\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{t39\_instalg1 (TMNHFn3Pj1gJnyLzB9rSp19xYevP3gQaxgZ)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m3\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_pboole : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_msafree : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}(v1\_funct\_1~\\
X2)){\unicdbdjdcd}((X0 \in X1){\unicdbdjdcd}(k1\_funct\_1~(k5\_relat\_1~X2~X1)~X0=k1\_funct\_1~X2~\\
X0))\end{array}
\label{hyp:ehedjdpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((v1\_funct\_1~X2){\unicdcdcdhd}\\
(m1\_subset\_1~X2~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(k2\_partfun1~\\
X0~X1~X2~X3=k5\_relat\_1~X2~X3)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~\\
X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0))))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m2\_pboole~X3~X0~X1~X2){\unicdbdjdcd}((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~\\
X3~X0){\unicdcdcdhd}((v1\_funct\_1~X3){\unicdcdcdhd}(v1\_partfun1~X3~X0)))))\end{array}
\label{hyp:egehpfngcdpfahcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  {\unicdcdadad} X4 .  (((v1\_relat\_1~\\
X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdcdcdhd}\\
(((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~\\
X2~X0)))){\unicdcdcdhd}((m3\_pboole~X3~X0~X1){\unicdcdcdhd}(m2\_pboole~X4~X0~X1~X2)))){\unicdbdjdcd}(m2\_pboole~\\
(k1\_msafree~X0~X1~X2~X3~X4)~X0~X3~X2)\end{array}
\label{hyp:egehpflgbdpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m3\_pboole~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_pboole~X4~X0~X1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (m2\_pboole~X5~X0~X3~X2){\unicdbdjdcd}((X5=k1\_msafree~X0~X1~X2~\\
X3~X4){\unicdbdjded}({\unicdcdadad} X6 .  (X6 \in X0){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_funct\_1~X7){\unicdcdcdhd}((v1\_funct\_2~\\
X7~(k1\_funct\_1~X1~X6)~(k1\_funct\_1~X2~X6)){\unicdcdcdhd}(m1\_subset\_1~X7~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k1\_funct\_1~X1~X6)~(k1\_funct\_1~X2~X6)))))){\unicdbdjdcd}((X7=\\
k1\_funct\_1~X4~X6){\unicdbdjdcd}(k1\_funct\_1~X5~X6=k2\_partfun1~(k1\_funct\_1~X1~\\
X6)~(k1\_funct\_1~X2~X6)~X7~(k1\_funct\_1~X3~X6))))))))))\end{array}
\label{hyp:egbdpfngdhbgggchfgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v4\_relat\_1~X3~X0){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v1\_partfun1~X3~X0)))){\unicdbdjdcd}((m2\_pboole~X3~X0~X1~X2){\unicdbdjded}({\unicdcdadad} X4 .  \\
(X4 \in X0){\unicdbdjdcd}((v1\_funct\_1~(k1\_funct\_1~X3~X4)){\unicdcdcdhd}((v1\_funct\_2~(k1\_funct\_1~\\
X3~X4)~(k1\_funct\_1~X1~X4)~(k1\_funct\_1~X2~X4)){\unicdcdcdhd}(m1\_subset\_1~(k1\_funct\_1~\\
X3~X4)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k1\_funct\_1~X1~X4)~(k1\_funct\_1~\\
X2~X4))))))))))\end{array}
\label{hyp:egbdfdpfahcgpgpgmgfg}
\end{equation}
\begin{theorem}\label{thm:ehddjdpfjgogdhehbgmghgbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v4\_relat\_1~X1~X0){\unicdcdcdhd}(\\
(v1\_funct\_1~X1){\unicdcdcdhd}(v1\_partfun1~X1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~\\
X2){\unicdcdcdhd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_partfun1~X2~X0)))){\unicdbdjdcd}\\
({\unicdcdadad} X3 .  (m3\_pboole~X3~X0~X1){\unicdbdjdcd}({\unicdcdadad} X4 .  (m2\_pboole~X4~X0~X1~\\
X2){\unicdbdjdcd}({\unicdcdadad} X5 .  (X5 \in X0){\unicdbdjdcd}({\unicdcdadad} X6 .  ((v1\_relat\_1~X6){\unicdcdcdhd}(v1\_funct\_1~\\
X6)){\unicdbdjdcd}({\unicdcdadad} X7 .  ((v1\_relat\_1~X7){\unicdcdcdhd}(v1\_funct\_1~X7)){\unicdbdjdcd}(((X6=k1\_funct\_1~\\
X4~X5){\unicdcdcdhd}(X7=k1\_funct\_1~(k1\_msafree~X0~X1~X2~X3~X4)~X5)){\unicdbdjdcd}({\unicdcdadad} X8 .  \\
(X8 \in k1\_funct\_1~X3~X5){\unicdbdjdcd}(k1\_funct\_1~X7~X8=k1\_funct\_1~X6~X8)))))))))\end{array}$$
\end{theorem}
\end{document}
