\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{l103\_toprealb (TMModNBxoYRoDLraH3xFd5r9QETVhDrKfSt)}
\maketitle
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ c31\_\_toprealb : {\iota}$ be given.
Let $ v1\_funct\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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 $ k2\_rcomp\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k6\_numbers : {\iota}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ v5\_pre\_topc : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ 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 $ v2\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ l1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k2\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_xboole\_0 : {\iota}$ be given.
Let $ r1\_tarski : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k3\_topmetr : {\iota}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ k1\_real\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ v1\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_pre\_topc : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_fcont\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k6\_toprealb : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ l1\_struct\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((\preoh v2\_struct\_0~X0){\unicdcdcdhd}((v2\_pre\_topc~X0){\unicdcdcdhd}(l1\_pre\_topc~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X1 .  ((\preoh v2\_struct\_0~X1){\unicdcdcdhd}((v2\_pre\_topc~X1){\unicdcdcdhd}(l1\_pre\_topc~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m1\_subset\_1~X2~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X0))){\unicdbdjdcd}({\unicdcdadad} X3 .  (m1\_subset\_1~X3~(k1\_zfmisc\_1~(u1\_struct\_0~\\
X1))){\unicdbdjdcd}({\unicdcdadad} X4 .  ((v1\_funct\_1~X4){\unicdcdcdhd}((v1\_funct\_2~X4~(u1\_struct\_0~\\
X0)~(u1\_struct\_0~X1)){\unicdcdcdhd}((v5\_pre\_topc~X4~X0~X1){\unicdcdcdhd}(m1\_subset\_1~X4~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~X0)~(u1\_struct\_0~X1))))))){\unicdbdjdcd}\\
({\unicdcdadad} X5 .  ((v1\_funct\_1~X5){\unicdcdcdhd}((v1\_funct\_2~X5~(u1\_struct\_0~(k1\_pre\_topc~\\
X0~X2))~(u1\_struct\_0~(k1\_pre\_topc~X1~X3))){\unicdcdcdhd}(m1\_subset\_1~X5~(k1\_zfmisc\_1~\\
(k2\_zfmisc\_1~(u1\_struct\_0~(k1\_pre\_topc~X0~X2))~(u1\_struct\_0~(\\
k1\_pre\_topc~X1~X3))))))){\unicdbdjdcd}((X5=k2\_partfun1~(u1\_struct\_0~X0)~(\\
u1\_struct\_0~X1)~X4~X2){\unicdbdjdcd}(v5\_pre\_topc~X5~(k1\_pre\_topc~X0~X2)~(k1\_pre\_topc~\\
X1~X3))))))))\end{array}
\label{hyp:ehidpfehpgahchfgbgmgbg}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xboole\_0}~{X0}})}{\unicdbdjdcd}{({{X0}={k1\_xboole\_0}})}}}\label{hyp:ehgdpfcgpgpgmgfg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  (m1\_subset\_1~X0~(k1\_zfmisc\_1~X1)){\unicdbdjded}(r1\_tarski~\\
X0~X1)\end{array}
\label{hyp:ehddpfdhfhcgdhfgeh}
\end{equation}
Assume the following.
\begin{equation}
{{{u1\_struct\_0}~{k3\_topmetr}}={k1\_numbers}}\label{hyp:ehbdhdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}((v2\_xxreal\_0~np\_\_1){\unicdcdcdhd}(m2\_subset\_1~np\_\_1~k1\_numbers~k5\_numbers)){\unicdcdcdhd}\\
((m1\_subset\_1~np\_\_1~k5\_numbers){\unicdcdcdhd}(m1\_subset\_1~np\_\_1~k1\_numbers))\end{array}
\label{hyp:dhahdgbdpfogfhngfgchbgmgdh}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{\unicdcdadad} X1 .  {{{r1\_tarski}~{X0}}~{X0}}}}\label{hyp:chfgggmgfgihjgghjgehjhpfchbdpfehbgchdhlgjg}
\end{equation}
Assume the following.
\begin{equation}
{{k6\_numbers}={k1\_xboole\_0}}\label{hyp:chfgegfgggjgogjgehjgpgogpflggdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
{{k2\_topalg\_2}={k3\_topmetr}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfehpgahbgmghgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{{k1\_real\_1}~{X0}}={{k4\_xcmplx\_0}~{X0}}})}}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgbdpfchfgbgmgpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdaddd} X0 .  (v1\_xboole\_0~X0){\unicdcdcdhd}((v1\_xcmplx\_0~X0){\unicdcdcdhd}((v1\_xxreal\_0~\\
X0){\unicdcdcdhd}(v1\_xreal\_0~X0)))\end{array}
\label{hyp:chdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{{{k1\_relset\_1}~{k1\_numbers}}~{({{{k1\_fcont\_1}~{({{k1\_real\_1}~{np\_\_1}})}}~{np\_\_1}})}}={k1\_numbers}}\label{hyp:mgjdhdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
{{{{k1\_pre\_topc}~{k2\_topalg\_2}}~{({{k2\_struct\_0}~{k2\_topalg\_2}})}}={k2\_topalg\_2}}\label{hyp:mgbdadcdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
{{{{k2\_relset\_1}~{k1\_numbers}}~{({{{k1\_fcont\_1}~{({{k1\_real\_1}~{np\_\_1}})}}~{np\_\_1}})}}={k1\_numbers}}\label{hyp:mgbdadbdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v1\_xreal\_0~X0){\unicdbdjdcd}((v1\_xcmplx\_0~(k4\_xcmplx\_0~X0)){\unicdcdcdhd}\\
(v1\_xreal\_0~(k4\_xcmplx\_0~X0)))\end{array}
\label{hyp:ggdgddpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(\preoh v2\_struct\_0~k3\_topmetr){\unicdcdcdhd}((v1\_pre\_topc~k3\_topmetr){\unicdcdcdhd}(v2\_pre\_topc~\\
k3\_topmetr))\end{array}
\label{hyp:ggdgcdpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}((v1\_fcont\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~k1\_numbers~k1\_numbers))))){\unicdbdjdcd}((v1\_funct\_1~\\
(k6\_toprealb~X0)){\unicdcdcdhd}((v1\_funct\_2~(k6\_toprealb~X0)~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k1\_relset\_1~k1\_numbers~\\
X0))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~\\
k1\_numbers~X0))))){\unicdcdcdhd}(v5\_pre\_topc~(k6\_toprealb~X0)~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_relset\_1~k1\_numbers~X0)))~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~k1\_numbers~X0))))))\end{array}
\label{hyp:ggdgbdhdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}((v1\_funct\_1~\\
(k1\_fcont\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k1\_fcont\_1~X0~X1)~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(v1\_fcont\_1~(k1\_fcont\_1~X0~X1))))\end{array}
\label{hyp:ggdgbdfdpfggdgpgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{l1\_pre\_topc}~{X0}})}{\unicdbdjdcd}{({{l1\_struct\_0}~{X0}})}}}\label{hyp:egehpfmgbdpfahchfgpfehpgahdg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_funct\_1~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))){\unicdbdjdcd}((v1\_funct\_1~(k6\_toprealb~X0)){\unicdcdcdhd}(\\
(v1\_funct\_2~(k6\_toprealb~X0)~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_relset\_1~k1\_numbers~X0))))~(u1\_struct\_0~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~k1\_numbers~X0))))){\unicdcdcdhd}(m1\_subset\_1~\\
(k6\_toprealb~X0)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k1\_pre\_topc~\\
k2\_topalg\_2~(k5\_toprealb~(k1\_relset\_1~k1\_numbers~X0))))~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_relset\_1~k1\_numbers~\\
X0)))))))))\end{array}
\label{hyp:egehpflggdpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
{{({{v2\_pre\_topc}~{k3\_topmetr}})}{\unicdcdcdhd}{({{l1\_pre\_topc}~{k3\_topmetr}})}}\label{hyp:egehpflgddpfehpgahngfgehch}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xxreal\_0~X0){\unicdcdcdhd}(v1\_xxreal\_0~X1)){\unicdbdjdcd}(\\
m1\_subset\_1~(k2\_rcomp\_1~X0~X1)~(k1\_zfmisc\_1~k1\_numbers))\end{array}
\label{hyp:egehpflgcdpfchdgpgngahpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v1\_xreal\_0~X0){\unicdcdcdhd}(v1\_xreal\_0~X1)){\unicdbdjdcd}((v1\_funct\_1~\\
(k1\_fcont\_1~X0~X1)){\unicdcdcdhd}((v1\_funct\_2~(k1\_fcont\_1~X0~X1)~k1\_numbers~\\
k1\_numbers){\unicdcdcdhd}(m1\_subset\_1~(k1\_fcont\_1~X0~X1)~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
k1\_numbers~k1\_numbers)))))\end{array}
\label{hyp:egehpflgbdpfggdgpgogehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}(v1\_funct\_1~c31\_\_toprealb){\unicdcdcdhd}((v1\_funct\_2~c31\_\_toprealb~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_rcomp\_1~k6\_numbers~\\
np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~\\
(k2\_rcomp\_1~k6\_numbers~np\_\_1))))){\unicdcdcdhd}(m1\_subset\_1~c31\_\_toprealb~\\
(k1\_zfmisc\_1~(k2\_zfmisc\_1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k2\_rcomp\_1~k6\_numbers~np\_\_1))))~(u1\_struct\_0~(\\
k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_rcomp\_1~k6\_numbers~\\
np\_\_1))))))))\end{array}
\label{hyp:egehpfdgddbdpfpfehpgahchfgbgmgcg}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}c31\_\_toprealb=k2\_partfun1~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~\\
(k5\_toprealb~(k1\_relset\_1~k1\_numbers~(k1\_fcont\_1~(k1\_real\_1~\\
np\_\_1)~np\_\_1)))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~\\
(k2\_relset\_1~k1\_numbers~(k1\_fcont\_1~(k1\_real\_1~np\_\_1)~np\_\_1)))))~\\
(k6\_toprealb~(k1\_fcont\_1~(k1\_real\_1~np\_\_1)~np\_\_1))~(k5\_toprealb~\\
(k2\_rcomp\_1~k6\_numbers~np\_\_1))\end{array}
\label{hyp:egfgpfdgddbdpfpfehpgahchfgbgmgcg}
\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}
{{\unicdcdadad} X0 .  {{({{l1\_struct\_0}~{X0}})}{\unicdbdjdcd}{({{{k2\_struct\_0}~{X0}}={{u1\_struct\_0}~{X0}}})}}}\label{hyp:egddpfdhehchfhdgehpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{v1\_xreal\_0}~{X0}})}{\unicdbdjdcd}{({{v1\_xxreal\_0}~{X0}})}}}\label{hyp:dgdgedpfihchfgbgmgpfad}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k1\_numbers}})}{\unicdbdjdcd}{({{v1\_xreal\_0}~{X0}})}}}\label{hyp:dgdgbdpfihchfgbgmgpfad}
\end{equation}
\begin{theorem}\label{thm:mgbdadddpfehpgahchfgbgmgcg}
$$\begin{array}{c}(v1\_funct\_1~c31\_\_toprealb){\unicdcdcdhd}((v1\_funct\_2~c31\_\_toprealb~(u1\_struct\_0~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_rcomp\_1~k6\_numbers~\\
np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~\\
(k2\_rcomp\_1~k6\_numbers~np\_\_1))))){\unicdcdcdhd}((v5\_pre\_topc~c31\_\_toprealb~\\
(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_rcomp\_1~k6\_numbers~\\
np\_\_1)))~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_rcomp\_1~k6\_numbers~\\
np\_\_1)))){\unicdcdcdhd}(m1\_subset\_1~c31\_\_toprealb~(k1\_zfmisc\_1~(k2\_zfmisc\_1~\\
(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(k5\_toprealb~(k2\_rcomp\_1~\\
k6\_numbers~np\_\_1))))~(u1\_struct\_0~(k1\_pre\_topc~k2\_topalg\_2~(\\
k5\_toprealb~(k2\_rcomp\_1~k6\_numbers~np\_\_1)))))))))\end{array}$$
\end{theorem}
\end{document}
