\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{t5\_scmbsort (TMbWfXhLUdXTrYWsRuyGESDgsy5ekHFnvoM)}
\maketitle
Let $ v1\_relat\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v4\_relat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ u1\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_2 : {\iota}$ be given.
Let $ v1\_funct\_1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v5\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_3 : {\iota}$ be given.
Let $ v1\_partfun1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ m2\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}$ be given.
Let $ k1\_numbers : {\iota}$ be given.
Let $ k5\_numbers : {\iota}$ be given.
Let $ v1\_ami\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ m1\_subset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}$ be given.
Let $ k2\_nat\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ np\_\_1 : {\iota}$ be given.
Let $ k1\_funct\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k2\_extpro\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}}$ be given.
Let $ k6\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ k4\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k1\_scmfsa\_m : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_struct\_0 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_card\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k5\_memstr\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}}$ be given.
Let $ m1\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ r2\_relset\_1 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{o}}}}}$ be given.
Let $ k4\_numbers : {\iota}$ be given.
Let $ k18\_scmfsa\_2 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v1\_scmfsa\_m : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v7\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v2\_xxreal\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ v1\_xboole\_0 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Let $ k1\_zfmisc\_1 : {{\iota}{\unicdbdjdcd}{\iota}}$ be given.
Let $ k4\_ordinal1 : {\iota}$ be given.
Let $ k2\_xcmplx\_0 : {{\iota}{\unicdbdjdcd}{{\iota}{\unicdbdjdcd}{\iota}}}$ be given.
Let $ v3\_ordinal1 : {{\iota}{\unicdbdjdcd}{o}}$ be given.
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_ami\_2~X0){\unicdcdcdhd}(m1\_subset\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X1 .  ((v1\_ami\_2~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}\\
({\unicdcdadad} X2 .  ((v1\_relat\_1~X2){\unicdcdcdhd}((v4\_relat\_1~X2~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X2){\unicdcdcdhd}((v5\_funct\_1~X2~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X2~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((k1\_funct\_1~\\
(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k6\_scmfsa\_2~X0~X1)~X2)~(k4\_struct\_0~\\
k1\_scmfsa\_2)=k4\_card\_1~(k5\_memstr\_0~np\_\_3~k1\_scmfsa\_2~X2)){\unicdcdcdhd}\\
((k1\_funct\_1~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k6\_scmfsa\_2~X0~X1)~\\
X2)~X0=k1\_funct\_1~X2~X1){\unicdcdcdhd}(({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}((X3{\unicdcdgdad}X0){\unicdbdjdcd}(k1\_funct\_1~(k2\_extpro\_1~\\
np\_\_3~k1\_scmfsa\_2~(k6\_scmfsa\_2~X0~X1)~X2)~X3=k1\_funct\_1~X2~X3))){\unicdcdcdhd}\\
({\unicdcdadad} X3 .  (m1\_scmfsa\_2~X3){\unicdbdjdcd}(r2\_relset\_1~k5\_numbers~k4\_numbers~\\
(k18\_scmfsa\_2~(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k6\_scmfsa\_2~X0~\\
X1)~X2)~X3)~(k18\_scmfsa\_2~X2~X3))))))))\end{array}
\label{hyp:ehgdddpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}(({\unicdcdadad} X1 .  \\
((v1\_ami\_2~X1){\unicdcdcdhd}((\preoh v1\_scmfsa\_m~X1){\unicdcdcdhd}(m1\_subset\_1~X1~(u1\_struct\_0~\\
k1\_scmfsa\_2)))){\unicdbdjdcd}(k1\_funct\_1~(k1\_scmfsa\_m~X0)~X1=k1\_funct\_1~\\
X0~X1)){\unicdcdcdhd}({\unicdcdadad} X1 .  (m1\_scmfsa\_2~X1){\unicdbdjdcd}(k18\_scmfsa\_2~(k1\_scmfsa\_m~\\
X0)~X1=k18\_scmfsa\_2~X0~X1)))\end{array}
\label{hyp:ehddhdpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}({\unicdcdadad} X1 .  (v7\_ordinal1~X1){\unicdbdjdcd}(\preoh \\
(X0{\unicdcdgdad}X1){\unicdcdcdhd}(k4\_scmfsa\_2~X0=k4\_scmfsa\_2~X1)))\end{array}
\label{hyp:ehbdadbdpfdhdgngggdhbgpfcd}
\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}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((\preoh v1\_xboole\_0~X0){\unicdcdcdhd}((\preoh v1\_xboole\_0~X1){\unicdcdcdhd}\\
(m1\_subset\_1~X1~(k1\_zfmisc\_1~X0)))){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~X0~X1){\unicdbdjded}(m1\_subset\_1~X2~X1))\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpfngcdpfdhfhcgdhfgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{k5\_numbers}={k4\_ordinal1}}\label{hyp:chfgegfgggjgogjgehjgpgogpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((m1\_subset\_1~X0~k5\_numbers){\unicdcdcdhd}(v7\_ordinal1~\\
X1)){\unicdbdjdcd}(k2\_nat\_1~X0~X1=k2\_xcmplx\_0~X0~X1)\end{array}
\label{hyp:chfgegfgggjgogjgehjgpgogpflgcdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
{{({\preoh{{{v1\_xboole\_0}~{k4\_ordinal1}}}})}{\unicdcdcdhd}{({{v3\_ordinal1}~{k4\_ordinal1}})}}\label{hyp:ggdggdpfpgchegjgogbgmgbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}((v1\_relat\_1~\\
(k1\_scmfsa\_m~X0)){\unicdcdcdhd}((v4\_relat\_1~(k1\_scmfsa\_m~X0)~(u1\_struct\_0~\\
k1\_scmfsa\_2)){\unicdcdcdhd}((v1\_funct\_1~(k1\_scmfsa\_m~X0)){\unicdcdcdhd}((v5\_funct\_1~\\
(k1\_scmfsa\_m~X0)~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}(v1\_partfun1~\\
(k1\_scmfsa\_m~X0)~(u1\_struct\_0~k1\_scmfsa\_2))))))\end{array}
\label{hyp:ggdgedpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
{\preoh{{{v1\_xboole\_0}~{k1\_numbers}}}}\label{hyp:ggdgbdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  {\unicdcdadad} X1 .  ((v7\_ordinal1~X0){\unicdcdcdhd}(v7\_ordinal1~X1)){\unicdbdjdcd}(\\
v7\_ordinal1~(k2\_xcmplx\_0~X0~X1))\end{array}
\label{hyp:ggdgbdpfogbgehpfbd}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (m1\_subset\_1~X0~k5\_numbers){\unicdbdjdcd}((v1\_ami\_2~(k4\_scmfsa\_2~\\
(k2\_nat\_1~X0~np\_\_1))){\unicdcdcdhd}(\preoh v1\_scmfsa\_m~(k4\_scmfsa\_2~(k2\_nat\_1~X0~\\
np\_\_1))))\end{array}
\label{hyp:ggdgbdbdpfdhdgngggdhbgpfng}
\end{equation}
Assume the following.
\begin{equation}
{{{m1\_subset\_1}~{k5\_numbers}}~{({{k1\_zfmisc\_1}~{k1\_numbers}})}}\label{hyp:egehpflgfdpfogfhngcgfgchdh}
\end{equation}
Assume the following.
\begin{equation}
\begin{array}{c}{\unicdcdadad} X0 .  (v7\_ordinal1~X0){\unicdbdjdcd}((v1\_ami\_2~(k4\_scmfsa\_2~X0)){\unicdcdcdhd}(m1\_subset\_1~\\
(k4\_scmfsa\_2~X0)~(u1\_struct\_0~k1\_scmfsa\_2)))\end{array}
\label{hyp:egehpflgedpfdhdgngggdhbgpfcd}
\end{equation}
Assume the following.
\begin{equation}
{{\unicdcdadad} X0 .  {{({{{m1\_subset\_1}~{X0}}~{k4\_ordinal1}})}{\unicdbdjdcd}{({{v7\_ordinal1}~{X0}})}}}\label{hyp:dgdgidpfpgchegjgogbgmgbd}
\end{equation}
\begin{theorem}\label{thm:ehfdpfdhdgngcgdhpgcheh}
$$\begin{array}{c}{\unicdcdadad} X0 .  ((v1\_relat\_1~X0){\unicdcdcdhd}((v4\_relat\_1~X0~(u1\_struct\_0~k1\_scmfsa\_2)){\unicdcdcdhd}\\
((v1\_funct\_1~X0){\unicdcdcdhd}((v5\_funct\_1~X0~(k2\_memstr\_0~np\_\_3~k1\_scmfsa\_2)){\unicdcdcdhd}\\
(v1\_partfun1~X0~(u1\_struct\_0~k1\_scmfsa\_2)))))){\unicdbdjdcd}({\unicdcdadad} X1 .  \\
(m2\_subset\_1~X1~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X2 .  (m2\_subset\_1~\\
X2~k1\_numbers~k5\_numbers){\unicdbdjdcd}({\unicdcdadad} X3 .  ((v1\_ami\_2~X3){\unicdcdcdhd}(m1\_subset\_1~\\
X3~(u1\_struct\_0~k1\_scmfsa\_2))){\unicdbdjdcd}((X1{\unicdcdgdad}k2\_nat\_1~X2~np\_\_1){\unicdbdjdcd}(k1\_funct\_1~\\
(k2\_extpro\_1~np\_\_3~k1\_scmfsa\_2~(k6\_scmfsa\_2~(k4\_scmfsa\_2~X1)~\\
X3)~(k1\_scmfsa\_m~X0))~(k4\_scmfsa\_2~(k2\_nat\_1~X2~np\_\_1))=k1\_funct\_1~\\
X0~(k4\_scmfsa\_2~(k2\_nat\_1~X2~np\_\_1)))))))\end{array}$$
\end{theorem}
\end{document}
