc\_1~X2~X3~X5))))))){\unicdbdjdcd}((r4\_modelc\_1~X2~X3~\\
X5~X6~X4~(k8\_modelc\_1~X0~X1)){\unicdbdjded}((r4\_modelc\_1~X2~X3~X5~X6~X4~X0){\unicdcdcdhd}(r4\_modelc\_1~\\
X2~X3~X5~X6~X4~X1)))))))))\end{array}$$
\end{theorem}
\end{document}
