\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{t84\_rfunct\_1 (TMUhWPZ26JdK2Xi4pVmvgM3NYw2pPXRpYia)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v3\_valued\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_comseq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k18\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k3\_xboole\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k45\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_valued\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v2\_seq\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k54\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k30\_valued\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_valued\_0 : {{\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){\unicdcdcdhd}(v3\_valued\_0~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v3\_valued\_0~X3))){\unicdbdjdcd}((((v1\_seq\_2~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}(v1\_seq\_2~\\
(k5\_relat\_1~X3~X1))){\unicdbdjdcd}(v1\_seq\_2~(k5\_relat\_1~(k1\_valued\_1~X2~X3)~\\
(k3\_xboole\_0~X0~X1)))){\unicdcdcdhd}((((v2\_seq\_2~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}(v2\_seq\_2~\\
(k5\_relat\_1~X3~X1))){\unicdbdjdcd}(v2\_seq\_2~(k5\_relat\_1~(k1\_valued\_1~X2~X3)~\\
(k3\_xboole\_0~X0~X1)))){\unicdcdcdhd}(((v1\_comseq\_2~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}(v1\_comseq\_2~\\
(k5\_relat\_1~X3~X1))){\unicdbdjdcd}(v1\_comseq\_2~(k5\_relat\_1~(k1\_valued\_1~X2~\\
X3)~(k3\_xboole\_0~X0~X1)))))))\end{array}
\label{hyp:ehidddpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v3\_valued\_0~\\
X1))){\unicdbdjdcd}((v1\_comseq\_2~(k5\_relat\_1~X1~X0)){\unicdbdjdcd}((v1\_comseq\_2~(k5\_relat\_1~\\
(k54\_valued\_1~X1)~X0)){\unicdcdcdhd}(v1\_comseq\_2~(k5\_relat\_1~(k30\_valued\_1~\\
X1)~X0))))\end{array}
\label{hyp:ehidcdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (v1\_relat\_1~X2){\unicdbdjdcd}(k5\_relat\_1~\\
(k5\_relat\_1~X2~X0)~X1=k5\_relat\_1~X2~(k3\_xboole\_0~X0~X1))\end{array}
\label{hyp:ehhdbdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~X2){\unicdcdcdhd}(v1\_valued\_0~\\
X2))){\unicdbdjdcd}((k5\_relat\_1~(k18\_valued\_1~X1~X2)~X0=k18\_valued\_1~(k5\_relat\_1~\\
X1~X0)~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}((k5\_relat\_1~(k18\_valued\_1~X1~X2)~X0=\\
k18\_valued\_1~(k5\_relat\_1~X1~X0)~X2){\unicdcdcdhd}(k5\_relat\_1~(k18\_valued\_1~\\
X1~X2)~X0=k18\_valued\_1~X1~(k5\_relat\_1~X2~X0)))))\end{array}
\label{hyp:ehedfdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v1\_funct\_1~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
(k5\_relat\_1~X0~X1)){\unicdcdcdhd}(v1\_funct\_1~(k5\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgidpfggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v3\_valued\_0~X0))){\unicdbdjdcd}\\
((v1\_relat\_1~(k30\_valued\_1~X0)){\unicdcdcdhd}((v1\_funct\_1~(k30\_valued\_1~\\
X0)){\unicdcdcdhd}((v1\_valued\_0~(k30\_valued\_1~X0)){\unicdcdcdhd}(v3\_valued\_0~(k30\_valued\_1~\\
X0)))))\end{array}
\label{hyp:ggdgfdgdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v3\_valued\_0~X0)){\unicdbdjdcd}((\\
v1\_relat\_1~(k5\_relat\_1~X0~X1)){\unicdcdcdhd}(v3\_valued\_0~(k5\_relat\_1~X0~X1)))\end{array}
\label{hyp:ggdgedfdpfghbgmgfhfgegpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}((\\
v3\_valued\_0~X0){\unicdcdcdhd}(v1\_comseq\_2~X0)))){\unicdcdcdhd}((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~\\
X1){\unicdcdcdhd}((v3\_valued\_0~X1){\unicdcdcdhd}(v1\_comseq\_2~X1))))){\unicdbdjdcd}((v1\_relat\_1~(k18\_valued\_1~\\
X0~X1)){\unicdcdcdhd}((v1\_funct\_1~(k18\_valued\_1~X0~X1)){\unicdcdcdhd}((v3\_valued\_0~(k18\_valued\_1~\\
X0~X1)){\unicdcdcdhd}(v1\_comseq\_2~(k18\_valued\_1~X0~X1)))))\end{array}
\label{hyp:ggdgbdhdpfchggfhogdgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (v1\_relat\_1~X0){\unicdbdjdcd}(v1\_relat\_1~(k5\_relat\_1~\\
X0~X1))\end{array}
\label{hyp:egehpflgfdpfchfgmgbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v1\_funct\_1~X0){\unicdcdcdhd}(v1\_valued\_0~X0))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}((v1\_funct\_1~X1){\unicdcdcdhd}(v1\_valued\_0~\\
X1))){\unicdbdjdcd}(k45\_valued\_1~X0~X1=k1\_valued\_1~X0~(k30\_valued\_1~X1)))\end{array}
\label{hyp:egjdpfghbgmgfhfgegpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}(v3\_valued\_0~X0)){\unicdbdjdcd}((v1\_relat\_1~\\
X0){\unicdcdcdhd}(v1\_valued\_0~X0))\end{array}
\label{hyp:dgdggdpfghbgmgfhfgegpfad}
\end{equation}
\begin{theorem}\label{thm:ehidedpfchggfhogdgehpfbd}
$$\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v1\_funct\_1~\\
X2){\unicdcdcdhd}(v3\_valued\_0~X2))){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_relat\_1~X3){\unicdcdcdhd}((v1\_funct\_1~\\
X3){\unicdcdcdhd}(v3\_valued\_0~X3))){\unicdbdjdcd}(((v1\_comseq\_2~(k5\_relat\_1~X2~X0)){\unicdcdcdhd}(\\
v1\_comseq\_2~(k5\_relat\_1~X3~X1))){\unicdbdjdcd}((v1\_comseq\_2~(k5\_relat\_1~(\\
k18\_valued\_1~X2~X3)~(k3\_xboole\_0~X0~X1))){\unicdcdcdhd}(v1\_comseq\_2~(k5\_relat\_1~\\
(k45\_valued\_1~X2~X3)~(k3\_xboole\_0~X0~X1))))))\end{array}$$
\end{theorem}
\end{document}
