\documentclass{article}
\newtheorem{axiom}{Axiom}
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\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}
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\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{l101\_fomodel0 (TMcCQ2oR3ajyPEnZZyDSATiiBapfdN7rS32)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\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 $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k20\_fomodel0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k7\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_monoid\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k19\_fomodel0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k3\_finseq\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
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 .  {\unicdcdadad} X2 .  ((m1\_finseq\_1~X1~X0){\unicdcdcdhd}(m1\_finseq\_1~\\
X2~X0)){\unicdbdjdcd}(k1\_monoid\_0~X0~X1~X2=k7\_finseq\_1~X1~X2)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfngpgogpgjgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finseq\_1~X3)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v5\_relat\_1~\\
X4~X1){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~X4)))){\unicdbdjdcd}(k19\_fomodel0~X1~\\
X0~X2~(k7\_finseq\_1~X3~X4)=k1\_monoid\_0~X1~(k19\_fomodel0~X1~X0~X2~X3)~\\
(k19\_fomodel0~X1~X0~X2~X4)))))\end{array}
\label{hyp:mgjdidpfggpgngpgegfgmgad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v5\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))){\unicdcdcdhd}\\
((v1\_relat\_1~X2){\unicdcdcdhd}((v5\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_finseq\_1~\\
X2)))))){\unicdbdjdcd}((v1\_relat\_1~(k7\_finseq\_1~X1~X2)){\unicdcdcdhd}((v5\_relat\_1~(k7\_finseq\_1~\\
X1~X2)~X0){\unicdcdcdhd}((v1\_funct\_1~(k7\_finseq\_1~X1~X2)){\unicdcdcdhd}(v1\_finseq\_1~(k7\_finseq\_1~\\
X1~X2)))))\end{array}
\label{hyp:ggdgcdidpfggpgngpgegfgmgad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_finseq\_1~\\
X0))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_finseq\_1~X1)))){\unicdbdjdcd}\\
((v1\_relat\_1~(k7\_finseq\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k7\_finseq\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_finseq\_1~(k7\_finseq\_1~X0~X1))))\end{array}
\label{hyp:egehpflghdpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_subset\_1~\\
X2~X0)){\unicdbdjdcd}((v1\_funct\_1~(k20\_fomodel0~X0~X1~X2)){\unicdcdcdhd}((v1\_funct\_2~(k20\_fomodel0~\\
X0~X1~X2)~(k3\_finseq\_2~X0)~(k3\_finseq\_2~X0)){\unicdcdcdhd}(m1\_subset\_1~(k20\_fomodel0~\\
X0~X1~X2)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_finseq\_2~X0)~(k3\_finseq\_2~\\
X0))))))\end{array}
\label{hyp:egehpflgcdadpfggpgngpgegfgmgad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}\\
((m1\_subset\_1~X2~X0){\unicdcdcdhd}((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~X0){\unicdcdcdhd}((\\
v1\_funct\_1~X3){\unicdcdcdhd}(v1\_finseq\_1~X3)))))){\unicdbdjdcd}(m2\_finseq\_1~(k19\_fomodel0~\\
X0~X1~X2~X3)~X0)\end{array}
\label{hyp:egehpflgbdjdpfggpgngpgegfgmgad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}((v1\_funct\_2~X3~(k3\_finseq\_2~\\
X0)~(k3\_finseq\_2~X0)){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(k3\_finseq\_2~X0)~(k3\_finseq\_2~X0)))))){\unicdbdjdcd}((X3=k20\_fomodel0~X0~\\
X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v5\_relat\_1~X4~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X4){\unicdcdcdhd}(v1\_finseq\_1~X4)))){\unicdbdjdcd}(k1\_funct\_1~X3~X4=k19\_fomodel0~X0~X1~\\
X2~X4)))))\end{array}
\label{hyp:egcdddpfggpgngpgegfgmgad}
\end{equation}
\begin{theorem}\label{thm:mgbdadbdpfggpgngpgegfgmgad}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (\preoh v1\_xboole\_0~X1){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~\\
X2~X1){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v5\_relat\_1~X3~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_finseq\_1~X3)))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_relat\_1~X4){\unicdcdcdhd}((v5\_relat\_1~\\
X4~X1){\unicdcdcdhd}((v1\_funct\_1~X4){\unicdcdcdhd}(v1\_finseq\_1~X4)))){\unicdbdjdcd}(k1\_funct\_1~(k20\_fomodel0~\\
X1~X0~X2)~(k7\_finseq\_1~X3~X4)=k7\_finseq\_1~(k1\_funct\_1~(k20\_fomodel0~\\
X1~X0~X2)~X3)~(k1\_funct\_1~(k20\_fomodel0~X1~X0~X2)~X4)))))\end{array}$$
\end{theorem}
\end{document}
