\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{t21\_rfunct\_3 (TMFmnDTuKMQgrARa6gzuaBA3bqyxJH5M7J7)}
\maketitle
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k14\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k8\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\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 $ k2\_zfmisc\_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 $ v2\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ v1\_setwiseo : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ r1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k3\_finseq\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_finsop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ k5\_binop\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k13\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ m1\_finseq\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k4\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ m1\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ m2\_rfunct\_3 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~X0){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~X0){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_funct\_1~X3){\unicdcdcdhd}\\
((v1\_funct\_2~X3~(k2\_zfmisc\_1~X0~X0)~X0){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(k2\_zfmisc\_1~X0~X0)~X0))))){\unicdbdjdcd}((v2\_binop\_1~X3~X0){\unicdbdjdcd}\\
(((\preoh v1\_setwiseo~X3~X0){\unicdcdcdhd}(\preoh (r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X1)){\unicdcdcdhd}\\
(r1\_xxreal\_0~np\_\_1~(k3\_finseq\_1~X2)))){\unicdcdcdid}(k1\_finsop\_1~X0~(k8\_finseq\_1~\\
X0~X1~X2)~X3=k5\_binop\_1~X0~X3~(k1\_finsop\_1~X0~X1~X3)~(k1\_finsop\_1~\\
X0~X2~X3)))))))\end{array}
\label{hyp:ehfdpfggjgogdhpgahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(v1\_setwiseo~(k13\_rfunct\_3~X0)~\\
(k3\_rfunct\_3~X0~k1\_numbers))\end{array}
\label{hyp:ehbdidpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}(v2\_binop\_1~(k13\_rfunct\_3~X0)~(\\
k3\_rfunct\_3~X0~k1\_numbers))\end{array}
\label{hyp:ehbdfdpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  {\unicdcdadad} X3 .  ((m1\_subset\_1~X2~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))){\unicdcdcdhd}(m1\_subset\_1~X3~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1)))){\unicdbdjdcd}(r2\_relset\_1~X0~X1~X2~X2)\end{array}
\label{hyp:chfgggmgfgihjgghjgehjhpfchcdpfchfgmgdhfgehpfbd}
\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}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{k3\_rfunct\_3}~{X0}}~{X1}}={{{k4\_partfun1}~{X0}}~{X1}}}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgddpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {\preoh{{{v1\_xboole\_0}~{({{{k4\_partfun1}~{X0}}~{X1}})}}}}}}\label{hyp:ggdgbdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  ((\preoh v1\_xboole\_0~X2){\unicdcdcdhd}(m1\_rfunct\_3~\\
X2~X0~X1)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_rfunct\_3~X3~X0~X1~X2){\unicdbdjdcd}((v1\_funct\_1~X3){\unicdcdcdhd}\\
(m1\_subset\_1~X3~(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1)))))\end{array}
\label{hyp:egehpfngcdpfchggfhogdgehpfdd}
\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}(m2\_finseq\_1~(k8\_finseq\_1~X0~X1~X2)~X0)\end{array}
\label{hyp:egehpflgidpfggjgogdhfgbhpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{{m1\_rfunct\_3}~{({{{k3\_rfunct\_3}~{X0}}~{X1}})}}~{X0}}~{X1}}}}\label{hyp:egehpflgddpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}(m1\_finseq\_1~X1~(k3\_rfunct\_3~\\
X0~k1\_numbers))){\unicdbdjdcd}(m2\_rfunct\_3~(k14\_rfunct\_3~X0~X1)~X0~k1\_numbers~\\
(k3\_rfunct\_3~X0~k1\_numbers))\end{array}
\label{hyp:egehpflgbdedpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}((v1\_funct\_1~(k13\_rfunct\_3~X0)){\unicdcdcdhd}\\
((v1\_funct\_2~(k13\_rfunct\_3~X0)~(k2\_zfmisc\_1~(k3\_rfunct\_3~X0~k1\_numbers)~\\
(k3\_rfunct\_3~X0~k1\_numbers))~(k3\_rfunct\_3~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~\\
(k13\_rfunct\_3~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_rfunct\_3~\\
X0~k1\_numbers)~(k3\_rfunct\_3~X0~k1\_numbers))~(k3\_rfunct\_3~X0~k1\_numbers))))))\end{array}
\label{hyp:egehpflgbdddpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k3\_rfunct\_3~\\
X0~k1\_numbers)){\unicdbdjdcd}(k14\_rfunct\_3~X0~X1=k1\_finsop\_1~(k3\_rfunct\_3~\\
X0~k1\_numbers)~X1~(k13\_rfunct\_3~X0)))\end{array}
\label{hyp:egfdpfchggfhogdgehpfdd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  ((v1\_funct\_1~X1){\unicdcdcdhd}(\\
(v1\_funct\_2~X1~(k2\_zfmisc\_1~(k3\_rfunct\_3~X0~k1\_numbers)~(k3\_rfunct\_3~\\
X0~k1\_numbers))~(k3\_rfunct\_3~X0~k1\_numbers)){\unicdcdcdhd}(m1\_subset\_1~X1~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k2\_zfmisc\_1~(k3\_rfunct\_3~X0~k1\_numbers)~\\
(k3\_rfunct\_3~X0~k1\_numbers))~(k3\_rfunct\_3~X0~k1\_numbers)))))){\unicdbdjdcd}\\
((X1=k13\_rfunct\_3~X0){\unicdbdjded}({\unicdcdadad} X2 .  (m2\_rfunct\_3~X2~X0~k1\_numbers~\\
(k3\_rfunct\_3~X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X3 .  (m2\_rfunct\_3~X3~X0~k1\_numbers~\\
(k3\_rfunct\_3~X0~k1\_numbers)){\unicdbdjdcd}(k5\_binop\_1~(k3\_rfunct\_3~X0~k1\_numbers)~\\
X1~X2~X3=k5\_rfunct\_3~X0~k1\_numbers~X2~X3)))))\end{array}
\label{hyp:egedpfchggfhogdgehpfdd}
\end{equation}
\begin{theorem}\label{thm:ehcdbdpfchggfhogdgehpfdd}
$$\begin{array}{c}{\unicdcdadad} X0 .  (\preoh v1\_xboole\_0~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (m2\_finseq\_1~X1~(k3\_rfunct\_3~\\
X0~k1\_numbers)){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_finseq\_1~X2~(k3\_rfunct\_3~X0~k1\_numbers)){\unicdbdjdcd}\\
(r2\_relset\_1~X0~k1\_numbers~(k14\_rfunct\_3~X0~(k8\_finseq\_1~(k3\_rfunct\_3~\\
X0~k1\_numbers)~X1~X2))~(k5\_rfunct\_3~X0~k1\_numbers~(k14\_rfunct\_3~\\
X0~X1)~(k14\_rfunct\_3~X0~X2)))))\end{array}$$
\end{theorem}
\end{document}
