\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{l145\_toprealb (TMNSU1w66nK67jkMKZWsfEx4Nk5snN8zZAc)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_topalg\_2 : {\iota}$ be given.
Let $ k5\_toprealb : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ k32\_sin\_cos : {\iota}$ be given.
Let $ c33\_\_toprealb : {\iota}$ be given.
Let $ c44\_\_toprealb : {\iota}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ c45\_\_toprealb : {\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 $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k10\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k9\_xtuple\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v5\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_toprealb : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_sin\_cos6 : {\iota}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v1\_funct\_1~X1)){\unicdbdjdcd}((r1\_tarski~\\
(k10\_xtuple\_0~X1)~X0){\unicdbdjdcd}((v1\_funct\_1~X1){\unicdcdcdhd}((v1\_funct\_2~X1~(k9\_xtuple\_0~\\
X1)~X0){\unicdcdcdhd}(m1\_subset\_1~X1~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(k9\_xtuple\_0~\\
X1)~X0))))))\end{array}
\label{hyp:ehcdpfggfhogdgehpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v5\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k2\_relset\_1~X0~X1=k10\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_relat\_1~X1){\unicdcdcdhd}(v4\_relat\_1~X1~X0)){\unicdbdjdcd}(\\
k1\_relset\_1~X0~X1=k9\_xtuple\_0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}r1\_tarski~(k2\_relset\_1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos))))~(k2\_partfun1~\\
(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~\\
(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos))))~c33\_\_toprealb~\\
(k5\_toprealb~c44\_\_toprealb)))~c45\_\_toprealb\end{array}
\label{hyp:mgbdededpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}k1\_relset\_1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~\\
(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1))))~(k2\_partfun1~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~(k1\_real\_1~\\
np\_\_1)~np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~\\
(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos))))~c33\_\_toprealb~(k5\_toprealb~\\
c44\_\_toprealb))=c44\_\_toprealb\end{array}
\label{hyp:mgbdedddpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~c45\_\_toprealb))=\\
k5\_toprealb~c45\_\_toprealb\end{array}
\label{hyp:mgbdcdfdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~c44\_\_toprealb))=\\
k5\_toprealb~c44\_\_toprealb\end{array}
\label{hyp:mgbdcdedpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~\\
k6\_numbers~k32\_sin\_cos)))=k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos\end{array}
\label{hyp:mgbdbdadpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~\\
(k1\_real\_1~np\_\_1)~np\_\_1)))=k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1\end{array}
\label{hyp:mgbdadidpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~(k6\_toprealb~k4\_sin\_cos6)){\unicdcdcdhd}((v1\_funct\_2~(k6\_toprealb~\\
k4\_sin\_cos6)~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~\\
(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos))))){\unicdcdcdhd}\\
((v5\_pre\_topc~(k6\_toprealb~k4\_sin\_cos6)~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1)))~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos)))){\unicdcdcdhd}\\
(m1\_subset\_1~(k6\_toprealb~k4\_sin\_cos6)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~\\
(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~k32\_sin\_cos)))))))))\end{array}
\label{hyp:mgbdadedpfehpgahchfgbgmgcg}
\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}((v1\_funct\_1~\\
(k2\_partfun1~X0~X1~X2~X3)){\unicdcdcdhd}(m1\_subset\_1~(k2\_partfun1~X0~X1~X2~X3)~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~X0~X1))))\end{array}
\label{hyp:egehpflgcdpfahbgchehggfhogbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v1\_xboole\_0~c45\_\_toprealb){\unicdcdcdhd}(m1\_subset\_1~c45\_\_toprealb~(k1\_zfmisc\_1~\\
k1\_numbers))\end{array}
\label{hyp:egehpfdgedfdpfpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v1\_xboole\_0~c44\_\_toprealb){\unicdcdcdhd}(m1\_subset\_1~c44\_\_toprealb~(k1\_zfmisc\_1~\\
k1\_numbers))\end{array}
\label{hyp:egehpfdgededpfpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
{{c33\_\_toprealb}={{k6\_toprealb}~{k4\_sin\_cos6}}}\label{hyp:egfgpfdgddddpfpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~k1\_numbers)){\unicdbdjdcd}(k5\_toprealb~\\
X0=X0)\end{array}
\label{hyp:egddpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}((v4\_relat\_1~X2~X0){\unicdcdcdhd}(v5\_relat\_1~X2~X1))\end{array}
\label{hyp:dgdgcdpfchfgmgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  {\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~X0~X1))){\unicdbdjdcd}(v1\_relat\_1~X2)\end{array}
\label{hyp:dgdgbdpfchfgmgdhfgehpfbd}
\end{equation}
\begin{theorem}\label{thm:mgbdedfdpfehpgahchfgbgmgcg}
$$\begin{array}{c}(v1\_funct\_1~(k2\_partfun1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~\\
k32\_sin\_cos))))~c33\_\_toprealb~(k5\_toprealb~c44\_\_toprealb))){\unicdcdcdhd}\\
((v1\_funct\_2~(k2\_partfun1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~\\
k32\_sin\_cos))))~c33\_\_toprealb~(k5\_toprealb~c44\_\_toprealb))~\\
(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~c44\_\_toprealb)))~\\
(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~c45\_\_toprealb)))){\unicdcdcdhd}\\
(m1\_subset\_1~(k2\_partfun1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_rcomp\_1~(k1\_real\_1~np\_\_1)~np\_\_1))))~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_rcomp\_1~k6\_numbers~\\
k32\_sin\_cos))))~c33\_\_toprealb~(k5\_toprealb~c44\_\_toprealb))~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~c44\_\_toprealb)))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~c45\_\_toprealb)))))))\end{array}$$
\end{theorem}
\end{document}
